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One of the most captivating properties of polaritons is their capacity to confine light at the nanoscale. This confinement is even more extreme in two-dimensional (2D) materials. 2D polaritons have been investigated by optical measurements using an external photodetector. However, their effective spectrally resolved electrical detection via far-field excitation remains unexplored. This fact hinders their potential exploitation in crucial applications such as sensing molecules and gases, hyperspectral imaging and optical spectrometry, banking on their potential for integration with silicon technologies. Herein, we present the first electrical spectroscopy of polaritonic nanoresonators based on a high-quality 2D-material heterostructure, which serves at the same time as the photodetector and the polaritonic platform. We employ metallic nanorods to create hybrid nanoresonators within the hybrid plasmon-phonon polaritonic medium in the mid and long-wave infrared ranges. Subsequently, we electrically detect these resonators by near-field coupling to a graphene pn-junction. The nanoresonators simultaneously present a record of lateral confinement and high-quality factors of up to 200, exhibiting prominent peaks in the photocurrent spectrum, particularly at the underexplored lower reststrahlen band of hBN. We exploit the geometrical and gate tunability of these nanoresonators to investigate their impact on the photocurrent spectrum and the polaritonic's waveguided modes. This work opens a venue for studying this highly tunable and complex hybrid system, as well as for using it in compact platforms for sensing and photodetection applications.

Biased bilayer graphene (BBG) is an important system for studies of excitonic effects in graphene--based systems, with its easily tunable bandgap. This bandgap is governed by an external gate voltage, allowing one to tune the optical response of the system. In this paper, we study the excitonic linear and nonlinear optical response of Bernal stacked BBG as a function of the gate voltage, both for in--plane (IP) and out--of--plane (OOP) directions. Based on a semi-analytical model of the electronic structure of BBG describing the influence of gate voltage on excitonic binding energies, we focus our discussion on both the IP and OOP excitonic response. Both linear and second harmonic generation (SHG) nonlinear responses are shown to be very sensitive to the gate voltage, as both the interband momentum matrix elements and the bandgap of the system will vary greatly with bias potential.

In this paper we study the topology of the bands of a plasmonic crystal composed of graphene and of a metallic grating. Firstly, we derive a Kronig-Penney type of equation for the plasmonic bands as function of the Bloch wavevector and discuss the propagation of the surface plasmon polaritons on the polaritonic crystal using a transfer-matrix approach considering a finite relaxation time. Second, we reformulate the problem as a tight-binding model that resembles the Su-Schrieffer-Heeger (SSH) Hamiltonian, one difference being that the hopping amplitudes are, in this case, energy dependent. In possession of the tight-binding equations it is a simple task to determine the topology (value of the winding number) of the bands. This allows to determine the existense or absence of topological end modes in the system. Similarly to the SSH model, we show that there is a tunable parameter that induces topological phase transitions from trivial to non-trivial. In our case, it is the distance d between the graphene sheet and the metallic grating. We note that d is a parameter that can be easily tuned experimentally simply by controlling the thickness of the spacer between the grating and the graphene sheet. It is then experimentally feasible to engineer devices with the required topological properties. Finally, we suggest a scattering experiment allowing the observation of the topological states.

Magnetized ferromagnetic disks or wires support strong inhomogeneous fields in their borders. Such magnetic fields create an effective potential, due to Zeeman and diamagnetic contributions, that can localize charge carriers. For the case of two-dimensional transition metal dichalcogenides, this potential can valley-localize excitons due to the Zeeman term, which breaks the valley symmetry. We show that the diamagnetic term is negligible when compared to the Zeeman term for monolayers of transition metal dichalcogenides. The latter is responsible for trapping excitons near the magnetized structure border with valley-dependent characteristics, in which, for one of the valleys, the exciton is confined inside the disk, while for the other, it is outside. This spatial valley separation of exciton can be probed by circularly polarized light, and moreover, we show that the inhomogeneous magnetic field magnitude, the dielectric environment, and the magnetized structure parameters can tailor the spatial separation of the exciton wavefunctions.

In this paper a thorough theoretical study of a new class of collective excitations, dubbed hyperbolic surface phonon plasmon polaritons, is performed. This new type of light-matter excitations are shown to have unique properties that allows to explore them both as the basis of ultra-sensitive devices to the dielectric nature of its surroundings. The system is a van der Waals heterostructure -- a layered metamaterial, composed of different 2D materials in direct contact one with another, namely graphene ribbons and hexagonal boron nitride slabs of nanometric size. In the paper we discuss the spectrum of these new class of excitations, the associated electromagnetic fields, the sensitivity to the dielectric function of its surroundings, and the absorption spectrum. All this is accomplished using an analytical model that considerably diminishes the computational burden, as well as elucidates the underling physical mechanism of the excitations supported by the device.

In this paper we discussed the topological transition between trivial and nontrivial phases of a quasi-periodic (Aubry-André like) mechanical Su-Schrieffer-Heeger (SSH) model. We find that there exists a nontrivial boundary separating the two topological phases and an analytical expression for this boundary is found. We discuss the localization of the vibrational modes using the calculation of the inverse participation ratio (IPR) and access the localization nature of the states of the system. We find three different regimes: extended, localized, and critical, depending on the intensity of the Aubry-André spring. We further study the energy dependent mobility edge (ME) separating localized from extended eigenstates and find its analytical expression for both commensurate and incommensurate modulation wavelengths, thus enlarging the library of models possessing analytical expressions for the ME. Our results extend previous results for the theory of fermionic topological insulators and localization theory in quantum matter to the classical realm.

