Cyclotron quantization and mirror-time transition on nonreciprocal lattices

• Published in: arXiv.org
• Main Authors: Shao, Kai, Zhuo-Ting Cai, Geng, Hao, Chen, Wei, Xing, D Y
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 09.08.2022
• Subjects: Boundary conditions; Broken symmetry; Charged particles; Cyclotrons; Energy spectra; Magnetic fields; Measurement; Order parameters; Phase transitions; Physics - Mesoscale and Nanoscale Physics; Physics - Optics; Physics - Quantum Physics; Physics - Strongly Correlated Electrons; Skin effect; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2111.04412

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.