Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity

TL;DR

This paper presents experimental observations and a unified theoretical framework for understanding band conductivity oscillations in a gate-tunable graphene superlattice, linking Brown-Zak and Weiss oscillations within the Hofstadter butterfly spectrum.

Contribution

It provides the first comprehensive experimental and theoretical analysis unifying Brown-Zak and Weiss oscillations in a tunable graphene superlattice.

Findings

Observation of band conductivity oscillations governed by Hofstadter butterfly structure.

Identification of the interplay between Brown-Zak and Weiss oscillations.

Complete match between experimental data and theoretical predictions.

Abstract

Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similiar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum oscillations (Brown-Zak oscillations) were discovered in graphene moir\'{e} systems, whose origin lie in the repetitive occurrence of extended minibands/magnetic Bloch states at rational fractions of magnetic flux per unit cell giving rise to an increase in band conductivity. In this work, we report on the experimental observation of band conductivity oscillations in an electrostatically defined and gate-tunable graphene superlattice, which are governed both by the internal structure of the Hofstadter butterfly (Brown-Zak oscillations) and by a commensurability relation between the cyclotron radius of electrons and the superlattice period (Weiss oscillations). We obtain a complete, unified description of band conductivity oscillations in two-dimensional superlattices, yielding a detailed match between theory and experiment.