Exotic Multifractal Conductance Fluctuations in Graphene

TL;DR

This study reveals multifractality in conductance fluctuations of graphene, linked to incipient Anderson localization, and suggests such multifractality may be common in low-dimensional quantum systems.

Contribution

First observation of multifractality in conductance fluctuations of graphene, connecting it to localization phenomena and expanding understanding of quantum transport.

Findings

Multifractality decreases with temperature and doping away from the Dirac point.

Evidence suggests incipient Anderson localization causes multifractality.

Multifractality may be a universal feature in low-dimensional quantum transport.

Abstract

In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic-field-induced universal conductance fluctuations of the conductance in a quantum condensed-matter system, namely, high-mobility single-layer graphene field-effect transistors. This multifractality decreases as the temperature increases or as doping moves the system away from the Dirac point. Our measurements and analysis present evidence for an incipient Anderson-localization near the Dirac point as the most plausible cause for this multifractality. Our experiments suggest that multifractality in the scaling behaviour of local eigenfunctions are reflected in macroscopic transport coefficients. We conjecture that an incipient Anderson-localization transition may be the origin of this multifractality. It is possible that multifractality is ubiquitous in transport properties of low-dimensional systems. Indeed, our work suggests that we should look for multifractality in transport in other low-dimensional quantum condensed-matter systems.