Interplay between topology and disorder in a two-dimensional semi-Dirac material

TL;DR

This paper explores how disorder influences topological phase transitions in a two-dimensional semi-Dirac material, revealing disorder-induced transitions and enriching the topological phase diagram with potential experimental implications.

Contribution

It demonstrates that disorder can induce topological Lifshitz and Chern transitions in semi-Dirac materials, expanding understanding of disorder effects in topological phases.

Findings

Disorder drives a transition from insulator to semi-metal.

Breaking time-reversal symmetry introduces new topological regimes.

Disorder can induce transitions to the two-node Chern phase.

Abstract

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes-- single-node trivial, two-node trivial and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice, by calculating the real-space Chern number. Additionally we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.