Planckian properties of 2D semiconductor systems

TL;DR

This paper investigates the low-temperature resistivity and inelastic scattering in doped 2D semiconductors, finding approximate adherence to the Planckian bound and exploring the effects of Coulomb interactions and carrier density.

Contribution

It provides a detailed analysis of Planckian behavior in 2D semiconductors, introducing a generalized bound and examining the role of Coulomb interactions and density.

Findings

Resistivity is nearly linear in temperature at low T due to screening and disorder.

The Planckian bound approximately holds, with scattering rates not exceeding $k_B T$ by more than an order of magnitude.

Electron-electron scattering rates also obey the Planckian bound within an order of magnitude.

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.