Cyclotron quantization and mirror-time transition on nonreciprocal lattices

• URL: http://arxiv.org/abs/2111.04412v3
• Date: Tue, 9 Aug 2022 13:36:45 GMT
• Title: Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Authors: Kai Shao, Zhuo-Ting Cai, Hao Geng, Wei Chen, and D. Y. Xing
• Abstract summary: We show that, in the long-wavelength limit, the trajectories of the wave packets always form closed orbits in four-dimensional (4D) complex space. We predict a different type of non-Hermitian spectral transition induced by the spontaneous breaking of the combined mirror-time reversal symmetry.
• Score: 6.648777634896275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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