Floquet engineering has emerged as a powerful route to dynamically control band structure and topology in quantum materials, but most implementations rely on externally imposed laser fields that are power intensive, difficult to integrate into devices, and weakly coupled to the electronic system. We propose and analyze an alternative paradigm in which a self-generated cavity field Floquet-dresses the electronic bands and produces a geometric Hall response in an electrically driven cavity material system. We consider a semiconductor layer embedded in a cavity and coupled to external leads and a bath of acoustic phonons, where dc pumping leads to the buildup of a coherent intracavity field through light-matter coupling. We determine the resulting nonequilibrium steady state self-consistently and show that, above threshold, the coupled system settles into a stable time-periodic limit cycle with a field amplitude set by the cavity quality factor and dissipation. This emergent periodic field Floquet-dresses the electronic bands and modifies the anomalous Hall response of a material with broken time-reversal symmetry. We demonstrate that the resulting Hall conductivity can be directly probed via in-plane dc transport measurements. Our work establishes a route to self organized Floquet band reconstruction and geometric transport without external laser illumination, highlighting cavity driven steady states as a platform for electrically controlled nonequilibrium phases.

Photo-excited quantum materials can be driven into thermally inaccessible metastable states that exhibit structural, charge, spin, topological and superconducting orders. Metastable states typically emerge on timescales set by the intrinsic electronic and phononic energy scales, ranging from femtoseconds to picoseconds, and can persist for weeks. Therefore, studies have primarily focused on ultrafast or quasi-static limits, leaving the intermediate time window less explored. Here we reveal a metastable state with broken glide-plane symmetry in photo-doped Ca2RuO4 using time-resolved optical second-harmonic generation and birefringence measurements. We find that the metastable state appears long after intralayer antiferromagnetic order has melted and photo-carriers have recombined. Its properties are distinct from all known states in the equilibrium phase diagram and are consistent with intralayer ferromagnetic order. Furthermore, model Hamiltonian calculations reveal that a non-thermal trajectory to this state can be accessed via photo-doping. Our results expand the search space for out-of-equilibrium electronic matter to metastable states emerging at intermediate timescales. Searches for metastable states with properties not found in thermal equilibrium have been restricted to either ultrafast or slow timescales. A metastable state in an intermediate time window has now been identified in a photo-doped Mott insulator.

Phonon polaritons are quasiparticles resulting from the coherent coupling of photons with optical phonons in polar dielectrics1. Owing to their exceptional ability to confine electric fields to deep-subwavelength scales with low loss, they are uniquely poised to enable a suite of applications beyond the reach of conventional photonics, such as subdiffraction imaging2 and near-field energy transfer3-5. The conventional approach to exciting phonon polaritons through optical methods, however, involves costly light sources along with near-field schemes6,7, and generally leads to low excitation efficiency owing to substantial momentum mismatch between phonon polaritons and free-space photons. Here we demonstrate that under proper conditions, phonon polaritons can be excited all-electrically by drifting charge carriers. Specifically, in hexagonal boron nitride (hBN)/graphene heterostructures, by electrically driving charge carriers in ultrahigh-mobility graphene out of equilibrium, we observe bright electroluminescence of hBN's hyperbolic phonon polaritons (HPhPs) at mid-infrared frequencies, which shows a temperature and carrier density dependence distinct from black-body thermal emission. Moreover, the carrier density dependence of the HPhP electroluminescence spectra reveals that HPhP electroluminescence can arise from both interband transition and intraband Cherenkov radiation8 of charge carriers in graphene. The HPhP electroluminescence offers avenues for realizing electrically pumped mid-infrared and terahertz phonon-polariton light sources.

