• Corpus ID: 238857095

Fredholm Homotopies for Strongly-Disordered 2D Insulators

@inproceedings{Bols2021FredholmHF,
  title={Fredholm Homotopies for Strongly-Disordered 2D Insulators},
  author={Alex Bols and Jeffrey H. Schenker and Jacob Shapiro},
  year={2021}
}
We devise a method to interpolate between certain Fredholm operators arising in the context of strongly-disordered 2D topological insulators. We use this technique to prove the bulk-edge correspondence for mobility-gapped 2D topological insulators possessing a (Fermionic) time-reversal symmetry (class AII) and provide an alternative route to a theorem by Elgart-Graf-Schenker [13] about the bulk-edge correspondence for strongly-disordered integer quantum Hall systems. 
View PDF on arXiv
2 Citations
Background Citations
2

Figures from this paper

2 Citations

Citation Type

Citation Type

Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a timereversal symmetric version…
General bulk-edge correspondence at positive temperature
By extending the gauge covariant magnetic perturbation theory to operators defined on half planes, we prove that for general 2d random ergodic magnetic Schrödinger operators the celebrated bulk-edge…

References

SHOWING 1-10 OF 30 REFERENCES
Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we…
Charge deficiency, charge transport and comparison of dimensions
We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the…
Localization bounds for an electron gas
Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of…
Equality of the Bulk and Edge Hall Conductances in a Mobility Gap
We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when…
Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
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…
On stable quantum currents
We study the transport properties of discrete quantum dynamical systems on the lattice, in particular, coined quantum walks and the Chalker–Coddington model. We prove the existence of a non-trivial…
Tight-Binding Reduction and Topological Equivalence in Strong Magnetic Fields
Strongly Disordered Floquet Topological Systems
We study the strong disorder regime of Floquet topological systems in dimension two that describe independent electrons on a lattice subject to a periodic driving. In the spectrum of the Floquet…
The Bulk-Edge Correspondence for Disordered Chiral Chains
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk)…
The topology of mobility-gapped insulators
Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that…
...
1
2
3
...