Magnetic Bloch States at Integer Flux Quanta Induced by Super-moir\'e Potential in Graphene Aligned with Twisted Boron Nitride

TL;DR

This study demonstrates the creation of a super-moiré pattern in graphene aligned with twisted boron nitride, enabling the observation of magnetic Bloch states at integer flux quanta, thus expanding the understanding of Hofstadter butterfly spectra.

Contribution

The paper introduces a super-moiré strategy to realize long-wavelength periodic modulations, allowing observation of magnetic Bloch states at integer flux quanta in graphene-hBN systems.

Findings

Observation of magnetic Bloch states at integer flux quanta (1-9).

Expansion of flux quanta from fractional to integer values.

Theoretical models successfully reproduce experimental results.

Abstract

Two-dimensional electron systems in both magnetic fields and periodic potentials are described by Hofstadter butterfly, a fundamental problem of solid-state physics. While moir\'e systems provide a powerful method to realize this spectrum, previous experiments, however, have been limited to fractional flux quanta regime due to the difficulty of building ~ 50 nm periodic modulations. Here, we demonstrate a super-moir\'e strategy to overcome this challenge. By aligning monolayer graphene (G) with 1.0{\deg} twisted hexagonal boron nitride (t-hBN), a 63.2 nm bichromatic G/t-hBN super-moir\'e is constructed, made possible by exploiting the electrostatic nature of t-hBN potential. Under magnetic field B, magnetic Bloch states at integer flux quanta (1-9) are achieved and observed as integer Brown-Zak oscillations, expanding the flux quanta from factions to integers. Theoretical analysis reproduces these experimental findings. This work opens new avenues to study unexplored Hofstadter butterfly, explore emergent topological order at integer flux quanta and engineer long-wavelength periodic modulations.