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

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, ρ yy /ρ 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.

Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit

“…The corresponding dispersion is anisotropic, being suppressed in the y-direction as a consequence of the anisotropy of the BP electronic structure. Similar results have been previously obtained in the long-wavelength limit for 1L- [14,29,30] and 2L-BP [29,31] using low-energy continuum and TB Hamiltonians.…”

“…Other aspects of electron screening in 2D BP related to strain engineering of plasmons and to the Coulomb drag have been respectively addressed in Refs. 30 Up to now, screening in BP has been studied on the basis of the random phase approximation (RPA) for the dielectric function [14,[29][30][31]. Moreover, simple form of the Coulomb interaction in reciprocal space (V ∼ 1/q) was always assumed, which corresponds to the long-wavelength limit (q → 0).…”

Effects of the Short-Range Exchange Interaction on Plasmon Modes of Monolayer Black Phosphorous

“…The temperaturedependent dynamic polarization function for a 2D material with anisotropic parabolic energy dispersion is given by [21]:…”

“…The dispersion relation of plasmons can be obtained by looking for the zeros of the dynamical dielectric function of the system. Recently, the many-body aspects of phosphorene have been also addressed through the study of highly anisotropic collective excitation modes in the doped monolayer and Coulomb coupled few-layer black phosphorus [18][19][20][21][22]. In these nanosheets, the direction-dependent plasmon resonances are located in the mid-infrared region of the electromagnetic spectrum which make phosphorene a good potential candidate for the molecular sensing and nano-optics.…”

Anisotropic charge density wave in electron-hole double monolayers: Applied to phosphorene

“…a monolayer of black phosphorus(BP), has been investigated theoretically and experimentally, which has attracted a lot of interest due to its highly anisotropic electronic and optical properties. [2][3][4][5][6][7] Phosphorene has a puckered honeycomb structure with each phosphorus atom covalently bonded with three adjacent atoms. Unlike graphene, phosphorene is not perfectly flat and forms a puckered surface due to the sp 3 hybridization of the 3s and 3p atomic orbitals.…”