Ultrafast zero balance of the oscillator-strength sum rule in graphene

TL;DR

This study demonstrates that in graphene, the oscillator-strength sum rule remains valid in a nonequilibrium state, with ultrafast measurements showing a precise balance between low- and high-energy oscillators after photo-excitation.

Contribution

The paper provides the first experimental verification of the oscillator-strength sum rule in a nonequilibrium regime using ultrafast spectroscopy in graphene.

Findings

Ultrafast depletion of high-energy oscillators observed after photo-excitation.

Complementary increase in terahertz absorption oscillators.

Sum rule holds true in nonequilibrium conditions in graphene.

Abstract

Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in a nonequilibrium regime has been a long-standing unexplored question. The simple band structure of graphene is an ideal system for investigating this question due to the linear Dirac-like energy dispersion. Here, we employed both ultrafast terahertz and optical spectroscopy to directly monitor the transient oscillator-strength balancing between quasi-free low-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitation of hot Dirac fermions, we observed that the ultrafast depletion of high-energy oscillators precisely complements the increased terahertz absorption oscillators. Our results may provide an experimental priori to understand, for example, the intrinsic free-carrier dynamics to the high-energy photo-excitation, responsible for optoelectronic operation such as graphene-based phototransistor or solar-energy harvesting devices.