Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
arXiv:2101.08603 · doi:10.1007/s00023-021-01097-2
Abstract
The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk, and has a nonvanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous.
References in corpus (11)
- The Non-Commutative Geometry of the Quantum Hall Effect
- Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
- Localization Bounds for an Electron Gas
- Simultaneous quantization of edge and bulk Hall conductivity
- Equality of bulk and edge Hall conductance revisited
- Equality of the bulk and edge Hall conductances in a mobility gap
- The topological classification of one-dimensional symmetric quantum walks
- On the extended nature of edge states of Quantum Hall Hamiltonians
- On edge states in semi-infinite quantum Hall systems
- Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries
- Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory