Planckian properties of two-dimensional semiconductor systems

Abstract

We describe and discuss the low-temperature resistivity (and the temperature-dependent inelastic scattering rate) of several different doped 2D semiconductor systems from the perspective of the Planckian hypothesis asserting that $\hbar/\tau =k_\mathrm{B}T$ provides a scattering bound, where $\tau$ is the appropriate relaxation time. The regime of transport considered here is well-below the Bloch-Gruneisen regime so that phonon scattering is negligible. The temperature-dependent part of the resistivity is almost linear-in-$T$ down to arbitrarily low temperatures, with the linearity arising from an interplay between screening and disorder, connected with carrier scattering from impurity-induced Friedel oscillations. The temperature dependence disappears if the Coulomb interaction between electrons is suppressed. The temperature coefficient of the resistivity is enhanced at lower densities, enabling a detailed study of the Planckian behavior both as a function of the materials system and carrier density. Although the precise Planckian bound never holds, we find somewhat surprisingly that the bound seems to apply approximately with the scattering rate never exceeding $k_\mathrm{B} T$ by more than an order of magnitude either in the experiment or in the theory. In addition, we calculate the temperature-dependent electron-electron inelastic scattering rate by obtaining the temperature-dependent self-energy arising from Coulomb interaction, also finding it to obey the Planckian bound within an order of magnitude at all densities and temperatures. We introduce the concept of a generalized Planckian bound where $\hbar/\tau$ is bounded by $\alpha k_\mathrm{B} T$ with $\alpha\sim 10$ or so in the super-Planckian regime with the strict Planckian bound of $\alpha$=1 being a nongeneric finetuned situation.