We construct a one-dimensional (1D) topological SSH-like model with chiral symmetry and a superimposed hopping modulation, which we call the chiral Aubry-André model. We show that its topological properties can be described in terms of a pair (C,W) of a two-dimensional (2D) Chern number C, stemming from a superspace description of the model, and a 1D winding number W, originating in its chiral symmetric nature. Thus, we showcase for the first time explicit coexistence of 1D and 2D topology in a model existing in 1D physical space. We detail the superspace description by showcasing how our model can be mapped to a Harper-Hofstadter model, familiar from the description of the integer quantum Hall effect, and analyze the vanishing field limit analytically. An extension of the method used for vanishing fields is provided in order to handle any finite fields, corresponding to hopping modulations both commensurate and incommensurate with the lattice. In addition, this formalism allows us to obtain certain features of the 2D superspace model, such as its number of massless Dirac nodes, purely in terms of topological quantities, computed without the need to go into momentum space.

We show that hexagonal boron nitride (hBN), a two-dimensional insulator, when subjected to an external superlattice potential forms a new paradigm for electrostatically tunable excitons in the near- and mid-ultraviolet (UV). The imposed potential has three consequences: (i) it renormalizes the effective mass tensor, leading to anisotropic effective masses; (ii) it renormalizes the band gap, eventually reducing it; (iii) it reduces the exciton binding energies. All these consequences depend on a single dimensionless parameter, which includes the product of strength of the external potential with its period. In addition to the excitonic energy levels, we compute the optical conductivity along two orthogonal directions, and from it the absorption spectrum. The results for the latter show that our system is able to mimic a grid polarizer. These characteristics make one-dimensional hBN superlattices a viable and unexplored platform for fine-tuned polaritonics in the UV to visible spectral range.

We study the effect of diluting a two-dimensional ferromagnetic insulator hosting a topological phase in the clean limit. By considering the ferromagnetic Heisenberg model in the honeycomb lattice with second nearest-neighbor Dzyanshikii-Moriya interaction, and working in the linear spin-wave approximation, we establish the topological phase diagram as a function of the fraction $p$ of diluted magnetic atoms. The topological phase with Chern number $C=1$ is robust up to a moderate dilution $p_{1}^{*}$, while above a higher dilution $p_{2}^{*}>p_{1}^{*}$ the system becomes trivial. Interestingly, both $p_{1}^{*}$ and $p_{2}^{*}$ are below the classical percolation threshold $p_{c}$ for the honeycomb lattice, which gives physical significance to the obtained phases. In the topological phase for $p<p_{1}^{*}$, the magnon spectrum is gapless but the states filling the topological, clean-limit gap region are spatially localized. For energies above and below the region of localized states, there are windows composed of extended states. This is at odds with standard Chern insulators, where extended states occur only at single energies. For dilutions $p_{1}^{*}<p<p_{2}^{*}$, the two regions of extended states merge and a continuum of delocalized states appears around the middle of the magnon spectrum. For this range of dilutions the Chern number seems to be ill defined in the thermodynamic limit, and only for $p>p_{2}^{*}$, when all states become localized, the system shows $C=0$ as expected for a trivial phase. Replacing magnetic with non-magnetic atoms in a systems hosting a magnon Chern insulator in the clean limit puts all the three phases within experimental reach.

Using the tight-binding model, we report a gap opening in the energy spectrum of the twisted bilayer graphene under the application of pressure, that can be further amplified by the presence of a perpendicular bias voltage. The valley edges are located along the K-Gamma path of the superlattice Brillouin Zone, with the bandgap reaching values up to 200 meV in the single-particle picture. Employing the formalism of the semiconductor Bloch equations, we observe an enhancement of the bandgap due to the electron-electron interaction, with a renormalization of the bandgap of about 160 meV. From the solution of the corresponding Bethe-Salpeter equation, we show that this system supports highly anisotropic bright excitons whose electrons and holes are strongly hybridized between the adjacent layers.

Beyond the extensively studied microcavity polaritons, which are coupled modes of semiconductor excitons and microcavity photons, nearly 2D semiconductors placed in a suitable environment can support spatially localized exciton-polariton modes. We demonstrate theoretically that two distinct types of such modes can exist in a photonic crystal with an embedded transition metal dichalcogenide (TMD) monolayer and derive an equation that determines their dispersion relations. The localized modes of two types occur in the zeroth- and first-order stop-bands of the crystal, respectively, and have substantially different properties. The latter type of the localized modes, which appear inside the light cone, can be described as a result of coupling of the TMD exciton and an optical Tamm state of the TMD-intercalated photonic crystal. We suggest an experiment for detecting these modes and simulate it numerically.

We argue that strain engineering is a powerful tool which may facilitate the experimental realization and control of topological phases in laser-driven 2D ferromagnetic systems. To this extent, we show that by applying a circularly polarized laser field to a 2D honeycomb ferromagnet which is uniaxially strained in either the zig-zag or armchair direction, it is possible to generate a synthetic Dzyaloshinskii-Moriya interaction (DMI) tunable by the intensity of the applied electric field, as well as by the magnitude of applied strain. Such deformations enable transitions to phases with opposite sign of Chern number, or to trivial phases. These are basic results that could pave the way for the development of a new field of Strain Engineered Topological Spintronics (SETS).

Magnons and plasmons are two very different types of collective modes, acting on the spin and charge degrees of freedom, respectively. At first sight, the formation of hybrid plasmon-magnon polaritons in heterostructures of plasmonic and magnetic systems would face two challenges, the small mutual interaction, via Zeeman coupling of the electromagnetic field of the plasmon with the spins, and the energy mismatch, as in most systems plasmons have energies in the eV range, orders of magnitude larger than magnons. Here we show that graphene plasmons form polaritons with the magnons of two-dimensional ferrromagnetic insulators, placed up to to half a micron apart, with Rabi couplings in the range of 100 GHz (dramatically larger than cavity QED magnonics). This strong coupling is facilitated both by the small energy of graphene plasmons and the cooperative super-radiant nature of the plasmon-magnon coupling afforded by phase matching. We show that the Rabi coupling can be modulated both electrically and mechanically and we propose a attenuated total internal reflection experiment to implement ferromagnetic resonance experiments on 2D ferromagnets driven by plasmon excitation.

