Quantized heat flow in the Hofstadter butterfly

TL;DR

This study demonstrates the quantized heat flow in the Hofstadter butterfly states within a graphene/hBN moiré superlattice, confirming the universal link between topological invariants and heat transport in quantum Hall-like states.

Contribution

First experimental observation of quantized heat flow in Hofstadter butterfly states, including Chern insulators, confirming the topological origin of heat transport quantization.

Findings

Quantized heat flow observed in Hofstadter butterfly states.

Universality of heat transport quantization linked to topology.

Quantization persists across various topological states, including symmetry-broken Chern insulators.

Abstract

When subjected to a strong magnetic field, electrons on a two-dimensional lattice acquire a fractal energy spectrum called Hofstadter's butterfly. In addition to its unique recursive structure, the Hofstadter butterfly is intimately linked to non-trivial topological orders, hosting a cascade of ground states characterized by non-zero topological invariants. These states, called Chern insulators, are usually understood as replicas of the ground states of the quantum Hall effect, with electrical and thermal conductances that should be quantized, reflecting their topological order. The Hofstadter butterfly is now commonly observed in van-der-Waals heterostructures-based moir\'e superlattices. However, its thermal properties, particularly the quantized heat flow expected in the Chern insulators, have not been investigated, potentially questioning their similarity with standard quantum Hall states. Here we probe the heat transport properties of the Hofstadter butterfly, obtained in a graphene~/~hexagonal boron nitride moir\'e superlattice. We observe a quantized heat flow, uniquely set by the topological invariant, for all investigated states of the Hofstadter butterfly: quantum Hall states, Chern insulators, and even symmetry-broken Chern insulators emerging from strong electronic interactions. Our work firmly establishes the universality of the quantization of heat transport and its intimate link with topology.