Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene

Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Abstract

We numerically investigate critically delocalized wave functions in models of two-dimensional Dirac fermions, subject to vector potential disorder. These describe the surface states of three-dimensional topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A “frozen” regime can occur for strong disorder in these systems, wherein a single wave function presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a “Quantum Hall critical metal.” For the case of two valleys and non-Abelian disorder, we verify predictions of conformal field theory. Our results for the non-Abelian case imply that both delocalization and conformal invariance are topologically protected for multivalley topological superconductor surface states.

Description
Advisor
Degree
Type
Journal article
Keywords
Citation

Chou, Yang-Zhi and Foster, Matthew S.. "Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene." Physical Review B, 89, no. 16 (2014) American Physical Society: https://doi.org/10.1103/PhysRevB.89.165136.

Has part(s)
Forms part of
Rights
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Link to license
Citable link to this page