[Paper Review] Observing light-induced Floquet band gaps in the longitudinal conductivity of graphene

Lukas Broers, Ludwig Mathey|arXiv (Cornell University)|Mar 2, 2021

Graphene research and applications30 references36 citations

TL;DR

This paper proposes using the optical longitudinal conductivity of graphene under circularly polarized light as a direct probe to observe light-induced Floquet band gaps. By modeling electron dynamics via a dissipative master equation, the authors show that these gaps appear as resonant features in conductivity, with population inversion at strong driving leading to negative conductivity—offering both unambiguous detection of Floquet-Bloch bands and dynamic control of transport via light.

ABSTRACT

We propose optical longitudinal conductivity as a realistic observable to detect light-induced Floquet band gaps in graphene. These gaps manifest as resonant features in the conductivity, when resolved with respect to the probing frequency and the driving field strength. We demonstrate these features via a dissipative master equation approach which gives access to a frequency- and momentum-resolved electron distribution. This distribution follows the light-induced Floquet-Bloch bands, resulting in a natural interpretation as occupations of these bands. Furthermore, we show that there are population inversions of the Floquet-Bloch bands at the band gaps for sufficiently strong driving field strengths. This strongly reduces the conductivity at the corresponding frequencies. Therefore our proposal puts forth not only an unambiguous demonstration of light-induced Floquet-Bloch bands, which advances the field of Floquet engineering in solids, but also points out the control of transport properties via light, that derives from the electron distribution on these bands.

Motivation & Objective

• To provide a realistic, experimentally accessible observable to unambiguously detect light-induced Floquet band gaps in solids.
• To address the challenge of detecting Floquet-Bloch bands in solids, where smoking-gun transport signatures are still lacking.
• To demonstrate that light can dynamically control electronic transport by manipulating the population of Floquet-Bloch bands.
• To identify a regime where the Dirac point band gap in graphene can be clearly resolved despite competing features.
• To link measurable optical conductivity to the effective occupation of Floquet-Bloch bands via a non-equilibrium master equation approach.

Proposed method

• Model the non-equilibrium dynamics of graphene under circularly polarized light using a dissipative master equation in momentum space.
• Use a four-level Hilbert space per momentum k to describe electron distributions and compute two-time correlation functions.
• Include Lindblad operators for dephasing (γz = 1 THz), decay (γ− = 2.25 THz), and substrate coupling (γbg = 2.5 THz) to model realistic dissipation.
• Compute the momentum- and energy-resolved electron distribution n(k, ω) via time-averaged correlation functions of creation and annihilation operators.
• Calculate the optical longitudinal conductivity as a function of probing frequency and driving field strength to identify resonant features.
• Relate conductivity features to transitions within and between Floquet zones, and to the effective occupation of Floquet-Bloch bands.

Experimental results

Research questions

• RQ1 Can the optical longitudinal conductivity serve as a direct and unambiguous probe for light-induced Floquet band gaps in graphene?
• RQ2 How do the relative occupations of Floquet-Bloch bands influence the optical conductivity, and can population inversion occur?
• RQ3 At what driving field strengths and probing frequencies do negative conductivity values emerge, and what is their physical origin?
• RQ4 Can the Dirac point band gap be resolved in the presence of competing resonant features from higher-order photon processes?
• RQ5 How does the comoving band velocity relate to the observed conductivity features and band gap locations?

Key findings

• The optical longitudinal conductivity displays clear resonant features at frequencies corresponding to light-induced Floquet band gaps, especially when resolved as a function of driving field strength.
• A regime exists—specifically for driving field strengths Ed ≥ 28 MV/m and probing frequencies ωL ≈ 14 THz—where the Dirac point band gap ∆0 becomes unambiguously visible.
• All band gaps except ∆0 first increase with driving strength, reach a maximum, and then decrease, with the decreasing phase showing negative optical conductivity.
• Negative conductivity arises due to population inversion of Floquet-Bloch bands, which occurs at strong driving fields and corresponds to the decreasing regime of the band gaps.
• The comoving band velocity ∂Πϵ(k) shows strong qualitative agreement with the observed conductivity features and band gap locations, supporting the interpretation in terms of effective band occupations.
• The model predicts that for high-mobility graphene (e.g., hBN-encapsulated), the gap features can be resolved at experimentally accessible parameters, with the proposed setup compatible with existing ultrafast imaging and transport measurements.