With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states.

Scattering of excitons by free carriers is a phenomena which is especially important when considering moderately to heavily doped semiconductors in low temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal Boron Nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova--Keldysh potential. Making the distinction between elastic and inelastic scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence.

When transition-metal dichalcogenide monolayers lack inversion symmetry, their low-energy single particle spectrum can described by tilted massive Dirac Hamiltonians. The so-called Janus materials fall into that category. Inversion symmetry can also be broken by the application of out-of-plane electric fields, or by the mere presence of a substrate. Here we explore the properties of excitons in TMDC monolayers lacking inversion symmetry. We find that exciton binding energies can be larger than the electronic band gap, making such materials promising candidates to host the elusive exciton insulator phase. We also investigate the excitonic contribution to their optical conductivity and discuss the associated optical selection rules.

In this paper we consider a honeycomb antiferromagnet subject to an external laser field. Obtaining a time-independent effective Hamiltonian, we find that the external laser renormalizes the exchange interaction between the in-plane components of the spin-operators, and induces a synthetic Dzyaloshinskii-Moria interaction (DMI) between second neighbors. The former allows the control of the magnon dispersion's bandwidth and the latter breaks time-reversal symmetry inducing non-reciprocity in momentum space. The eigen-excitations of the system correspond to squeezed magnons whose squeezing parameters depend on the properties of the laser. When studying how these spin excitations couple with cavity photons, we obtain a coupling strength which can be enhanced by an order of magnitude via careful tuning of the laser's intensity, when compared to the case where the laser is absent. The transmission plots through the cavity are presented, allowing the mapping of the magnons' dispersion relation.

In this tutorial we introduce the reader to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semi-analytical, or numeric. We make explicit all the details associated with the different methods, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The tutorial starts with a variational method and ends with a simple semi-analytical approach to solve the Bethe-Salpeter equation in two-dimensional (2D) gapped materials. For the first methods addressed in this tutorial, we focus on a single layer of hexagonal Boron Nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe- Salpeter method we choose the biased bilayer graphene, which presents a tunnable band gap. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution of the Bethe-Salpeter equation in a context that can be easily generalized to more complex systems or to apply it to simpler models.

Trilayer graphene is receiving an increasing level of attention due to its stacking--dependent magnetoelectric and optoelectric properties, and its more robust ferromagnetism relative to monolayer and bilayer variants. Additionally, rhombohedral stacked trilayer graphene presents the possibility of easily opening a gap via either an external electric field perpendicular to the layers, or via the application of external strain. In this paper, we consider an external electric field to open a bandgap in rhombohedral trilayer graphene and study the excitonic optical response of the system. This is done via the combination of a tight binding model with the Bethe--Salpeter equation, solved semi--analytically and requiring only a simple numerical quadrature. We then discuss the valley--dependent optical selection rules, followed by the computation of the excitonic linear optical conductivity for the case of a rhombohedral graphene trilayer encapsulated in hexagonal boron nitride. The tunability of the excitonic resonances via an external field is also discussed, together with the increasing localization of the excitonic states as the field increases.

The use of graphene in surface plasmon resonance sensors, covering a metallic (plasmonic) film, has a number of demonstrated advantages, such protecting the film against corrosion/oxidation and facilitating the introduction of functional groups for selective sensing. Recently, a number of works have claimed that few-layer graphene can also increase the sensitivity of the sensor. However, graphene was treated as an isotropic thin film, with an out-of-plane refractive index that is identical to the in-plane index. Here, we critically examine the role of single and few layers of graphene in the sensitivity enhancement of surface plasmon resonance sensors. Graphene is introduced over the metallic film via three different descriptions: as an atomic-thick two-dimensional sheet, as a thin effective isotropic material (same conductivity in the three coordinate directions), and as an non-isotropic layer (different conductivity in the perpendicular direction to the two-dimensional plane). We find that only the isotropic layer model, which is known to be incorrect for the optically modelling of graphene, provides sizeable sensitivity increases, while the other, more accurate, models lead to negligible contribution to the sensitivity.

In this paper we discuss the optical response due to the excitonic effect of two types of hBN bilayers: AB and AA'. Understanding the properties of these bilayers is of great utility to the study of twisted bilayers at arbitrary angles, since these two configurations correspond to the limit cases of 0 and 60 degree rotation. To obtain the excitonic response we present a method to solve a four-band Bethe-Salpeter equation, by casting it into a 1D problem, thus greatly reducing the numerical burden of the calculation when compared with strictly 2D methods. We find results in good agreement with ab initio calculations already published in the literature for the AA' bilayer, and predict the excitonic conductivity of the AB bilayer, which remains largely unstudied. The main difference in the conductivity of these two types of bilayers is the appearance of a small, yet well resolved, resonance between two larger ones in the AB configuration. This resonance is due to a mainly interlayer exciton, and is absent in the AA' bilayer. Also, the conductivity of the AB bilayer is due to both intralayer and interlayer excitons and is dominated by p-states, while intralayer states are the relevant ones for the AA' configuration, like in a monolayer. The effect of introducing a bias in the AA' bilayer is also discussed.

Graphene plasmons have attracted significant attention due to their tunability, potentially long propagation lengths and ultracompact wavelengths. However, the latter characteristic imposes challenges to light-plasmon coupling in practical applications, generally requiring sophisticated coupling setups, extremely high doping levels and/or graphene nanostructuting close to the resolution limit of current lithography techniques. Here, we propose and theoretically demonstrate a method for alleviating such a technological strain through the use of a practical substrate whose low and negative dielectric function naturally enlarges the graphene polariton wavelength to more manageable levels. We consider silicon carbide (SiC), as it exhibits a dielectric function whose real part is between -1 and 0, while its imaginary part remains lower than 0.05, in the 951 to 970 cm$^{-1}$ mid-infrared spectral range. Our calculations show hybridization with the substrate's phonon polariton, resulting in a polariton wavelenth that is an order of magnitude longer than obtained with a silicon dioxide substrate, while the propagation length increases by the same amount.

