Non-Hermitian band topology in twisted bilayer graphene aligned with hexagonal boron nitride

TL;DR

This paper explores the non-Hermitian topological properties of twisted bilayer graphene with hBN and non-reciprocal hopping, revealing new phases and robustness of Dirac points influenced by non-Hermiticity and twist angles.

Contribution

It introduces a theoretical framework for NH topological phases in tBLG with hBN and non-reciprocal effects, highlighting the impact on band topology and gap formation.

Findings

NH effects can induce a valley Hall insulator phase.

Enhancing non-Hermiticity expands the gapless Dirac point range.

Topological phase transitions correlate with band gap closings.

Abstract

Utilizing the established Bistritzer-MacDonald model for twisted bilayer graphene (tBLG), we theoretically investigate the non-Hermitian (NH) topological properties of this in the presence of non-reciprocal (NR) hopping on both layers and hexagonal boron nitride (hBN) induced mass term incorporated only on the top layer of the tBLG system. It is well known that the hBN mass term breaks the \(C_{2}\) symmetry of tBLG and gaps out the Dirac cones inducing a valley Hall insulating phase. However, when NR hopping is introduced, this system transits into a NH valley Hall insulator (NH-VHI). Our analysis reveals that, in the chiral limit, the bandwidth of the system vanishes under NH effects for a wide range of twist angles. Such range can be visibly expanded as we enhance the degree of non-Hermiticity (\(\beta\)). At the magic angle, we observe that enhancement of \(\beta\) inflates the robustness of the gapless Dirac points, requiring a progressively larger mass term to induce a gap in the NH tBLG system. Additionally, for a fixed NH parameter, we identify a range of twist angles where gap formation is significantly obstructed. To explore the topological aspects of the NH tBLG, we analyze the direct band gap in the Moir\'e Brillouin zone (mBZ) and compute the Chern number for the NH system. We find that the corresponding topological phase transitions are associated with corresponding direct band gap closings in the mBZ.