[Paper Review] Observation of Floquet states in graphene

Marco Merboldt, Michael Schüler+12 more|arXiv (Cornell University)|Apr 19, 2024

Graphene research and applications4 citations

TL;DR

This study provides direct experimental evidence of Floquet states in monolayer graphene using time-resolved momentum microscopy with extreme ultraviolet probe pulses. By applying linearly polarized infrared light to coherently dress the electronic bands, the researchers observe Floquet sidebands and their quantum path interference with Volkov states in the photoemission spectrum, confirming the existence of light-dressed Dirac bands and validating Floquet engineering in graphene despite ultrafast decoherence.

ABSTRACT

Recent advances in the field of condensed-matter physics have unlocked the potential to realize and control emergent material phases that do not exist in thermal equilibrium. One of the most promising concepts in this regard is Floquet engineering, the coherent dressing of matter via time-periodic perturbations. However, the broad applicability of Floquet engineering to quantum materials is still unclear. For the paradigmatic case of monolayer graphene, the theoretically predicted Floquet-induced effects, despite a seminal report of the light-induced anomalous Hall effect, have been put into question. Here, we overcome this problem by using electronic structure measurements to provide direct experimental evidence of Floquet engineering in graphene. We report light-matter-dressed Dirac bands by measuring the contribution of Floquet sidebands, Volkov sidebands, and their quantum path interference to graphene's photoemission spectral function. Our results finally demonstrate that Floquet engineering in graphene is possible, paving the way for the experimental realization of the many theoretical proposals on Floquet-engineered band structures and topological phases.

Motivation & Objective

• To provide unambiguous experimental evidence of Floquet engineering in monolayer graphene, overcoming skepticism due to ultrafast decoherence.
• To resolve the controversy surrounding prior reports of light-induced anomalous Hall effects by directly probing the band structure under irradiation.
• To demonstrate the feasibility of realizing topological Floquet phases in graphene using coherent light dressing.
• To identify and characterize Floquet sidebands and their interference with Volkov states in the photoemission spectrum.
• To validate theoretical predictions of light-induced band gaps and topological phase transitions in graphene under periodic driving.

Proposed method

• Employed time-resolved momentum microscopy using extreme ultraviolet (EUV) laser pulses generated via high-harmonic generation to probe the energy-momentum dispersion of light-dressed graphene.
• Applied linearly polarized infrared (IR) pulses (650 meV, 100 fs, 3 MV/cm) to coherently drive the electronic structure, inducing Floquet states.
• Used a time-dependent Hamiltonian with effective vector potential $\mathbf{A}_{\text{eff}}(t)$ to model light-matter coupling, incorporating both pump and probe fields.
• Calculated photoemission spectra using the non-equilibrium Green's function formalism and ab initio matrix elements to simulate ARPES maps.
• Compared experimental ARPES data with theoretical simulations to identify signatures of Floquet sidebands, Volkov states, and their quantum interference.
• Modeled the phase factor $\varphi(\mathbf{k},t,t') = \int_{t'}^{t} d\bar{t} [\varepsilon_f(\bar{t}) - \omega_{\text{pr}}] $ to account for time-dependent energy shifts in the photoemission process.

Experimental results

Research questions

• RQ1 Can Floquet states be experimentally observed in monolayer graphene under coherent infrared irradiation?
• RQ2 What are the spectroscopic signatures of Floquet sidebands and their interference with Volkov states in time-resolved ARPES?
• RQ3 Is the energy resolution of current ultrafast ARPES setups sufficient to resolve light-induced band gaps in graphene?
• RQ4 How do quantum path interference effects between Floquet and Volkov states manifest in the photoemission spectrum?
• RQ5 To what extent do experimental broadening effects obscure the detection of Floquet-induced energy gaps in graphene?

Key findings

• Direct experimental observation of Floquet sidebands and their quantum path interference with Volkov states in the photoemission spectrum of graphene under infrared irradiation.
• Theoretical modeling confirms the presence of a 70 meV Floquet energy gap at the K₁ point, though it remains spectroscopically obscured by broadening effects.
• The measured ARPES spectra show distinct spectral weight broadening (155 meV FWHM), exceeding the 20 fs probe pulse width, indicating additional broadening mechanisms beyond the probe duration.
• Despite the absence of clear energy gap signatures in experiment, the agreement between measured and calculated ARPES maps confirms the existence of light-dressed electronic states.
• The study validates the theoretical framework of Floquet engineering in graphene, demonstrating that coherent light dressing can produce observable band structure modifications.
• The results resolve prior controversies by providing unambiguous evidence of Floquet states through interference effects, even in the presence of ultrafast decoherence (~10–20 fs).