Emergence of Non-Hermitian Magic Angles and Topological Phase Transitions in Twisted Bilayer $\alpha$-$T_3$ Lattices

TL;DR

This paper explores how non-Hermitian effects in twisted bilayer $ ext{alpha-}T_3$ lattices lead to new flat-band phenomena, multiple non-Hermitian magic angles, and complex topological phase transitions, revealing the destabilizing role of non-Hermiticity.

Contribution

It introduces the concept of non-Hermitian magic angles and analyzes their impact on topological phases in twisted bilayer $ ext{alpha-}T_3$ systems, a novel extension of moiré physics.

Findings

Identification of three distinct non-Hermitian magic angles with flat bands.

Observation of complex eigenspectrum structures indicating nontrivial topology.

Demonstration that strong non-Hermiticity suppresses topological phases.

Abstract

We investigate the flat-band properties and topological phase transitions in a non-Hermitian twisted bilayer $\alpha-T_3$ lattice. Here, non-Hermiticity is introduced via Hatano-Nelson-type asymmetric hopping, while an aligned hexagonal boron nitride substrate provides a staggered sublattice mass to the system. We find that the introduction of non-reciprocal hopping splits the conventional single magic angle into three distinct non-Hermitian magic angles (NHMAs). Unlike the exceptional magic angles driven by spectral singularities, these NHMAs host perfectly isolated flat bands where the real and imaginary parts of the bandwidth simultaneously vanish. By mapping the complex eigenspectrum across the moir\'e Brillouin zone, we show that the scattered energy eigenvalues coalesce into well-defined, closed loop-like structures as the non-Hermitian parameter strength increases, indicating emergence of a nontrivial point-gap topology and hence the non-Hermitian skin effect. Furthermore, we characterize the topological phases by computing the direct band gap and the biorthogonal Chern number. While the system exhibits a transition to a higher topological phase at weak non-Hermiticity, we demonstrate that stronger non-Hermiticity drives the gap-closing boundaries to merge and their topological charges to mutually annihilate. This convergence results in a trivial gap closing and a complete suppression of the intermediate topological phase, confirming that non-Hermiticity fundamentally plays a crucial role with regard to destabilizing the robust topological features of this moir\'e system.