Quantum theory of mechanical deformations

Abstract

We construct a general metric-tensor framework for treating inhomogenous adiabatic deformations applied to crystalline insulators, by deriving an effective time-dependent Schrödinger equation in the undistorted frame. The response can be decomposed into "static" and "dynamic" terms that correspond, respectively, to the amplitude and the velocity of the distortion. We then focus on the dynamic contributon, which takes the form of a gauge field entering the effective Hamiltonian, in the linear-response limit. We uncover an intimate relation between the dynamic response to the rotational component of the inhomogeneous deformation and the diamagnetic response to a corresponding inhomogeneous magnetic field. We apply this formalism to the theory of flexoelectric response, where we resolve a previous puzzle by showing that the currents generated by the dynamic term, while real, generate no bound charges even at surfaces, and so may be dropped from a practical theory of flexoelectricity.

arXiv comment21 pages, 2 figures

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Cited by in corpus (9)

• Phonon Magnetic Moment from Electronic Topological Magnetization
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Geometric orbital magnetization in adiabatic processes
• Nonadiabatic Born effective charges in metals and the Drude weight
• Metric-wave approach to flexoelectricity within density-functional perturbation theory
• Lattice-mediated bulk flexoelectricity from first principles
• Rotational $g$ factors and Lorentz forces of molecules and solids from density-functional perturbation theory
• Beyond Gaussian fluctuations of quantum anharmonic nuclei
• Rototranslational sum rules for nuclear dynamics via traveling pseudopotentials