Ultrafast pseudospin dynamics in graphene

M. Trushin, A. Grupp, G. Soavi, A. Budweg, D. De Fazio, U. Sassi, A. Lombardo, A. C. Ferrari, W. Belzig, A. Leitenstorfer, and D. Brida

Phys. Rev. B 92, 165429 – Published 26 October 2015

Abstract

Interband optical transitions in graphene are subject to pseudospin selection rules. Impulsive excitation with linearly polarized light generates an anisotropic photocarrier occupation in momentum space that evolves at time scales shorter than 100 fs. Here, we investigate the evolution of nonequilibrium charges towards an isotropic distribution by means of fluence-dependent ultrafast spectroscopy and develop an analytical model able to quantify the isotropization process. In contrast to conventional semiconductors, the isotropization is governed by optical phonon emission, rather than electron-electron scattering, which nevertheless contributes in shaping the anisotropic photocarrier occupation within the first few femtoseconds.

Received 30 July 2015
Revised 29 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.165429

Authors & Affiliations

M. Trushin¹, A. Grupp¹, G. Soavi^1,2, A. Budweg¹, D. De Fazio², U. Sassi², A. Lombardo², A. C. Ferrari², W. Belzig¹, A. Leitenstorfer¹, and D. Brida^1,*

¹Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany
²Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA, United Kingdom

^*daniele.brida@uni-konstanz.de

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Vol. 92, Iss. 16 — 15 October 2015

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Images

Figure 1
(a) Anisotropic carrier distribution after excitation with linearly polarized light due to pseudospin-momentum coupling. The pseudospin can be seen as an external momentum and is shown by green arrows. The excitation rate is maximal for the pseudospins perpendicular to the electric field. (b) A linearly polarized pump pulse is followed, after time delay $Δ t$ , by a probe pulse with polarization rotated by $45^{\circ}$ . After interaction with graphene, a polarizing beam splitter (BS) separates parallel ( $E_{∥}$ ) and perpendicular ( $E_{⊥}$ ) components of the probe field for simultaneous detection. (c) The pseudospin-field interaction is similar to the influence of an external momentum (shown by arrows) on a gyroscope: The momentum parallel to the gyroscope's axis does not change its orientation, whereas the torque is maximal in the perpendicular configuration.
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Figure 2
Relative transmission change $Δ T / T$ after optical excitation, probed with parallel ( $∥$ ) and orthogonal ( $⊥$ ) polarization. Representative measurements for (a) high and (b) low fluences. Insets: signals normalized to unity.
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Figure 3
Fundamental assumptions of our model. (a) Pump and probe pulses are approximated by rectangular profiles. They share the same spectrum and duration but different polarizations, described by the angles $θ_{1}$ and $θ_{2}$ with $Δ θ = θ_{2} - θ_{1}$ . The time delay between the two pulses is $Δ t$ . The model is valid in the case of nonoverlapping pulses. (b) The photoexcited carriers relax towards the neutrality point by emitting optical phonons with energy $ℏ ω_{0}$ . The electron cooling becomes inefficient at the bottleneck energy near $ℏ ω_{0} / 2$ . e-e scattering does not change the total energy of the electronic subsystem. (c) Two-electron scattering across the Dirac cone shown schematically in cross section at energy $E$ . (d) Optical phonons scatter the electrons into any direction. A lower-lying cross section of the Dirac cone at energy $E - ℏ ω_{0}$ is shown by a thinner circle.
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Figure 4
Ratio of relative transmission changes for parallel and perpendicular probe polarizations for a pump-probe delay of 15 fs, when the pulses are negligibly overlapping in time ( $Δ t > δ t$ ), but the occupation anisotropy is still substantial ( $Δ t < τ$ ) (here τ is the “orientational” relaxation time, see also Fig. 3 for further notations). Experiments (blue triangles) are in good agreement with Eq. (1) (red line). The inset is the experimental ratio at time delays between 5 and 100 fs.
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