Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems

Abstract

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed to characterize the topology of these systems. While the topological classification of non-Hermitian systems is being developed, little attention has been paid to the impact of the new geometric phases on dynamics and transport. In this work, we derive the full set of semiclassical equations of motion for wave-packet dynamics in a system governed by a non-Hermitian Hamiltonian, including corrections induced by the Berry connection. We show that non-Hermiticity is manifested in anomalous weight rate and velocity terms that are present already in one-dimensional systems, in marked distinction from the Hermitian case. We express the anomalous weight and velocity in terms of the Berry connections defined in the space of left and right eigenstates and compare the analytical results with numerical lattice simulations. Our work specifies the conditions for observing the anomalous contributions to the semiclassical dynamics and thereby paves the way to their experimental detection, which should be within immediate reach in currently available metamaterials.

arXiv comment24 pages, 5 figures; v3: accepted manuscript

References in corpus (71)

• Topological Insulators
• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Colloquium: Topological Band Theory
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Anomalous Hall effect in ferromagnetic semiconductors
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• The Quantum-Mechanical Position Operator in Extended Systems
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Biorthogonal Quantum Mechanics
• Non-reciprocal robotic metamaterials
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• New topological invariants in non-Hermitian systems
• Berry phase, hyperorbits, and the Hofstadter spectrum
• Topological states of non-Hermitian systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• General description of quasi-adiabatic dynamical phenomena near exceptional points
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Tenfold Way for Quadratic Lindbladians
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Non-Bloch band collapse and chiral Zener tunneling
• Topological Insulators from Group Cohomology
• Coherent wave-packet evolution in coupled bands
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Adiabaticity condition for non-Hermitian Hamiltonians
• Nonreciprocal response theory of nonhermitian mechanical metamaterials: response phase transition from the skin effect of zero modes
• Non-Hermitian fractional quantum Hall states
• Semi-classical wave packet dynamics in non-uniform electric fields
• Noncommutative geometry and nonabelian Berry phase in the wave-packet dynamics of Bloch electrons
• A Classification of Non-Hermitian Random Matrices
• Random matrices beyond the Cartan classification
• Topological Phase Transition Independent of System Non-Hermiticity
• Wave packet evolution in non-Hermitian quantum systems
• High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase
• Topological Field Theory far from Equilibrium
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Topology by Dissipation: Transport properties
• Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Non-Hermitian Chiral Magnetic Effect in Equilibrium
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models

Cited by in corpus (29)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Topological Phases: Principles and Prospects
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Current-voltage characteristics of the N-I-PT-symmetric non-Hermitian superconductor junction as a probe of non-Hermitian formalisms
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Non-orthogonal cavity modes near exceptional points in the far field
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Complex semiclassical theory for non-Hermitian quantum systems
• Non-Hermitian band topology from momentum-dependent relaxation in two-dimensional metals with spiral magnetism
• Geometric contribution to adiabatic amplification in non-Hermitian systems
• Higher-order gap ratios of singular values in open quantum systems
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Quantum geometrical effects in non-Hermitian systems
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Exceptionally deficient topological square-root insulators
• Non-Hermitian magnetic moment
• Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Covariant formulation of the Berry connection in non-Hermitian systems