Strong-coupling topological states and phase transitions in helical trilayer graphene

TL;DR

This paper explores the rich array of topological and correlated phases in magic-angle helical trilayer graphene, revealing how external fields induce various symmetry-breaking and topological phase transitions with potential for novel quantum states.

Contribution

It provides a comprehensive analysis of the phase diagram of helical trilayer graphene, identifying new topological and symmetry-broken phases driven by strong interactions and external displacement fields.

Findings

Multiple symmetry-broken ferromagnetic phases with high Chern numbers

Topological phase transitions induced by displacement fields

Existence of translation symmetry-broken Kekulé spiral order

Abstract

Magic-angle helical trilayer graphene relaxes into commensurate moir\'e domains, whose topological and well-isolated set of narrow bands possess ideal characteristics for realizing robust correlated topological phases, compared with other graphene-based moir\'e heterostructures. Combining strong-coupling analysis and Hartree-Fock calculations, we investigate the ground states at integer fillings $\nu$, and uncover a rich phase diagram of correlated insulators tuned by an external displacement field $D$. For small $D$, the system realizes several competing families of symmetry-broken generalized flavor ferromagnets, which exhibit various anomalous Hall signatures and Chern numbers as high as $|C|=6$. The interaction-induced dispersion renormalization is weak, so that the band flatness and the validity of strong-coupling theory are maintained at all integer fillings. For experimentally accessible displacement fields, the strong-coupling insulators at all $\nu$ undergo topological phase transitions, which appear continuous or weakly first-order. For larger $D$, we also find translation symmetry-broken phases such as Kekul\'e spiral order. Our results demonstrate the robust capability of helical trilayer graphene to host gate-tunable topological and symmetry-broken correlated phases, and lay the groundwork for future theoretical studies on other aspects such as fractional topological states.