Topological Polarization in Graphene-like Systems

TL;DR

This paper explores how topological properties in graphene-like systems under periodic deformation can induce piezoelectric polarization, extending the analysis to disordered systems and confirming non-trivial effects in a specific strain model.

Contribution

It introduces a topological framework for understanding piezoelectric polarization in deformed graphene-like systems, including disordered cases, using non-commutative geometry and homotopy theory.

Findings

Polarization depends on the homotopy class of parameter loops.

Non-trivial piezo effects require a non-trivial fundamental group of the gapped parameter space.

Uniaxial strain model for graphene supports non-trivial piezo effects.

Abstract

In this article we investigate the possibility of generating piezoelectric orbital polarization in graphene-like systems which are deformed periodically. We start with discrete two-level models which depend on control parameters; in this setting, time-dependent model hamiltonians are described by loops in parameter space. Then, the gap structure at a given Fermi energy generates a non-trivial topology on parameter space which then leads to possibly non-trivial polarizations. More precisely, we show the polarization, as given by the *King-Smith--Vanderbilt formula*, depends only on the homotopy class of the loop; hence, a necessary condition for non-trivial piezo effects is that the fundamental group of the gapped parameter space must not be trivial. The use of the framework of non-commutative geometry implies our results extend to systems with weak disorder. We then apply this analysis to the uniaxial strain model for graphene which includes nearest-neighbor hopping and a stagger potential, and show that it supports non-trivial piezo effects; this is in agreement with recent physics literature.