Cyclotron quantization and mirror-time transition on nonreciprocal lattices

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 ($\mathcal{M}\mathcal{T}$) symmetry, which generally exists in such systems. An order parameter is proposed to describe the $\mathcal{M}\mathcal{T}$ phase transition, not only to determine the $\mathcal{M}\mathcal{T}$ phase boundary but also to quantify the degree of $\mathcal{M}\mathcal{T}$-symmetry breaking. Such an order parameter can be generally applied to all types of non-Hermitian phase transitions.

arXiv comment18 pages, including supplemental material, major revision, the version to be published in PRB Letter

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• Manipulating non-reciprocity in a two-dimensional magnetic quantum walk
• Continuum of Bound States in a Non-Hermitian Model
• Manipulating non-Hermitian skin effect via electric fields
• A Non-Hermitian Moiré Valley Filter
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• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field