Spatially dispersive dynamical response of hot carriers in doped graphene

• Dynamic conductivity tensor (DCT) of doped graphene in a strong dc field is calculated.
• Frequency and wave-vector dispersion of DCT are analyzed in detail.
• Electrical instabilities associated with electron drift are found for THz frequencies.
• Energy spectrum nonlinearity is important for DCT dispersion near kinematic resonance.
• Screening by charge carriers leads to considerable modification of DCT dispersion.

We study theoretically wave-vector and frequency dispersion of the complex dynamic conductivity tensor (DCT), σlm(k,ω)σlm(k,ω), 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 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 ω=vF|k|ω=vF|k| (vF 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.