Biased bilayer graphene, with its easily tunable band gap, presents itself as the ideal system to explore the excitonic effect in graphene based systems. In this paper we study the excitonic optical response of such a system by combining a tight binding model with the solution of the Bethe-Salpeter equation, the latter being solved in a semi-analytical manner, requiring a single numerical quadrature, thus allowing for a transparent calculation. With our approach we start by analytically obtaining the optical selection rules, followed by the computation of the absorption spectrum for the case of a biased bilayer encapsulated in hexagonal boron nitride, a system which has been the subject of a recent experimental study. An excellent agreement is seen when we compare our theoretical prediction with the experimental data.

We explore ways in which the close proximity between graphene sheets and monolayers of 2D superconductors can lead to hybridization between their collective excitations. We consider heterostructures formed by combinations of graphene sheets and 2D superconductor monolayers. The broad range of energies in which the graphene plasmon can exist, together with its tunability, makes such heterostrucutres promising platforms for probing the many-body physics of superconductors. We show that the hybridization between the graphene plasmon and the Bardasis-Schrieffer mode of a 2D superconductor results in clear signatures on the near-field reflection coefficient of the heterostructure, which in principle can be observed in scanning near-field microscopy experiments.

In this paper we review the theory of open quantum systems and macroscopic quantum electrodynamics, providing a self-contained account of many aspects of these two theories. The former is presented in the context of a qubit coupled to a electromagnetic thermal bath, the latter is presented in the context of a quantization scheme for surface-plasmon polaritons (SPPs) in graphene based on Langevin noise currents. This includes a calculation of the dyadic Green's function (in the electrostatic limit) for a Graphene sheet between two semi-infinite linear dieletric media, and its subsequent application to the construction of SPP creation and annihilation operators. We then bring the two fields together and discuss the entanglement of two qubits in the vicinity of a graphene sheet which supports SPPs. The two qubits communicate with each other via the emission and absorption of SPPs. We find that a Schödinger cat state involving the two qubits can be partially protected from decoherence by taking advantage of the dissipative dynamics in graphene. A comparison is also drawn between the dynamics at zero temperature, obtained via Schrodinger's equation, and at finite temperature, obtained using the Lindblad equation.

In this paper we present an analytical solution for the eigenmodes and corresponding electric field of a composite system made of a nanorod in the vicinity of a plasmonic semi-infinite metallic system. To be specific, we choose Silver as the material for both the nanorod and the semi-infinite metal. The system is composed of two sub-systems with different symmetries: the rod has symmetry, while the interface has a rectangular one. Using a boundary integral method, proposed by Eyges, we are able to compute analytically the integrals that sew together the two systems. In the end, the problem is reduced to one of linear algebra, where all the terms in the system are known analytically. For large distances between the rod and the planar surface, only a few of those integrals are needed and a full analytical solution can be obtained. Our results are important to benchmark other numerical approaches and represent a starting point in the discussion of systems composed of nanorods and two-dimensional materials.

In this paper, we employ a fully microscopic approach to the study of interlayer excitons in hetero-bilayers. We use Fowler's and Karplus' method to access the dynamical polarizability of non--interacting interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsen's variational method to the calculation of the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$ hetero--bilayer, discussing the various selection rules of intra--excitonic energy level transitions.

In this paper we give an application of Dalgarno-Lewis method, the latter not usually taught in quantum mechanics courses. This is very unfortunate since this method allows to bypass the sum over states appearing in the usual perturbation theory. In this context, and as an example, we study the effect of an external field, both static and frequency dependent, on a model-atom at fixed distance from a substrate. This can happen, for instance, when some organic molecule binds from one side to the substrate and from the other side to an atom or any other polarizable system. We model the polarizable atom by a short range potential, a Dirac$-\delta$ and find that the existence of a bound state depends on the ratio of the effective "nuclear charge" to the distance of the atom to the substrate. Using an asymptotic analysis, previously developed in the context of a single $\delta-$function potential in an infinite medium, we determine the ionization rate and the Stark shift of our system. Using Dalgarno-Lewis theory we find an exact expression for the static and dynamic polarizabilities of our system valid to all distances. We show that the polarizability is extremely sensitive to the distance to the substrate creating the possibility of using this quantity as a nanometric ruler. Furthermore, the line shape of the dynamic polarizability is also extremely sensitive to the distance to the substrate, thus providing another route to measure nanometric distances. The ditactic value of the $\delta-$function potential is well accepted in teaching activities due to its simplicity, while keeping the essential ingredients of a given problem.

We obtain an analytical expression for the linewidth of the 1s-exciton as a function of temperature in transition metal dichalcogenides. The total linewidth, as function of temperature, is dominated by three contributions: (i) the radiative decay (essentially temperature independent); (ii) the phonon-induced intravalley scattering; (iii) the phonon-induced intervalley scattering. Our approach uses a variational \emphAnsatz to solve the Wannier equation allowing for an analytical treatment of the excitonic problem, including rates of the decay dynamics. Our results are in good agreement with experimental data already present in the literature and can be used to readily predict the value of the total linewidth at any temperature in the broad class of excitonic two-dimensional materials.

In this paper, we study the third-order nonlinear optical response due to transitions between excitonic levels in two-dimensional transition metal dichalcogeniedes. To accomplish this, we use methods not applied to the description of excitons in two-dimensional materials so far and combined with a variational approach to describe the $1s$ excitonic state. The aforementioned transitions allow to probe dark states which are not revealed in absorption experiments. We present general formulas capable of describing any third-order process. The specific case of two-photon absorption in WSe2 is studied. The case of the circular well is also studied as a benchmark of the theory.

