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.

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

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological Origin of Non-Hermitian Skin Effects
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Observation of non-Bloch parity-time symmetry and exceptional points
• Guided accumulation of active particles by topological design of a second-order skin effect
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Magnetic suppression of non-Hermitian skin effects

Cited by in corpus (20)

• Topological Non-Hermitian skin effect
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• 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
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Pseudomagnetic suppression of non-Hermitian skin effect
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Complex semiclassical theory for non-Hermitian quantum systems
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Non-Hermitian reshaping of high-order Landau modes
• Controllable suppression of Non-Hermitian skin effects
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Recurrence method in Non-Hermitian Systems
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field