Cyclotron quantization and mirror-time transition on nonreciprocal lattices
Kai Shao, Zhuo-Ting Cai, Hao Geng, Wei Chen, D. Y. Xing
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 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.