Robust Bulk States

TL;DR

This paper predicts the existence of topologically robust zero energy bulk states in disordered lattices, linking their presence to the noninvertibility of the Hamiltonian, and demonstrating their robustness against disorder.

Contribution

It introduces a novel connection between noninvertibility of the Hamiltonian and the existence of robust zero energy states in disordered systems.

Findings

Zero energy states exist iff the Hamiltonian is noninvertible.

These states are robust against any disorder if the Hamiltonian remains noninvertible.

The work links topological robustness to algebraic properties of the Hamiltonian.

Abstract

We predict topologically robust zero energy bulk states in a disordered tight binding lattice. We explore a new kind of order and discuss that zero energy states exist in a system iff its Hamiltonian is noninvertible. We show that they are robust against any kind of disorder as long as the disordered Hamiltonian is noninvertible, too.