High-order fractal states in graphene superlattices

TL;DR

This paper reports the experimental observation of high-order fractal magnetic states in graphene superlattices at elevated temperatures, revealing complex fractal patterns linked to Hofstadter butterflies and supported by band structure calculations.

Contribution

It presents the first experimental detection of second, third, and fourth order magnetic Bloch states in graphene superlattices at high temperatures.

Findings

Observation of high-order magnetic Bloch states above 100 K

Identification of fractal patterns related to Hofstadter butterflies

Agreement between experimental results and band structure calculations

Abstract

Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here we report magnetotransport measurements that reveal second, third and fourth order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band structure calculations.