Cyclotron quantization and mirror-time transition on nonreciprocal lattices

TL;DR

This paper explores the complex interplay between unidirectional transport and cyclotron motion in nonreciprocal lattices under magnetic fields, revealing persistent Landau levels and a novel non-Hermitian spectral transition driven by mirror-time symmetry breaking.

Contribution

It introduces the concept of wave packet trajectories forming closed orbits in 4D complex space and proposes an order parameter for the mirror-time ($ ext{MT}$) symmetry-breaking phase transition in non-Hermitian systems.

Findings

Landau levels remain real despite nonreciprocity.

Wave packet trajectories form closed orbits in 4D complex space.

Identifies a new non-Hermitian spectral transition driven by $ ext{MT}$ symmetry breaking.

Abstract

Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength limit, the trajectories of the wave packets always form closed orbits in four-dimensional (4D) complex space. Therefore, the semiclassical quantization rules persist despite the nonreciprocity, which preserves real Landau levels. We predict a different type of non-Hermitian spectral transition induced by the spontaneous breaking of the combined mirror-time reversal ($\mathcal{MT}$) symmetry, which generally exists in such systems. An order parameter is proposed to describe the $\mathcal{MT}$ phase transition, not only to determine the $\mathcal{MT}$ phase boundary but also to quantify the degree of $\mathcal{MT}$-symmetry breaking. Such an order parameter can be generally applied to all types of non-Hermitian phase transitions.