Optical conductivity of an anharmonic large polaron gas at weak coupling

Abstract

In a polar solid, electrons or other charge carriers can interact with the phonons of the ionic lattice, leading to the formation of polaron quasiparticles. The optical conductivity and optical absorption spectrum of a material are affected by this electron-phonon coupling, most notably leading to an absorption peak in the midinfrared region. Recently, a model Hamiltonian for anharmonic electron-phonon coupling was derived [M. Houtput and J. Tempere, Phys. Rev. B 103, 184306 (2021)] that includes both the conventional Fr\"ohlich interaction as well as an interaction in which an electron interacts with two phonons simultaneously. In this article, we calculate and investigate the optical conductivity of the anharmonic large polaron gas, and we show that an additional characteristic absorption peak appears due to this one-electron--two-phonon interaction. We calculate a semianalytical expression for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ at finite temperatures and weak coupling using the Kubo formula. The electronic and phononic contributions can be split and treated separately, such that the many-body effects of the electron gas may be taken into account through the well-known dynamical structure factor $S(\mathbf{k},\ensuremath{\omega})$. From the resulting optical conductivity, we calculate the polaron effective mass, an estimate for the electron-phonon scattering times, and the optical absorption spectrum of the anharmonic polaron gas. It is shown that the effects are negligible for four common III-V semiconductors (BN, AlN, BP, AlP) in the zinc-blende structure, which justifies the commonly used harmonic approximation in these materials. We show that alongside the well-known polaron absorption peak at the phonon energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{LO}}$, the one-electron--two-phonon interaction leads to an additional absorption peak at $2\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{LO}}$. We propose this absorption peak as an experimentally measurable indicator for non-negligible one-electron--two-phonon interaction in a material, since the height of this peak is proportional to the strength of this anharmonic interaction.