Geometrodynamics of electrons in a crystal under position and time dependent deformation

Abstract

Semiclassical dynamics of Bloch electrons in a crystal under slowly varying deformation is developed in the geometric language of a lattice bundle. Berry curvatures and gradients of energy are introduced in terms of lattice covariant derivatives, with the corresponding connections given by the gradient and rate of strain. A number of physical effects are discussed: an effective post-Newtonian gravity at band bottom, polarization induced by spatial gradient of strain, orbital magnetization induced by strain rate, and electron energy stress tensor.

arXiv comment24 pages, 3 figures

References in corpus (17)

• Berry Phase Effects on Electronic Properties
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Anomalous Hall effect in ferromagnetic semiconductors
• Berry phase correction to electron density of states in solids
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Floquet-Bloch theory and topology in periodically driven lattices
• Viscosity of Quantum Hall Fluids
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Time-dependent density functional theory beyond the adiabatic local density approximation
• Energy Magnetization and Thermal Hall Effect
• Torsional Response and Dissipationless Viscosity in Topological Insulators
• Thermal Hall Effect and Geometry with Torsion
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
• Lorentz shear modulus of fractional quantum Hall states
• Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

Cited by in corpus (13)

• Phonon Magnetic Moment from Electronic Topological Magnetization
• Covariant Spin Kinetic Theory I: Collisionless Limit
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy
• Lattice dynamics with molecular Berry curvature: chiral optical phonons
• Gate-tunable phonon magnetic moment in bilayer graphene
• Geometric orbital magnetization in adiabatic processes
• Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
• Intrinsic torque on the orbital angular momentum in an electric field
• Nonreciprocal phonons in PT-symmetric antiferromagnet
• Gauge theory of giant phonon magnetic moment in doped Dirac semimetals
• Emergent curved space and gravitational lensing in quantum materials
• A Chiral Superlattice Route to Spin-Split Topological Antiferromagnetism