Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice. (English) Zbl 1533.81096
Summary: The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field \(B\) contains a \(B\)-independent “zeroth Landau level”, protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of “Wilson fermions”, the chiral symmetry is broken and the zeroth Landau level is broadened when \(B\) has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining \(+B\) and \(-B\) regions.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 82D37 | Statistical mechanics of semiconductors |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 81V74 | Fermionic systems in quantum theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 70F05 | Two-body problems |
| 78A30 | Electro- and magnetostatics |
| 39A12 | Discrete version of topics in analysis |
| 81R40 | Symmetry breaking in quantum theory |
| 35Q56 | Ginzburg-Landau equations |
Keywords:
topological insulator; quantum Hall effect; lattice fermion; Dirac fermion; fermion doublingReferences:
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