Electron conduction in solid state via time varying wavevectors

TL;DR

This paper develops a rigorous semiclassical framework for electron wavepacket dynamics in electric and magnetic fields, incorporating time-varying wavevectors and periodic potentials, revealing new insights into electron conduction.

Contribution

It introduces a novel derivation of semiclassical equations using time-varying wavevectors for electrons in fields and periodic potentials, extending classical models.

Findings

Wavepacket reproduces classical cyclotron orbits in magnetic fields.

Electron wavefunction follows adiabatic evolution of Bloch wavevector under electric fields.

Derived effective mass equations for conduction analysis.

Abstract

In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors $k(t)$. In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schr\"oedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics differ from classical Lorentz force equations. We show that in a periodic potential, on application of electric field, the electron wave function adiabatically follows the wavefunction of a time varying Bloch wavevector $k(t)$, with its energies suitably shifted with time. We derive the effective mass equation and discuss conduction in conductors and insulators.