Snapshots of non-equilibrium Dirac carrier distributions in graphene (1304.1389v1)

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 semiconducting 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 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 ultra-violet (EUV) pulses at 31.5 eV photon energy 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. While 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 indication for carrier multiplication, questioning the applicability of graphene for light harvesting. Time-resolved photoemission spectroscopy in the EUV emerges as the technique of choice to assess the suitability of new materials for optoelectronics, providing quantitatively accurate measurements of non-equilibrium carriers at all energies and wavevectors.

• The paper demonstrates that TR-ARPES mapping of non-equilibrium Dirac carrier distributions in graphene enables direct observation of transient population inversion using femtosecond EUV pulses.
• The study shows that excitation above 950 meV produces a ~130 fs transient inversion, suggesting graphene’s potential for terahertz lasing applications.
• The paper finds no evidence for carrier multiplication, challenging the use of graphene for efficient photovoltaic devices and prompting a reevaluation of theoretical models.

Analysis of Non-Equilibrium Dirac Carrier Dynamics in Graphene

The paper titled "Snapshots of non-equilibrium Dirac carrier distributions in graphene" investigates the optoelectronic properties of graphene through time- and angle-resolved photoemission spectroscopy (TR-ARPES). This technique allows for the probing of the non-equilibrium response of Dirac electrons in the graphene's band structure, specifically at the Brillouin zone's $\overline{\text{K}}$-point, by employing femtosecond extreme ultra-violet (EUV) pulses. The research hinges on the optical capabilities of graphene, which derive from its linear band structure and the vanishing density of states at the Dirac point, facilitating novel mechanisms like population inversion and terahertz lasing.

The investigation predominantly explores two excitation regimes: below and above the minimal photon energy required for direct interband transitions in lightly hole-doped epitaxial graphene. Below this threshold, where the excitation energy was 300 meV, only heating of the equilibrium carrier distribution was observed. Conversely, excitation above this threshold at 950 meV led to population inversion -- a critical condition for lasing -- albeit for a brief temporal duration, suggesting possibilities for terahertz lasing under specific conditions. However, the paper reveals no evidence for carrier multiplication, challenging the viability of graphene for efficient light-harvesting applications in photovoltaic devices.

Key Findings

1. Time-Resolved Spectroscopy and Dynamics:

By employing the TR-ARPES technique, the paper maps the electronic state occupations across various energies and time delays. The use of femtosecond EUV pulses enabled probing the dynamics close to the Dirac point, providing accuracy and insights beyond previous time-resolved optical experiments.

1. Population Inversion:

Near-infrared excitation at photon energies above 950 meV initiates a transient population inversion, as indicated by the distribution of carriers across separate Fermi-Dirac (FD) distributions for electrons and holes. This phenomenon persists for approximately 130 fs before convergence into a single distribution, thus setting a fundamental temporal constraint on achieving optical gain.

1. Carrier Multiplication:

Despite theoretical propositions, no experimental evidence supports intrinsic carrier multiplication in these graphene systems within the tested excitation regimes. The paper finds that required conditions for carrier multiplication, such as exceptionally high electronic temperatures, were not achieved.

Implications for Optoelectronics

The findings of this research hold significant implications for the application of graphene in optoelectronics, where understanding its electronic and optical behavior at ultrafast timescales is crucial. The observation of population inversion supports the conceptualization of graphene as a material amenable to lasing applications. However, the absence of carrier multiplication suggests limitations in its efficacy for photovoltaic applications, where carrier multiplication could enhance the conversion efficiency.

Future Directions

Future research should focus on optimizing conditions for enhanced electronic interactions and visibility of phenomena such as carrier multiplication. This could involve tuning graphene's doping levels, excitation fluences, and probing conditions to explore a broader spectrum of its optoelectronic properties. There is also potential in integrating real-time investigations of dynamics with spatial resolutions, such as through Photoemission Electron Microscopy (PEEM), to provide insights into nanoscale carrier dynamics in device-like environments.

In conclusion, the paper makes essential contributions to understanding graphene’s ultrafast carrier dynamics, serving as a foundation upon which future advancements in graphene-based optoelectronic devices can be constructed. The use of TR-ARPES provides critical, direct observations that will undoubtedly inform both theoretical and practical advancements in the field.