Magnetic square lattice with vertex coupling of a preferred orientation. (English) Zbl 1523.81082
Summary: We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum numerically for rational values of the flux per plaquette we show how the two effects compete; at the high energies it is the magnetic field which dominates restoring asymptotically the familiar Hofstadter’s butterfly pattern.
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 78A30 | Electro- and magnetostatics |
| 82B35 | Irreversible thermodynamics, including Onsager-Machlup theory |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 35B36 | Pattern formations in context of PDEs |
Keywords:
quantum graphs; magnetic field; periodic structure; time reversal non-invariance; spectral gaps; Hofstadter’s butterflyReferences:
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