Extended quantum anomalous Hall effect in moir\'e structures: phase transitions and transport

TL;DR

This paper investigates the extended quantum anomalous Hall effect in moiré structures, revealing phase transitions between crystalline, metallic, and fractional states driven by current and temperature, with interpretations based on symmetry breaking and depinning phenomena.

Contribution

It provides a theoretical interpretation of experimental observations of phase transitions and non-linear transport in moiré systems, introducing the concept of a crystalline state breaking moiré translation symmetry.

Findings

Identification of the EIQAH as a crystalline state breaking translation symmetry.

Depinning transition explains non-linear current-voltage behavior.

Large polarizability of FQAH states influences phase stability under electric fields.

Abstract

Recent experiments on multilayer rhombohedral graphene have unearthed a number of interesting phenomena in the regime where Integer and Fractional Quantum Anomalous Hall phenomena were previously reported. Specifically at low temperature ($T$) and low applied currents, an "Extended" Integer Quantum Anomalous Hall (EIQAH) is seen over a wide range of the phase diagram. As the current is increased, at low $T$, the EIQAH undergoes a phase transition to a metallic state at generic fillings, and to the fractional quantum anomalous Hall (FQAH) state at the Jain fillings. Increasing temperature at the Jain fillings also leads to an evolution out of the EIQAH to the Jain state. Here we provide an interpretation of many of these observations. We describe the EIQAH as a crystalline state (either of holes doped into the $\nu = 1$ state, or an Anomalous Hall Crystal of electrons) that breaks moir\'e translation symmetry. At generic fillings, we show how an electric current-induced depinning transition of the crystalline order leads to peculiar non-linear current-voltage curves consistent with the experiment. At Jain fillings, we propose that the depinning transition is pre-empted by an equilibrium transition between EIQAH and Jain FQAH states. This transition occurs due to the large polarizability of the Jain FQAH states which enables them to lower their energy effectively in an applied electric field compared to the crystal states. We also discuss the finite temperature evolution in terms of the relative entropies of the crystalline and FQAH states.