Electronic transport calculations showing electron-phonon separation in directions transverse to high current

Abstract

An electron-phonon Boltzmann transport equation is formulated which accounts for second order collisions with an electron-phonon vertex and a three-phonon vertex. This approach for electronic transport at second order reveals the existence of two forces perpendicular to the primary direction of electrical current, acting on the electrons and phonons. The force on electrons is equal and opposite to that on the phonons. Solutions for stationary states confirm that charge and thermal energy become separated. The force terms include both conservative and dissipative components, which for the phonons, lead to a modified Guyer-Krumhansl equation. The conservative components exist only when there exist explicit transverse gradients in the dissipated energy, and these terms may be incorporated into a Poisson kinematics. The dissipative force terms can cause threshold induced spontaneous symmetry breaking.