Coexisting edge states and gapless bulk in topological states of matter

TL;DR

This paper explores two-dimensional systems where edge states coexist with a gapless bulk, analyzing their protection mechanisms, effects of disorder, and proposing a physical realization in quantum wells.

Contribution

It introduces a model for coexisting edge states and gapless bulk, analyzing their stability and protection, and suggests a concrete experimental realization.

Findings

Edge states can be protected without disorder due to conservation laws.

Disorder can stabilize or destabilize edge states depending on bulk localization.

Proposes bilayer Hg(Cd)Te quantum wells as a physical realization.

Abstract

We consider two dimensional systems in which edge states coexist with a gapless bulk. Such systems may be constructed, for example, by coupling a gapped two dimensional state of matter that carries edge states to a gapless two dimensional system in which the spectrum is composed of a number of Dirac cones. We find that in the absence of disorder the edge states could be protected even when the two systems are coupled, due to momentum and energy conservation. We distinguish between weak and strong edge states by the level of their mixing with the bulk. In the presence of disorder, the edge states may be stabilized when the bulk is localized or destabilized when the bulk is metallic. We analyze the conditions under which these two cases occur. Finally, we propose a concrete physical realization for one of our models on the basis of bilayer Hg(Cd)Te quantum wells.