Abstract
We theoretically examine the effect of carrier-carrier scattering processes on the intraband radiation absorption and their contribution to the net dynamic conductivity in optically or electrically pumped graphene. We demonstrate that the radiation absorption assisted by the carrier-carrier scattering is comparable with Drude absorption due to impurity scattering and is even stronger in sufficiently clean samples. Since the intraband absorption of radiation effectively competes with its interband amplification, this can substantially affect the conditions of the negative dynamic conductivity in the pumped graphene and, hence, the interband terahertz and infrared lasing. We find the threshold values of the frequency and quasi-Fermi energy of nonequilibrium carriers corresponding to the onset of negative dynamic conductivity. The obtained results show that the effect of carrier-carrier scattering shifts the threshold frequency of the radiation amplification in pumped graphene to higher values. In particular, the negative dynamic conductivity is attainable at the frequencies above 6 THz in graphene on SiO2 substrates at room temperature. The threshold frequency can be decreased to markedly lower values in graphene structures with high-κ substrates due to screening of the carrier-carrier scattering, particularly at lower temperatures.
Highlights
Graphene, a two-dimensional carbon crystal, possesses no energy band gap and, is promising for detection and generation of far-infrared and terahertz (THz) radiation [1, 2, 3]
We find that in the pumped graphene, the main contribution to the intraband conductivity arises from electron-hole (e-h) scattering, while the electron-electron (e-e) and hole-hole (h-h) collisions yield less than one tenth of its total value
We have shown that in graphene there exists a strong mechanism of the intraband Drude-like radiation absorption, assisted by the carrier-carrier collisions
Summary
A two-dimensional carbon crystal, possesses no energy band gap and, is promising for detection and generation of far-infrared and terahertz (THz) radiation [1, 2, 3]. To treat the radiation absorption in pumped graphene, we introduce the different quasi-Fermi energies of electrons and holes, μe and μh. If otherwise not stated, we will consider symmetrically pumped graphene In such system, the occupation numbers of electrons and holes with energies εp > 0 are equal, the subscripts e and h of the distribution functions can be omitted. To obtain the real part of the intraband dynamic conductivity due to e-e collisions Reσee, we express the vector-potential in Eq (6) through electric field and equate (7) with ReσeeE02/2 As a result, this conductivity is expressed via the universal optical conductivity of clean graphene σq, the coupling constant αc = e2/(κ0hvF ), and the dimensionless ’collision integral’ Iee,ω : Reσee σq αc π3.
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