Topological Insulators in Three Dimensions

TLDR

In three dimensions, four Z₂ invariants distinguish 16 topological phases, yielding weak and strong topological insulators. The study investigates three‑dimensional generalizations of the quantum spin Hall effect. A tight‑binding model is presented that realizes both WTI and STI phases and is linked to real materials such as bismuth. WTI behave as layered 2D QSH states but are destroyed by disorder, whereas STI remain robust and produce novel topological‑metal surface states.

Abstract

We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.