Topological delocalization of two-dimensional massless Dirac fermions

TL;DR

This paper numerically investigates the beta function of 2D massless Dirac fermions in a random potential, revealing delocalization behavior and providing theoretical insights relevant to materials like graphene.

Contribution

It presents the first numerical computation of the beta function for 2D massless Dirac fermions and demonstrates their topological delocalization.

Findings

Beta function increases monotonically with decreasing coupling constant.

States of the massless Dirac Hamiltonian cannot be localized.

Provides spectral flow argument supporting delocalization.

Abstract

The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which e.g., underlies the theoretical description of graphene, is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing $g$. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of states of the massless Dirac Hamiltonian can be localized.