Topological phases in N-layer ABC-graphene boron-nitride moire superlattices

TL;DR

This paper explores how moire strain and nematic order influence topological phases in multilayer graphene on boron nitride, explaining experimental observations of valley Chern numbers through theoretical models.

Contribution

It introduces a low-energy model incorporating moire strain effects that explains topological phase transitions and valley Chern number variations in N-layer graphene on hBN.

Findings

Topological phase transitions can be induced by pseudomagnetic vector fields.

Nematic order can explain observed valley Chern numbers.

Strain patterns significantly alter topological properties.

Abstract

Rhombohedral $N = 3$ trilayer graphene on hexagonal boron nitride (TLG/BN) hosts gate-tunable, valley-contrasting, nearly flat topological bands that can trigger spontaneous quantum Hall phases under appropriate conditions of the valley and spin polarization. Recent experiments have shown signatures of C = 2 valley Chern bands at 1/4 hole filling, in contrast to the predicted value of C = 3. We discuss the low-energy model for rhombohedral N-layer graphene (N = 1, 2, 3) aligned with hexagonal boron nitride (hBN) subject to off-diagonal moire vector potential terms that can alter the valley Chern numbers. Our analysis suggests that topological phase transitions of the flat bands can be triggered by pseudomagnetic vector field potentials associated to moire strain patterns, and that a nematic order with broken rotational symmetry can lead to valley Chern numbers that are in agreement with recent Hall conductivity observations.