Spatially dispersive dynamical response of hot carriers in doped graphene

TL;DR

This paper theoretically analyzes the wave-vector and frequency dispersion of the dynamic conductivity tensor in doped graphene under strong electric fields, revealing anisotropic responses, resonances, and potential instability regions in terahertz frequencies.

Contribution

It provides a detailed theoretical framework for understanding the dispersive dynamical response of hot carriers in doped graphene, including anisotropy and resonance effects.

Findings

Real part of DCT is non-zero due to dissipation.

Identification of kinematic resonance at a0=a0v_F |k|.

Regions of negative power density indicating possible instabilities.

Abstract

We study theoretically wave-vector and frequency dispersion of the complex dynamic conductivity tensor (DCT), $\sigma_{lm}(\mathbf{k}, \omega)$, of doped monolayer graphene under a strong dc electric field. For a general analysis, we consider the weak ac field of arbitrary configuration given by two independent vectors, the ac field polarization and the wave vector $\mathbf{k}$. The high-field transport and linear response to the ac field are described on the base of the Boltzmann kinetic equation. We show that the real part of DCT, calculated in the collisionless regime, is not zero due to dissipation of the ac wave, whose energy is absorbed by the resonant Dirac quasiparticles effectively interacting with the wave. The role of the kinematic resonance at $\omega = v_F |{\bf k}|$ ($v_{F}$ is the Fermi velocity) is studied in detail taking into account deviation from the linear energy spectrum and screening by the charge carriers. The isopower-density curves and distributions of angle between the ac current density and field vectors are presented as a map which provides clear graphic representation of the DCT anisotropy. Also, the map shows certain ac field configurations corresponding to a negative power density, thereby it indicates regions of terahertz frequency for possible electrical (drift) instability in the graphene system.