Graphene hybrids, made of thin insulators, graphene, and metals can support propagating acoustic plasmons (AGPs). The metal screening modifies the dispersion relation of usual graphene plasmons leading to slowly propagating plasmons, with record confinement of electromagnetic radiation. Here, we show that a graphene monolayer, covered by a thin dielectric material and an array of metallic nanorods can be used as a robust platform to emulate the Su-Schrieffer-Heeger model. We calculate the Zak's phase of the different plasmonic bands to characterise their topology. The system shows bulk-edge correspondence: strongly localized interface states are generated in the domain walls separating arrays in different topological phases. We find signatures of the nontrivial phase which can directly be probed by far-field mid-IR radiation, hence allowing a direct experimental confirmation of graphene topological plasmons. The robust field enhancement, highly localized nature of the interface states, and their gate-tuned frequencies expand the capabilities of AGP-based devices.

We report the largest broadband terahertz (THz) polarizer based on a flexible ultra-transparent cyclic olefin copolymer (COC). The COC polarizers were fabricated by nanoimprint soft lithography with the lowest reported pitch of 2 or 3 micrometers and depth of 3 micrometers and sub-wavelength Au bilayer wire grid. Fourier Transform Infrared spectroscopy in a large range of 0.9 -20 THz shows transmittance of bulk materials such as doped and undoped Si and polymers. COC polarizers present more than doubled transmission intensity and larger transmitting band when compared to Si. COC polarizers present superior performance when compared to Si polarizers, with extinctions ratios of at least 4.4 dB higher and registered performance supported by numerical simulations. Fabricated Si and COC polarizers' show larger operation gap when compared to a commercial polarizer. Fabrication of these polarizers can be easily up-scaled which certainly meets functional requirements for many THz devices and applications, such as high transparency, lower cost fabrication and flexible material.

In this paper we study the phonon's effect on the position of the 1s excitonic resonance of the fundamental absorption transition line in two-dimensional transition metal dichalcogenides. We apply our theory to WS$_{2}$a two-dimensional material where the shift in absorption peak position has been measured as a function of temperature. The theory is composed of two ingredients only: i) the effect of longitudinal optical phonons on the absorption peak position, which we describe with second order perturbation theory; ii) the effect of phonons on the value of the single particle energy gap, which we describe with the Huang Rhys model. Our results show an excellent agreement with the experimentally measured shift of the absorption peak with the temperature.

In this paper we develop a fully microscopic theory of the polarizability of excitons in transition metal dichalcogenides. We apply our method to the description of the excitation $2$p dark states. These states are not observable in absorption experiments but can be excited in a pump-probe experiment. As an example we consider $2$p dark states in WSe\textsubscript2. We find a good agreement between recent experimental measurements and our theoretical calculations.

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light--matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultra-confined acoustic graphene plasmons (AGPs) in graphene--dielectric--metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman $d$-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the AGPs' dispersion, and demonstrate that the high field confinement of AGPs can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of AGPs as plasmon rulers with ångström-scale accuracy.

We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizing the previously obtained result for isotropic two-dimensional semiconductors. This approximation is shown to be valid in the weak-field limit by comparing it to the exact rates. The anisotropy is also apparent in the large difference between armchair and zigzag components of the exciton polarizability tensor, which we compute for the five lowest lying states. As expected, we also find much more pronounced Stark shifts in either the armchair or zigzag direction, depending on the symmetry of the state in question. Finally, an isotropic interaction potential is shown to be an excellent approximation to a more accurate anisotropic interaction derived from the Poisson equation, confirming that the anisotropy of phosphorene is largely due to the direction dependence of the effective masses.

Plasmonic excitations such as surface-plasmon-polaritons (SPPs) and graphene-plasmons (GPs), carry large momenta and are thus able to confine electromagnetic fields to small dimensions. This property makes them ideal platforms for subwavelength optical control and manipulation at the nanoscale. The momenta of these plasmons are even further increased if a scheme of metal-insulator-metal and graphene-insulator-metal are used for SPPs and GPs, respectively. However, with such large momenta, their far-field excitation becomes challenging. In this work, we consider hybrids of graphene and metallic nanostructures and study the physical mechanisms behind the interaction of far-field light with the supported high momenta plasmon modes. While there are some similarities in the properties of GPs and SPPs, since both are of the plasmon-polariton type, their physical properties are also distinctly different. For GPs we find two different physical mechanism related to either GPs confined to isolated cavities, or large area collective grating couplers. Strikingly, we find that although the two systems are conceptually different, under specific conditions they can behave similarly. By applying the same study to SPPs, we find a different physical behavior, which fundamentally stems from the different dispersion relations of SPPs as compared to GPs. Furthermore, these hybrids produce large field enhancements that can also be electrically tuned and modulated making them the ideal candidates for a variety of plasmonic devices.

We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is observable through the Purcell effect. When combining the superconductor, graphene, and the quantum emitters, a number of experimental knobs become available for unveiling and studying the electrodynamics of superconductors.

Non reciprocal spin waves have a chiral asymmetry so that their energy is different for two opposite wave vectors. They are found in atomically thin ferromagnetic overlayers with in plane magnetization and are linked to the anti-symmetric Dzyaloshinskii-Moriya surface exchange. We use an itinerant fermion theory based on first principles calculations to predict that non-reciprocal magnons can occur in Fe$_3$GeTe$_2$, the first stand alone metallic two dimensional crystal with off-plane magnetization. We find that both the energy and lifetime of magnons are non-reciprocal and we predict that acoustic magnons can have lifetimes up to hundreds of picoseconds, orders of magnitude larger than in other conducting magnets.

