Snapshots of non-equilibrium Dirac carrier distributions in graphene

Abstract

The optical properties of graphene are made unique by the linear band structure and the vanishing density of states at the Dirac point. It has been proposed that even in the absence of a bandgap, a relaxation bottleneck at the Dirac point may allow for population inversion and lasing at arbitrarily long wavelengths. Furthermore, efficient carrier multiplication by impact ionization has been discussed in the context of light harvesting applications. However, all of these effects are difficult to test quantitatively by measuring the transient optical properties alone, as these only indirectly reflect the energy- and momentum-dependent carrier distributions. Here, we use time- and angle-resolved photoemission spectroscopy with femtosecond extreme-ultraviolet pulses to directly probe the non-equilibrium response of Dirac electrons near the K-point of the Brillouin zone. In lightly hole-doped epitaxial graphene samples, we explore excitation in the mid- and near-infrared, both below and above the minimum photon energy for direct interband transitions. Whereas excitation in the mid-infrared results only in heating of the equilibrium carrier distribution, interband excitations give rise to population inversion, suggesting that terahertz lasing may be possible. However, in neither excitation regime do we find any indication of carrier multiplication, questioning the applicability of graphene for light harvesting.

Hot-carrier photocurrent effects at graphene–metal interfaces

“…Therefore, the observation of a similar photocurrent dip and similar dynamics at the graphene-metal interface suggest that the same intrinsic nonlinearity due to electron heating and the same hot electron dynamics give rise to the observed timeresolved signal at the graphene-metal interface. Thus for both the pn-junction and the graphene-metal interface the temporal dynamics are in agreement with PTE photocurrent generation, corresponding to femtosecond carrier heating [22,25,29,30], and relaxation corresponding to picosecond supercollision cooling [17,28,[45][46][47].…”

“…So a lower cooling rate (longer lifetime of hot electrons) leads to a larger photocurrent. The electron heating and cooling dynamics in bulk graphene have been studied using pump-probe measurements, such as optical pumpprobe [22,31,33,34], femtosecond time-resolved angleresolved photo-electron spectroscopy (ARPES) [30,32], and time-resolved optical pump-terahertz (THz) probe spectroscopy [26,[35][36][37][38][39][40][41]. The photoexcited carrier dynamics have also been studied in graphene-based devices through time-resolved photocurrent scanning microscopy [7,8,17,29].…”

Extracting the temperature of hot carriers in time- and angle-resolved photoemission

“…In order to arrive at a correct description of the relaxation dynamics of the hot electrons, it is critically important that such a determination is performed quantitatively and with high accuracy. This is evident in recent studies on topological insulators [12,13], superconductors [4,[14][15][16], graphite [17,18] and graphene [6,7], which all discuss various cooling mechanisms involving lattice modes.…”

“…In recent years, this techniques has been successfully carried into the time domain by applying various pump-probe schemes with femtosecond time resolution. Simultaneous acquisition of spectral and dynamic information about the out-of-equilibrium carrier excitation and relaxation processes at selected momenta in the Brillouin zone is thereby made possible, opening unprecedented opportunities for understanding the ultrafast transient changes in the charge ordered states in charge density wave materials [1][2][3], the time-scale for the interaction between electrons and bosonic particles in high-temperature superconductors [4,5] and the dynamics taking place on the Dirac cone in graphene [6,7].…”

Relaxation Dynamics in Graphene

“…Initially, the ultrafast optical pump pulse injects high-energy non-equilibrium electrons in the conduction band and holes in the valence band. The strong intraband and interband carrier-carrier scattering processes lead to ultrafast carrier relaxation and thermalization which establish a single uniform hot-carrier Fermi-Dirac distribution within ∼ 100 − 200 fs after photoexcitation [108]. At that point, carrier generation (through impact ionization) and carrier relaxation (through Auger recombination and intraband carrier-carrier scattering) processes just balance each other, while hot carriers cool via optical and acoustic phonon emission.…”