Topological properties of a class of Su-Schrieffer-Heeger variants

TL;DR

This paper reveals how complex one-dimensional lattices with intricate hopping patterns can be simplified to the SSH model, allowing exact analysis of topological phase transitions and edge states, and identifying conditions for their universality.

Contribution

It introduces a real space decimation method to recognize SSH structure in complex lattices and analytically determines the conditions for topological phase transitions.

Findings

Decimation uncovers SSH topology in complex lattices.

Exact eigenvalues at gap closures are derived.

Topological transitions depend on specific hopping correlations.

Abstract

We investigate the edge states and the topological phase transitions in a class of tight binding lattices in one dimension where a Su-Schrieffer-Heeger (SSH) model exists in disguise. The unit cells of such lattices may have an arbitrarily intricate staggering pattern woven in the hopping integrals, that apparently masks the basic SSH structure. We unmask the SSH character in such lattices using a simple real space decimation of a subset of the degrees of freedom. The decimation not only allows us to recognize the familiar SSH geometry, but at the same time enables us to determine, in an analytically exact way, the precise energy eigenvalues at which the gaps open up (or close) at the Brillouin zone boundaries. It is argued that, a topological phase transition and the existence of the protected edge states can be observed in such lattices only under definite numerical correlations between the hopping integrals decorating the unit cell. Such a correlation, achievable in a variety of ways, brings different such models under a kind of a universality class.