Microscopic Description of Intraband Absorption in Graphene: The Occurrence of Transient Negative Differential Transmission

We present a microscopic explanation of the controversially discussed transient negative differential transmission observed in degenerate optical pump-probe measurements in graphene. Our approach is based on the density matrix formalism allowing a time- and momentum-resolved study of carrier-light, carrier-carrier, and carrier-phonon interaction on microscopic footing. We show that phonon-assisted optical intraband transitions give rise to transient absorption in the optically excited hot carrier system counteracting pure absorption bleaching of interband transitions. While interband transition bleaching is relevant in the first hundreds of fs after the excitation, intraband absorption sets in at later times. In particular, in the low excitation regime, these intraband absorption processes prevail over the absorption bleaching resulting in a zero crossing of the differential transmission. Our findings are in good qualitative agreement with recent experimental pump-probe studies.

Figure 1

Illustration of the phonon-assisted intraband absorption within the linear band structure of graphene. Applying a pulse with the energy $\hslash {\omega }_L$ lifts electrons within the (conduction) band into an energetically higher electronic state. To conserve energy and momentum, this intraband absorption is assisted by an interaction with a phonon characterized by the energy $\hslash {\omega }_{\mathbf{q}}$ and the momentum $\mathbf{q}$.

Figure 2

Transient differential transmission spectrum as a function of the delay time $\tau$ between the pump and the probe pulse illustrating the impact of phonon-assisted intraband processes, which account for a zero crossing.

Figure 3

(a) Transient differential transmission spectrum for different pump fluences including the phonon-assisted intraband absorption processes. (b) Experimentally measured transient differential transmission at the same conditions (excitation energy of 1.5 eV and a pulse width of 50 fs). (c) Fluence-dependent ratio ${{\mathrm{I}}^{-}}_{\max }/{{\mathrm{I}}^{+}}_{\max }$ denoting the maximal negative and positive transient DT signal, respectively. The strongest relative impact of phonon-assisted intraband processes is predicted at small fluences—in good agreement with the experiment.