Coulomb drag in anisotropic systems: a theoretical study on a double-layer phosphorene

TL;DR

This theoretical study explores how the anisotropic band structure of double-layer phosphorene affects Coulomb drag resistivity, revealing control via layer rotation and sensitivity to various physical parameters.

Contribution

We develop a formalism to analyze Coulomb drag in anisotropic double-layer systems, specifically applying it to phosphorene, and demonstrate control of resistivity through layer orientation and other parameters.

Findings

Rotation of layers influences drag resistivity significantly.

Anisotropic drag resistivity is highly sensitive to momentum transfer direction.

Including local field corrections alters the results notably.

Abstract

We theoretically study the Coulomb drag resistivity in a double-layer electron system with highly anisotropic parabolic band structure using Boltzmann transport theory. As an example, we consider a double-layer phosphorene on which we apply our formalism. This approach, in principle, can be tuned for other double-layered systems with paraboloidal band structures. Our calculations show the rotation of one layer with respect to another layer can be considered a way of controlling the drag resistivity in such systems. As a result of rotation, the off-diagonal elements of drag resistivity tensor have non-zero values at any temperature. In addition, we show that the anisotropic drag resistivity is very sensitive to the direction of momentum transfer between two layers due to highly anisotropic inter-layer electron-electron interaction and also the plasmon modes. In particular, the drag anisotropy ratio, \r{ho}yy/\r{ho}xx, can reach up to ~ 3 by changing the temperature. Furthermore,our calculations suggest that including the local field correction in dielectric function changes the results significantly. Finally, We examine the dependence of drag resistivity and its anisotropy ratio on various parameters like inter-layer separation, electron density, short-range interaction and insulating substrate/spacer.