## 6 Citations

Is the continuum SSH model topological?

- Physics
- 2021

The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) [14] is a well-known onedimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cell…

Lower Bound on Quantum Tunneling for Strong Magnetic Fields

- PhysicsSIAM J. Math. Anal.
- 2022

We consider a particle bound to a two-dimensional plane and a double well potential, subject to a perpendicular uniform magnetic field . The energy difference between the lowest two eigenvalues--the…

Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher

- MathematicsArchive for Rational Mechanics and Analysis
- 2022

This work identifies an assumption under which it is proved that ELWFs can be constructed as the eigenfunctions of a sequence of self-adjoint operators acting on the Fermi projection and numerically verifies that the construction yields ELWF in various cases where this assumption holds.

Discrete honeycombs, rational edges and edge states

- Mathematics
- 2022

Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into…

Bistritzer-MacDonald dynamics in twisted bilayer graphene

- Physics
- 2022

The Bistritzer-MacDonald (BM) model, introduced in [10], attempts to capture the electronic properties of twisted bilayer graphene (TBG), even at incommensurate twist angles, by an effective periodic…

Fredholm Homotopies for Strongly-Disordered 2D Insulators

- Physics
- 2021

We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between…

## References

SHOWING 1-10 OF 86 REFERENCES

Continuum Schroedinger Operators for Sharply Terminated Graphene-Like Structures

- MathematicsCommunications in Mathematical Physics
- 2020

We study the single electron model of a semi-infinite graphene sheet interfaced with the vacuum and terminated along a zigzag edge. The model is a Schroedinger operator acting on $L^2(\mathbb{R}^2)$:…

Honeycomb Schrödinger Operators in the Strong Binding Regime

- Mathematics
- 2016

In this article, we study the Schrödinger operator for a large class of periodic potentials with the symmetry of a hexagonal tiling of the plane. The potentials we consider are superpositions of…

Edge States in Honeycomb Structures

- Physics, Mathematics
- 2015

An edge state is a time-harmonic solution of a conservative wave system, e.g. Schrödinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or…

Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields

- Physics
- 1976

An effective single-band Hamiltonian representing a crystal electron in a uniform magnetic field is constructed from the tight-binding form of a Bloch band by replacing…

Colloquium : Topological insulators

- Physics
- 2010

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to…

The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors

- Mathematics
- 2016

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological…

Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases

- MathematicsMathematical Physics, Analysis and Geometry
- 2018

In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable C∗-algebra by a…

The Colored Hofstadter Butterfly for the Honeycomb Lattice

- Mathematics
- 2014

We rely on a recent method for determining edge spectra and we use it to compute the Chern numbers for Hofstadter models on the honeycomb lattice having rational magnetic flux per unit cell. Based on…

Classification of topological insulators and superconductors in three spatial dimensions

- Physics
- 2008

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial…

Index Pairings in Presence of Symmetries with Applications to Topological Insulators

- Mathematics
- 2016

In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal…