[Paper Review] Direct observation of Floquet-Bloch states in monolayer graphene

Dong-Seong Choi, Masataka Mogi+7 more|arXiv (Cornell University)|Apr 22, 2024

Graphene research and applications6 citations

TL;DR

The paper reports direct energy-momentum resolved observation of Floquet-Bloch states in monolayer graphene using time- and angle-resolved photoemission spectroscopy (trARPES) with mid-infrared pumping, and shows replica bands whose polarization dependence reveals Floquet–Volkov coupling.

ABSTRACT

Floquet engineering is a novel method of manipulating quantum phases of matter via periodic driving [1, 2]. It has successfully been utilized in different platforms ranging from photonic systems [3] to optical lattice of ultracold atoms [4, 5]. In solids, light can be used as the periodic drive via coherent light-matter interaction. This leads to hybridization of Bloch electrons with photons resulting in replica bands known as Floquet-Bloch states. After the direct observation of Floquet-Bloch states in a topological insulator [6], their manifestations have been seen in a number of other experiments [7-14]. By engineering the electronic band structure using Floquet-Bloch states, various exotic phase transitions have been predicted [15-22] to occur. To realize these phases, it is necessary to better understand the nature of Floquet-Bloch states in different materials. However, direct energy and momentum resolved observation of these states is still limited to only few material systems [6, 10, 14, 23, 24]. Here, we report direct observation of Floquet-Bloch states in monolayer epitaxial graphene which was the first proposed material platform [15] for Floquet engineering. By using time- and angle-resolved photoemission spectroscopy (trARPES) with mid-infrared (mid-IR) pump excitation, we detected replicas of the Dirac cone. Pump polarization dependence of these replica bands unequivocally shows that they originate from the scattering between Floquet-Bloch states and photon-dressed free-electron-like photoemission final states, called Volkov states. Beyond graphene, our method can potentially be used to directly observe Floquet-Bloch states in other systems paving the way for Floquet engineering in a wide range of quantum materials.

Motivation & Objective

• Motivate Floquet engineering as a route to manipulate quantum phases in solids and specifically in graphene.
• Demonstrate direct energy-momentum resolved observation of Floquet-Bloch states in monolayer graphene.
• Differentiate Floquet-Bloch contributions from Volkov final-state effects through pump polarization dependence.
• Develop and apply a simple analytical model to interpret replica-band evolution under polarization rotation.

Proposed method

• Use time- and angle-resolved photoemission spectroscopy (trARPES) with a mid-infrared pump (246 meV) and 26.4 eV probe to observe replica Dirac cones in graphene.
• Record ARPES spectra as pump polarization is rotated to track the evolution of replica bands in k-space.
• Compare experimental polarization-dependent replica-band evolution with simulations based on three scenarios: Floquet–Volkov coupling, only Volkov states, and only Floquet states.
• Employ a scattering-matrix formalism where the replica intensity P1 scales with |M|^2 |γ|^2, and γ encodes Floquet and Volkov interaction parameters (α, β).
• Incorporate pump incidence angle and in-plane vector potential to model γ and the resulting replica-band dynamics (Equation for γ and related terms).
• Use an analytical model inspired by prior work to distinguish Floquet-Bloch contributions from Volkov effects.

Figure 1: Generation of a replica band in graphene via 5 um pump excitation. a , Conceptual schematic of pump-probe experiments on graphene and the generation of replica bands. The red circle corresponds to the measurement window of our experiments. b , Illustration of the scattering between Floquet

Experimental results

Research questions

• RQ1 Can Floquet-Bloch states be directly observed in monolayer graphene using trARPES with mid-IR pumping?
• RQ2 Do the observed replica bands arise from Floquet-Bloch states, Volkov states, or their coupling, as evidenced by pump-polarization dependence?
• RQ3 How does the polarization of the pump influence the evolution of replica bands, and what does this imply about Floquet–Volkov interactions?

Key findings

• Replica Dirac-cone replicas appear in graphene after mid-IR pump excitation, indicative of photon-dressed states.
• The evolution of replica bands with pump-polarization rotation cannot be explained by Volkov states alone and is consistent with Floquet–Volkov scattering.
• A Floquet-Bloch and Volkov coupling model reproduces the observed polarization-dependent arc rotation and coexistence of two arcs, matching experimental trends.
• A purely Floquet or purely Volkov scenario fails to capture the full evolution of replica bands across polarization angles.
• The results provide direct evidence for Floquet-Bloch states in graphene and offer a framework extendable to other materials for Floquet engineering.

Figure 2: Evolution of photoemission intensity at constant energy as a function of pump polarization angle $\theta_{p}$ . a , ARPES spectra showing k x – k y cuts at $E$ – $E_{F}$ = 0.219 eV (averaged by $\pm$ 0.025 eV). The displayed $\theta_{p}$ range is divided into three segments: range I, middl