Ultrafast Formation of a Fermi-Dirac Distributed Electron Gas

Abstract

Time-and angle-resolved photoelectron spectroscopy with 13 fs temporal resolution is used to follow the different stages in the formation of a Fermi-Dirac distributed electron gas in graphite after absorption of an intense 7 fs laser pulse. Within the first 50 fs after excitation a sequence of time frames is resolved which are characterized by different energy and momentum exchange processes among the involved photonic, electronic, and phononic degrees of freedom. The results reveal experimentally the complexity of the transition from a nascent non-thermal towards a thermal electron distribution due to the different timescales associated with the involved interaction processes. 63.20.kd, 81.05.ue, 81.05.uf The extraordinary nonlinearities and optical response times of graphitic materials suggest useful applications in photonics and electronics including light harvesting [1, 2], ultrafast photodetection [3,4], THz lasing [5,6], and saturable absorption [7,8]. Both characteristics are closely linked to the ultrafast dynamics of photoexcited carriers which for this material class is governed by weakly screened carrier-carrier scattering and carrier-phonon interaction. Fundamental aspects related to these processes were addressed in different time-domain studies in the past [9][10][11][12][13]. Because of limitations in the time resolution, most of these studies were restricted, however, to the characteristic timescales of electron-lattice equilibration, i.e., timescales ranging from ≈100 fs to ≈10 ps. The primary processes directly after photoexcitation are, in contrast, still largely unexplored and were investigated experimentally only in a few studies so far [14][15][16]. The dynamics in this strongly non-thermal regime is determined by phenomena such as transient population inversion, carrier multiplication, Auger recombination, but also phonon-mediated carrier redistribution [17][18][19][20]. The challenge is to decode the relative importance and temporal sequence of these processes that drive the electronic system from a nascent non-thermal distribution as generated by photoexcitation towards a Fermi-Dirac (FD) distribution within only ≈ 50 fs [14,15]. It is obvious that such investigations rely on experiments capable of sampling this time window at an adequate time resolution of the order of 10 fs, as well as high energy and momentum resolution. This letter reports on the non-thermal carrier dynamics in highly-oriented pyrolytic graphite (HOPG) as probed in a time-and angle-resolved photoemission spectroscopy (trARPES) experiment that is operated near the transform limit at a resolution of 13 fs (FWHM of the pumpprobe cross correlation) [21]. Over the first 100 fs, we monitor the different stages in the temporal evolution of an initially non-thermal carrier distribution generated by the absorption of a 7 fs near-infrared pulse. We are able to dissect the non-thermal to thermal transition into FIG. 1. (a) WL-pump/XUV-probe cross correlation signal of the experiment. For details see Refs. [21] and [24]. (b) ...

Time- and momentum-resolved phonon population dynamics with ultrafast electron diffuse scattering

“…corresponds to a mode-projected electron-phonon coupling value of g 2 e,A 1 = 0.035 ± 0.001 eV 2 (see appendix B for details). These values are in agreement with recent trARPES measurements and simulations12,14,15,62 .…”

First‐principles dynamics of photoexcited molecules and materials towards a quantum description

“…Fitting to the exponential decay of hole occupation averaged over 12 beads, the relaxation time obtained from the quantum nuclei approach is 14 fs, significantly shorter than 63 fs computed from classical nuclei simulations. In experiment, the energy level of holes is 0.8 eV below the Fermi level, 10 compared to 3.0 eV below the Fermi level found in the present simulations, and thus the calculated life time is expected to be smaller than that in experiment. Evidently, the quantum electronic‐nuclear simulations can capture and well depict the ultrafast charge carrier redistribution in graphene observed in experiment, while the imprecise description obtained from classical nuclear simulations may be due to improper treatment of electron–electron and electron–phonon scatterings by the rigid ion approximation.…”

“…Ultrafast dynamics of photocarriers in graphene has attracted much attention, 7,98–101 attributed to the high mobility and potential high‐tech applications of Dirac carriers. For example, recent photoelectron spectroscopy measurements suggest a sequence of three stages within 50 fs for the carrier transfer process in graphene: photo‐absorption process (<8 fs), momentum redistribution (~10–22 fs) and hot Fermi‐Dirac distribution 10 . Electron–electron and electron–phonon scatterings are believed to control such photoexcitation dynamics and the subsequent carrier relaxation processes.…”

Observing photo-induced chiral edge states of graphene nanoribbons in pump-probe spectroscopies

“…In previous trARPES studies of graphitic materials, people are mainly interested in the electron relaxation dynamics after the pump creates an electron-hole pair. The relaxation process includes complicate combinations of electron-phonon coupling, as well as Auger heating and impact ionization caused by electron-electron scattering that are still not fully understood [49][50][51][52] . While phonons dominate~250 fs after the pump when hot Fermi-Dirac distributions of electrons and holes establish 53 , both electron-phonon coupling and electron-electron scattering are involved in the relaxation almost immediately after the excitation.…”