Using a semi-classical approach, we derive a fully analytical expression for the ionization rate of excitons in two-dimensional materials due to an external static electric field, which eliminates the need for complicated numerical calculations. Our formula shows quantitative agreement with more sophisticated numerical methods based on the exterior complex scaling approach, which solves a non-hermitian eigenvalue problem yielding complex energy eigenvalues, where the imaginary part describes the ionization rate. Results for excitons in hexagonal boron nitride and the $A-$exciton in transition metal dichalcogenides are given as a simple examples. The extension of the theory to include spin-orbit-split excitons in transition metal dichalcogenides is trivial.

Magnons dominate the magnetic response of the recently discovered insulating ferromagnetic two dimensional crystals such as CrI$_3$. Because of the arrangement of the Cr spins in a honeycomb lattice, magnons in CrI$_3$ bear a strong resemblance with electronic quasiparticles in graphene. Neutron scattering experiments carried out in bulk CrI$_3$ show the existence of a gap at the Dirac points, that has been conjectured to have a topological nature. Here we propose a theory for magnons in ferromagnetic CrI$_3$ monolayers based on an itinerant fermion picture, with a Hamiltonian derived from first principles. We obtain the magnon dispersion for 2D CrI$_3$ with a gap at the Dirac points with the same Berry curvature in both valleys. For CrI$_3$ ribbons, we find chiral in-gap edge states. Analysis of the magnon wave functions in momentum space further confirms their topological nature. Importantly, our approach does not require to define a spin Hamiltonian, and can be applied to both insulating and conducting 2D materials with any type of magnetic order.

Acoustic-graphene-plasmons (AGPs) are highly confined electromagnetic modes, carrying large momentum and low loss in the mid-infrared/Terahertz spectra. Owing to their ability to confine light to extremely small dimensions, they bear great potential for ultra-strong light-matter interactions in this long wavelength regime, where molecular fingerprints reside. However, until now AGPs have been restricted to micron-scale areas, reducing their confinement potential by several orders-of-magnitude. Here, by utilizing a new type of graphene-based magnetic-resonance, we realize single, nanometric-scale AGP cavities, reaching record-breaking mode-volume confinement factors of $\thicksim5\cdot10^{-10}$. This AGP cavity acts as a mid-infrared nanoantenna, which is efficiently excited from the far-field, and electrically tuneble over an ultra-broadband spectrum. Our approach provides a new platform for studying ultra-strong-coupling phenomena, such as chemical manipulation via vibrational-strong-coupling, and a path to efficient detectors and sensors, in this challenging spectral range.

In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed.

In this paper we develop the excitonic theory of Kerr rotation angle in a two-dimensional (2D) transition metal dichalcogenide at zero magnetic field. The finite Kerr angle is induced by the interplay between spin-orbit splitting and proximity exchange coupling due to the presence of a ferromagnet. We compare the excitonic effect with the single particle theory approach. We show that the excitonic properties of the 2D material lead to a dramatic change in the frequency dependence of the optical response function. We also find that the excitonic corrections enhance the optical response by a factor of two in the case of MoS2 in proximity to a Cobalt thin film.

We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous. We derive the Fresnel coefficients of the system and the Poynting vectors at the interface, in order to compute the reflectance and transmittance of the system. We use a particular parametrisation of the referred Fresnel coefficients so as to make a connection with the ones obtained for refraction by an interface between two lossless media. This analysis allows the discussion of an actual application, namely the Fresnel polarisation of infra-red radiation by elemental bismuth, based on the concept of pseudo Brewster's angle.

We describe exciton-polariton modes formed by the interaction between excitons in a 2D layer of a transition metal dichalcogenide embedded in a cylindrical microcavity and the microcavity photons. For this, an expression for the excitonic susceptibility of a semiconductor disk placed in the symmetry plane perpendicular to the axis of the microcavity is derived. Semiclassical theory provides dispersion relations for the polariton modes, while the quantum-mechanical treatment of a simplified model yields the Hopfield coefficients, measuring the degree of exciton-photon mixing in the coupled modes. The density of states (DOS) and its projection onto the photonic and the excitonic subspaces are calculated taking monolayer MoS 2 embedded in a Si 3 N 4 cylinder as an example. The calculated results demonstrate a strong enhancement, for certain frequencies, of the total and local DOS (Purcell effect) caused by the presence of the 2D layer.

Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number $\pm 1/2$, that entails both a quantized dc Hall response and a subgap full-quarter Kerr rotation. The observation of these effects in 2D massive Dirac materials such as gapped graphene, hexagonal boron nitride or transition metal dichalcogenides (TMDs) is obscured by the fact that Dirac cones come in pairs with opposite sign Berry curvatures, leading to a vanishing Chern number. Here, we show that the presence of spin-orbit interactions, combined with an exchange spin splitting induced either by diluted magnetic impurities or by proximity to a ferromagnetic insulator, gives origin to a net magneto-optical Kerr effect in such systems. We focus on the case of TMD monolayers and study the dependence of Kerr rotation on frequency and exchange spin splitting. The role of the substrate is included in the theory and found to critically affect the results. Our calculations indicate that state-of-the-art magneto-optical Kerr spectroscopy can detect a single magnetic impurity in diluted magnetic TMDs.

In this paper we develop a semi-analytical perturbation-theory approach to the calculation of the energy levels (binding energies) and wave functions of excitons in phosphorene. Our method gives both the exciton wave function in real and reciprocal spaces with the same ease. This latter aspect is important for the calculation of the nonlinear optical properties of phosphorene. We find that our results are in agreement with calculations based both on the Bethe-Salpeter equation and on Monte Carlo simulations, which are computationally much more demanding. Our approach thus introduces a simple, viable, and accurate method to address the problem of excitons in anisotropic two-dimensional materials.

