Observation of Floquet-induced gap in graphene

Abstract

Floquet engineering provides a powerful pathway for creating non-equilibrium phases of matter with tailored electronic structures and properties through time-periodic driving. As the original theoretical prototype, graphene established the framework in which the Floquet topological insulator with light-induced anomalous Hall effect was proposed. However, the defining spectroscopic signature of Floquet engineering in graphene--light-induced hybridization (avoided-crossing) gap at Floquet band crossings, has remained experimentally elusive. Here, we report direct observation of Floquet-induced hybridization gap in monolayer graphene under resonant driving by a strong light field. Time- and angle-resolved photoemission spectroscopy reveals gap opening at Floquet band crossings, accompanied by coherent Floquet sidebands. The gap exhibits pronounced momentum anisotropy, featuring two Dirac nodes protected by the spatiotemporal symmetry and tunable by light polarization. These results provide long-sought experimental demonstration of Floquet band engineering in graphene, opening up opportunities for light-field engineered quantum phases in graphene and related materials.

Figures (12)

• Figure : Fig. 1 ${\mid}$ Schematic illustration of Bloch states, Floquet-Bloch states and gap opening.a, Dispersion of free electrons. b, Folding of the electronic bands by the reciprocal lattice vector $\vec{G}$ under a spatially-periodic potential with period $a$ being the lattice constant. c, Gap opening at the Brillouin zone (BZ) boundary due to interaction of electrons with the realistic spatially-periodic potential. d, Dispersion of graphene. e, Floquet sidebands under a time-periodic drive, where $\hbar\omega$ is the driving photon energy. f, Floquet-induced gap at the Floquet BZ boundary through the strong light-matter interaction. The yellow and blue shaded areas mark the first BZ in the momentum and energy space respectively.
• Figure : Fig. 2 ${\mid}$ Experimental observation of light-induced gap in monolayer graphene.a,b, Dispersion image measured before pumping ( a) and schematic dispersion ( b). The measurement direction is indicated by the red line in the inset (perpendicular to the $\Gamma$-K direction). The gray dots in ( b) mark the resonance points upon driving at $\hbar\omega$ = 490 meV. c,d, Dispersion image measured upon pumping at $\hbar\omega$ = 490 meV with pump fluence of 4.1 mJ/cm$^2$ ( c) and schematic dispersion ( d). The pump polarization is along the $\Gamma$-K direction. The Floquet-induced gap is labelled by $\Delta$. e,f, EDCs at resonance points ($k_5$ and $k_7$) indicated in ( d). Tick marks indicate peak positions in the EDCs. g,h, Zoom-in EDCs at resonance points with fitting peaks appended.
• Figure : Fig. 3 ${\mid}$ Evidence of Floquet-induced gap from time-dependent measurements.a-e, Dispersion images measured at different delay times upon driving at $\hbar\omega$ = 490 meV with pump fluence of 3.8 mJ/cm$^2$. f, Differential image obtained by subtracting data measured at $\Delta$t = -300 fs ( a) from 0 fs ( b). Red arrow and black dashed box indicate the light-induced sideband (SB). g, EDCs at resonance points measured at different delay times with fitting peaks appended. h, Extracted Floquet-induced gap at different delay times. The gray curve is the same as that in ( i). i, Integrated intensity of the light-induced sideband over the box in ( f) as a function of delay time. The gray curve is the fitting curve of the sideband intensity.
• Figure : Fig. 4 ${\mid}$ Momentum anisotropy of the Floquet-induced gap and the emergence of spatiotemporal symmetry protected Dirac nodes.a-c, Dispersion images measured at $\Delta t$ = 0 at azimuthal angle $\phi$ = 90$^\circ$, 60$^\circ$ and 0$^\circ$ upon pumping at $\hbar\omega$ = 490 meV with pump fluence of 4.1 mJ/cm$^2$. d, Schematic illustration for the resonance rings in the VB and CB. The red arrow indicates the pump light field direction. e, Zoom-in EDCs at the resonance points, together with fitting curves to extract the Floquet-induced gap for data shown in ( a-c). f, Schematic illustration of the anisotropic gap opening along the resonance rings, and the emergence of two spatiotemporal symmetry protected Dirac nodes.
• Figure : Extended Data Fig. 1 ${\mid}$ Calibration of the Fermi energy $E_F$ and negligible pump-induced band broadening at high binding energy.a, Dispersion image measured before pumping. b, Extracted EDCs within the region marked by the red box and fitting using Fermi-Dirac distribution (red curve), from which $E_F$ is extracted. c, Dispersion image measured upon pumping. d, EDCs cut through black box at different delay times with fitting peaks appended.