Survival of Floquet-Bloch States in the Presence of Scattering

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

Light-Induced Ideal Weyl Semimetal in HgTe via Nonlinear Phononics

Interactions between light and matter allow the realization of out-of-equilibrium states in quantum solids. In particular, nonlinear phononics is one of the most efficient approaches to realizing the stationary electronic state in nonequilibrium. Herein, by an extended ab initio molecular dynamics method, we identify that long-lived light-driven quasistationary geometry could stabilize the topological nature in the material family of HgTe compounds. We show that coherent excitation of the infrared-active phonon mode results in a distortion of the atomic geometry with a lifetime of several picoseconds. We show that four Weyl points are located exactly at the Fermi level in this nonequilibrium geometry, making it an ideal long-lived metastable Weyl semimetal. We propose that such a metastable topological phase can be identified by photoelectron spectroscopy of the Fermi arc surface states or ultrafast pump-probe transport measurements of the nonlinear Hall effect.

Floquet Engineering of Black Phosphorus upon Below-Gap Pumping

Time-periodic light field can dress the electronic states and lead to light-induced emergent properties in quantum materials. While below-gap pumping is regarded favorable for Floquet engineering, so far direct experimental evidence of momentum-resolved band renormalization still remains missing. Here, we report experimental evidence of light-induced band renormalization in black phosphorus by pumping at photon energy of 160 meV, which is far below the band gap, and the distinction between below-gap pumping and near-resonance pumping is revealed. Our Letter demonstrates light-induced band engineering upon below-gap pumping, and provides insights for extending Floquet engineering to more quantum materials.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Optical Control of Slow Topological Electrons in Moiré Systems

Floquet moiré materials possess optically-induced flat-electron bands with steady-states sensitive to drive parameters. Within this regime, we show that strong interaction screening and phonon bath coupling can overcome enhanced drive-induced heating. In twisted bilayer graphene (TBG) irradiated by a terahertz-frequency continuous circularly polarized laser, the extremely slow electronic states enable the drive to control the steady state occupation of high-Berry curvature electronic states. In particular, above a critical field amplitude, high-Berry-curvature states exhibit a slow regime where they decouple from acoustic phonons, allowing the drive to control the anomalous Hall response. Our work shows that the laser-induced control of topological and transport physics in Floquet TBG are measurable using experimentally available probes.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Floquet Engineering of Nonequilibrium Valley-Polarized Quantum Anomalous Hall Effect with Tunable Chern Number

Here, we propose that Floquet engineering offers a strategy to realize the nonequilibrium quantum anomalous Hall effect (QAHE) with tunable Chern number. Using first-principles calculations and Floquet theorem, we unveil that QAHE related to valley polarization (VP-QAHE) is formed from the hybridization of Floquet sidebands in the two-dimensional family MSi₂Z₄ (M = Mo, W, V; Z = N, P, As) by irradiating circularly polarized light (CPL). Through the tuning of frequency, intensity, and handedness of CPL, the Chern number of VP-QAHE is highly tunable and up to C = ±4, which attributes to light-induced trigonal warping and multiple-band inversion at different valleys. The chiral edge states and quantized plateau of Hall conductance are visible inside the global band gap, thereby facilitating the experimental measurement. Our work not only establishes Floquet engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials but also provides an avenue to explore emergent topological phases under light irradiation.

Pseudospin-selective Floquet band engineering in black phosphorus

Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials^1-3, cold atoms⁴ and photonic systems⁵ through hybridization with photon-dressed Floquet states⁶ in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials^7-11, for example, modifications of the topological properties of Dirac materials^12,13 and modulation of the optical response^14-16. Despite extensive research interests over the past decade^3,8,17-20, there is no experimental evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report experimental signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is observed near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favouring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.

Controlling Floquet states on ultrashort time scales

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.

Dynamical Phase Transitions in the Photodriven Charge-Ordered Dirac-Electron System

We study photoinduced phase transitions and charge dynamics in the interacting Dirac-electron system with a charge-ordered ground state theoretically by taking an organic salt α-(BEDT-TTF)_{2}I_{3}. By analyzing the extended Hubbard model for this compound using a combined method of numerical simulations based on the time-dependent Schrödinger equation and the Floquet theory, we observe successive dynamical phase transitions from the charge-ordered insulator to a gapless Dirac semimetal and, eventually, to a Chern insulator phase under irradiation with circularly polarized light. These phase transitions occur as a consequence of two major effects of circularly polarized light, i.e., closing of the charge gap through melting the charge order and opening of the topological gap by breaking the time-reversal symmetry at the Dirac points. We demonstrate that these photoinduced phenomena are governed by charge dynamics of driven correlated Dirac electrons.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Through the Lens of a Momentum Microscope: Viewing Light-Induced Quantum Phenomena in 2D Materials

Van der Waals (vdW) materials at their 2D limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many 2D semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials are reviewed using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. The advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials are discussed. Then, the future research directions opened by these scientific and instrumental advancements are projected for studying the physics of 2D materials and the opportunities to engineer their band-structure and band-topology by laser fields.