arXiv subjects

Ilya Iakoub

Publications and source records attributed to Ilya Iakoub.

2 recordsLinked to original sources

arXiv2026

Topological Boundary States and the Edge Chain in Semi-Infinite Two-Dimensional Insulators

We show that it is possible to compute the adiabatically protected edge and corner states of semi-infinite, two-dimensional, topological insulators by considering the first layer of lattice sites, what we call the "edge chain," independently from the bulk. We start by accepting this claim as an ansatz, then, using the Shemesh theorem, we show that the edge states one finds using our procedure are adiabatically protected, provided we restrict ourselves to adiabatic evolutions that do not break chiral symmetry. We show explicit examples of our method in a 2D extension of the SSH model, the SSH3 model, the Haldane model and the Breathing Kagome Lattice.

cond-mat.mes-hall↗

arXiv2026

Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros

We provide an alternative derivation of the bulk-boundary correspondence for semi-infinite chains. To describe edge states, we analytically continue the usual Bloch Hamiltonian to complex wave vectors $k$. To start, we note that the zeros of a Bloch wavefunction are related to edge states, at least in systems with nearest-neighbour hoppings. We show that an analytically continued Bloch Hamiltonian with chiral symmetry has exceptional points, where two different states coalesce. These special points are related to the adiabatic protection of edge states. We derive a winding number that counts the number of topological edge states protected by chiral symmetry.

cond-mat.mes-hall↗