In this paper we discuss the magnetic Purcell effect of a magnetic dipole near a semi-infinite antiferromagnet. Contrary to the electric Purcell effect, the magnetic one is not so well studied in the literature. We derive the dispersion relation of the surface wave existing at an antiferromagnetic-dielectric interface from the calculation of the reflection coefficient of the structure. After characterizing the surface wave we quantize the electromagnetic vector potential of the surface wave. This allow us to discuss the magnetic Purcell effect via Fermi golden rule.

Excitons in monolayer transition-metal-dichalcogenides (TMDs) dominate their optical response and exhibit strong light-matter interactions with lifetime-limited emission. While various approaches have been applied to enhance light-exciton interactions in TMDs, the achieved strength have been far below unity, and a complete picture of its underlying physical mechanisms and fundamental limits has not been provided. Here, we introduce a TMD-based van der Waals heterostructure cavity that provides near-unity excitonic absorption, and emission of excitonic complexes that are observed at ultra-low excitation powers. Our results are in full agreement with a quantum theoretical framework introduced to describe the light-exciton-cavity interaction. We find that the subtle interplay between the radiative, non-radiative and dephasing decay rates plays a crucial role, and unveil a universal absorption law for excitons in 2D systems. This enhanced light-exciton interaction provides a platform for studying excitonic phase-transitions and quantum nonlinearities and enables new possibilities for 2D semiconductor-based optoelectronic devices.

Van der Waals (vdW) heterostructures ---formed by stacking or growing two-dimensional (2D) crystals on top of each other--- have emerged as a new promising route to tailor and engineer the properties of 2D materials. Twisted bilayer graphene (tBLG), a simple vdW structure where the interference between two misaligned graphene lattices leads to the formation of a moiré pattern, is a test bed to study the effects of the interaction and misalignment between layers, key players for determining the electronic properties of these stackings. In this chapter, we present in a pedagogical way the general theory used to describe lattice mismatched and misaligned vdW structures. We apply it to the study of tBLG in the limit of small rotations and see how the coupling between the two layers leads both to an angle dependent renormalization of graphene's Fermi velocity and appearance of low-energy van Hove singularities. The optical response of this system is then addressed by computing the optical conductivity and the dispersion relation of tBLG surface plasmon-polaritons.

In this paper we show that graphene surface plasmons can be excited when an electromagnetic wave packet impinges on a single metal slit covered with graphene. The excitation of the plasmons localized over the slit is revealed by characteristic peaks in the absorption spectrum. It is shown that the position of the peaks can be tuned either by the graphene doping level or by the dielectric function of the material filling the slit. The whole system forms the basis for a plasmonic sensor when the slit is filled with an analyte.

In this paper we theoretically describe the absorption of hexagonal boron nitride (hBN) single layer. We develop the necessary formalism and present an efficient method for solving the Wannier equation for excitons. We give predictions for the absorption of hBN on quartz and on graphite. We compare our predictions with recently published results [Elias \it et al., Nat. Comm. \bf 10, 2639 (2019)] for a monolayer of hBN on graphite. The spontaneous radiative lifetime of excitons in hBN is also computed. We argue that the optical properties of hBN in the ultraviolet are very useful for the study of peptides and other biomolecules.

We present a semi-analytical model that predicts the excitation of surface-plasmon polaritons (SPP) on a graphene sheet located in front of a sub-wavelength slit drilled in thick metal screen. We identify the signature of the SPP in the transmission, reflection, and absorption curves. Following previous literature on noble-metal plasmonics, we characterize the efficiency of excitation of SPP's in graphene computing a spatial probability density. This quantity shows the presence of plasmonics resonances dispersing with the Fermi energy, $E_F$, as $\sqrt{E_F}$ an unambiguous signature of graphene plasmons.

In this article we perform the quantization of graphene plasmons using both a macroscopic approach based on the classical average electromagnetic energy and a quantum hydrodynamic model, in which graphene charge carriers are modeled as a charged fluid. Both models allow to take into account the dispersion of graphenes optical response, with the hydrodynamic model also allowing for the inclusion of non-local effects. Using both methods, the electromagnetic field mode-functions, and the respective frequencies, are determined for two different graphene structures. we show how to quantize graphene plasmons, considering that graphene is a dispersive medium, and taking into account both local and nonlocal descriptions. It is found that the dispersion of graphene's optical response leads to a non-trivial normalization condition for the mode-functions. The obtained mode-functions are then used to calculate the decay of an emitter, represented by a dipole, via the excitation of graphene surface plasmon-polaritons. The obtained results are compared with the total spontaneous decay rate of the emitter and a near perfect match is found in the relevant spectral range. It is found that non-local effects in graphene's conductivity, become relevant for the emission rate for small Fermi energies and small distances between the dipole and the graphene sheet.

The magneto-optical response of monolayer transition metal dichalcogenides (TMDs), including excitonic effects, is studied using a nanoribbon geometry. We compute the diagonal optical conductivity and the Hall conductivity. Comparing the excitonic optical Hall conductivity to results obtained in the independent particle approximation, we find an increase in the amplitude corresponding to one order of magnitude when excitonic effects are included. The Hall conductivities are used to calculate Faraday rotation spectra for MoS2 and WSe2. Finally, we have also calculated the diamagnetic shift of the exciton states of WSe2 in different dielectric environments. Comparing the calculated diamagnetic shift to recent experimental measurements, we find a very good agreement between the two.

We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change of sign in the group velocity. Second, a surface plasmon-magnon polariton formed as a linear superposition of graphene surface plasmon and the antiferromagnetic bare magnon. This polariton has a dispersion with two branches, formed by the anticrossing between the dispersive surface plasmon and the magnon. We discuss the potential these new modes have for combining photons, magnons, and plasmons to reach new functionalities.

We use coupled-mode theory to describe the scattering of a surface-plasmon polariton (SPP) from a square wave grating (Bragg grating) of finite extension written on the surface of either a metal-dielectric interface or a dielectric-dielectric interface covered with a patterned graphene sheet. We find analytical solutions for the reflectance and transmittance of SPP's when only two modes (forward- and back-scattered) are considered. We show that in both cases the reflectance spectrum presents stop-bands where the SPP is completely back-scattered, if the grating is not too shallow. In addition, the reflectance coefficient shows Fabry-Pérot oscillations when the frequency of the SPP is out of the stop-band region. For a single dielectric well, we show that there are frequencies of transmission equal to 1. We also provide simple analytical expression for the different quantities in the electrostatic limit.

We study the optical properties of semiconducting transition metal dichalcogenide monolayers under the influence of strong out-of-plane magnetic fields, using the effective massive Dirac model. We pay attention to the role of spin-orbit coupling effects, doping level and electron-electron interactions, treated at the Hartree-Fock level. We find that optically-induced valley and spin imbalance, commonly attained with circularly polarized light, can also be obtained with linearly polarized light in the doped regime. Additionally, we explore an exchange-driven mechanism to enhance the spin-orbit splitting of the conduction band, in n-doped systems, controlling both the carrier density and the intensity of the applied magnetic field.

We consider a planar two-dimensional system between two media with different dielectric constants and in the presence of a third dielectric medium separated by a nonplanar interface. Extending a perturbative method for solving Poisson's equation, developed by Clinton, Esrick, and Sacks [Phys. Rev. B, 31, 7540 (1985)], in the presence of nonplanar conducting boundaries to the situation proposed here, we obtain, up to the first order in terms of the function which defines the nonplanar interface, the effective potential, the effective electrostatic field, the effective dielectric constant for the planar 2D system, and the effective external field acting in-plane in the 2D system. Implications of the results to properties of 2D systems are discussed. In the limit of planar surfaces, vacuum-dielectric or vacuum-conducting media, our results are in agreement with those found in the literature.

Using an equation of motion (EOM) approach, we calculate excitonic properties of monolayer transition metal dichalcogenides (TMDs) perturbed by an external magnetic field. We compare our findings to the widely used Wannier model for excitons in two-dimensional materials and to recent experimental results. We find good agreement between the calculated excitonic transition energies and the experimental results. In addition, we find that the exciton energies calculated using the EOM approach are slightly lower than the ones calculated using the Wannier model. Finally, we also show that the effect of the dielectric environment on the magnetoexciton transition energy is minimal due to counteracting changes in the exciton energy and the exchange self-energy correction.

The electronic and optical properties of 2D hexagonal boron nitride are studied using first principle calculations. GW and BSE methods are employed in order to predict with better accuracy the excited and excitonic properties of this material. We determine the values of the band gap, optical gap, excitonic binding energies and analyse the excitonic wave functions. We also calculate the exciton energies following an equation of motion formalism and the Elliot formula, and find a very good agreement with the GW+BSE method. The optical properties are studied for both the TM and TE modes, showing that 2D hBN is a good candidate to polaritonics in the UV range. In particular it is shown that a single layer of h-BN can act as an almost perfect mirror for ultraviolet electromagnetic radiation.

In this paper we analyze the effects of nonlocality on the optical properties of a system consisting of a thin metallic film separated from a graphene sheet by a hexagonal boron nitride (hBN) layer. We show that nonlocal effects in the metal have a strong impact on the spectrum of the surface plasmon-polaritons on graphene. If the graphene sheet is shaped into a grating, we show that the extinction curves can be used to shed light on the importance of nonlocal effects in metals. Therefore, graphene surface plasmons emerge as a tool for probing nonlocal effects in metallic nanostructures, including thin metallic films. As a byproduct of our study, we show that nonlocal effects lead to smaller losses for the graphene plasmons than what is predicted by a local calculation. We show that these effects can be very well mimicked using a local theory with an effective spacer thickness larger than its actual value.

We derive an integral equation describing surface-plasmon polaritons in graphene deposited on a substrate with a planar surface and a dielectric protrusion in the opposite surface of the dielectric slab. We show that the problem is mathematically equivalent to the solution of a Fredholm equation, which we solve exactly. In addition, we show that the dispersion relation of the localized surface plasmons is determined by the geometric parameters of the protrusion alone. We also show that such system supports both even and odd modes. We give the electrostatic potential and the stream plot of the electrostatic field, which clearly show the localized nature of the surface plasmons in a continuous and flat graphene sheet.

In this work, the difficulties inherent to perturbative calculations in the velocity gauge are addressed. In particular, it is shown how calculations of nonlinear optical responses in the independent particle approximation can be done to any order and for any finite band model. The procedure and advantages of the velocity gauge in such calculations are described. The addition of a phenomenological relaxation parameter is also discussed. As an illustration, the nonlinear optical response of monolayer graphene is numerically calculated using the velocity gauge.

We discuss the scattering of graphene surface plasmon-polaritons (SPPs) at an interface between two semi-infinite graphene sheets with different doping levels and/or different underlying dielectric substrates. We take into account retardation effects and the emission of free radiation in the scattering process. We derive approximate analytic expressions for the reflection and the transmission coefficients of the SPPs as well as the same quantities for the emitted free radiation. We show that the scattering problem can be recast as a Fredholm equation of the second kind. Such equation can then be solved by a series expansion, with the first term of the series correspond to our approximated analytical solution for the reflection and transmission amplitudes. We have found that almost no free radiation is emitted in the scattering process and that under typical experimental conditions the back-scattered SPP transports very little energy. This work provides a theoretical description of graphene plasmon scattering at an interface between distinct Fermi levels which could be relevant for the realization of plasmonic circuitry elements such as plasmonic lenses or reflectors, and for controlling plasmon propagation by modulating the potential landscape of graphene.