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

Jaeseok Kim,Seong Chu Lim,Inhee Maeng,Seung Jin Chae,Young Hee Lee,Younghwan Choi,Hyunyong Choi,Soonyoung Cha

doi:10.1038/srep02663

Jaeseok Kim, Seong Chu Lim + Show 6 more

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https://doi.org/10.1038/srep02663

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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.

Highlights

Correspondence and requests for materials should be addressed to Ultrafast zero balance of the oscillator-strength sum rule in graphene
Our ultrafast investigation demonstrated that the ensuring transient sum rule is precisely fulfilled when the graphene system is driven into an out-of-equilibrium state for the time scale of around a few ps
If the transient dynamics enter into the coherent interaction regime, i.e. time scale shorter than the dephasing or thermalization time, the sum rule may break down depending on the Rabi oscillation frequency and lead to intriguing phenomena of coherent population oscillation

Summary

Introduction

Correspondence and requests for materials should be addressed to Ultrafast zero balance of the oscillator-strength sum rule in graphene. The graphene sum-rule relationship in equilibrium state implies that the integrated low-energy absorption oscillators in doped graphene are the same as the depleted interband oscillators below twice the Fermi level jEFj9, i.e., ð 2 jEF j s1(E)dE~s02jEF j: ð1Þ where s1(E) is the real part of optical conductivity and s0 5 q2p/2h is the universal quantum conductivity (q is the electron charge and h is Planck’s constant)[7]. This relationship is equivalent to the transfer rule of Drudespectral weight. The two different transition strengths are supposed to balance each other such that the following simple relation holds[11,12,13]: www.nature.com/scientificreports a

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