Light-induced phenomena in materials can exhibit exotic behavior that extends beyond equilibrium properties, offering new avenues for understanding and controlling electronic phases. So far, non-equilibrium phenomena in solids have been predominantly explored using femtosecond laser pulses, which generate transient, ultra-fast dynamics. Here, we investigate the steady non-equilibrium regime in graphene induced by a continuous-wave (CW) mid-infrared laser. Our transport measurements reveal signatures of a long-lived Floquet phase, where a non-equilibrium electronic population is stabilized by the interplay between coherent photoexcitation and incoherent phonon cooling. The observation of non-equilibrium steady states using CW lasers stimulates further investigations of low-temperature Floquet phenomena towards Floquet engineering of steady-state phases of matter.

We show that energy dissipation in slowly driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower bounds on dissipation rates in two-tone protocols, such as those employed for topological frequency conversion. Notably, in appropriate limits these bounds are only determined by the topology of the protocol and an effective quality factor of the system-bath coupling. Our results bridge topological and geometric phenomena with energy dissipation in open quantum systems, and further provide design principles for optimal driving protocols.

External coherent fields can drive quantum materials into non-equilibrium states, revealing exotic properties that are unattainable under equilibrium conditions -- an approach known as ``Floquet engineering.'' While optical lasers have commonly been used as the driving fields, recent advancements have introduced nontraditional sources, such as coherent phonon drives. Building on this progress, we demonstrate that driving a metallic quantum nanowire with a coherent wave of terahertz phonons can induce an electronic steady state characterized by a persistent quantized current along the wire. The quantization of the current is achieved due to the coupling of electrons to the nanowire's vibrational modes, providing the low-temperature heat bath and energy relaxation mechanisms. Our findings underscore the potential of using non-optical drives, such as coherent phonon sources, to induce non-equilibrium phenomena in materials. Furthermore, our approach suggests a new method for the high-precision detection of coherent phonon oscillations via transport measurements.

An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions, a simple picture based on well-defined Floquet quasiparticles suggests that the system should host a quasisteady state current that depends only on the populations of the system's Floquet-Bloch bands and their associated quasienergy winding numbers. Here we show that such topological transport persists into the strongly interacting regime where the single-particle lifetime becomes shorter than the drive period. Analytically, we show that the value of the current is insensitive to interaction-induced band renormalizations and lifetime broadening when certain conditions are met by the system's nonequilibrium distribution function. We show that these conditions correspond to a quasisteady state. We support these predictions through numerical simulation of a system of strongly interacting fermions in a periodically modulated chain of Sachdev-Ye-Kitaev dots. Our paper establishes universal transport at high entropy density as a robust far from equilibrium topological phenomenon, which can be readily realized with cold atoms in optical lattices.

We show that rhombohedral multilayer graphene supports topological frequency conversion, whereby a fraction of electrons transfer energy between two monochromatic light sources at a quantized rate. The pristine nature and gate tunability of these materials, along with a Berry curvature that directly couples to electric fields, make them ideal platforms for the experimental realization of topological frequency conversion. Among the rhombohedral family, we find that Bernal bilayer graphene appears most promising for THz-scale applications due to lower dissipation. We discuss strategies to circumvent cancellations between the two valleys of graphene and to minimize dissipative losses using commensurate frequencies, thus opening a potential pathway for net amplification.

Phonon-polaritons are electromagnetic waves resulting from the coherent coupling of photons with optical phonons in polar dielectrics. Due to their exceptional ability to confine electric fields to deep subwavelength scales with low loss, they are uniquely poised to enable a suite of applications beyond the reach of conventional photonics, such as sub-diffraction imaging and near-field energy transfer. The conventional approach to exciting phonon-polaritons through optical methods, however, necessitates costly mid-infrared and terahertz coherent light sources along with near-field scanning probes, and generally leads to low excitation efficiency due to the substantial momentum mismatch between phonon-polaritons and free-space photons. Here, we demonstrate that under proper conditions, phonon-polaritons can be excited all-electrically by flowing charge carriers. Specifically, in hexagonal boron nitride (hBN)/graphene heterostructures, by electrically driving charge carriers in ultra-high-mobility graphene out of equilibrium, we observe bright electroluminescence of hBN's hyperbolic phonon-polaritons (HPhPs) at mid-IR frequencies. The HPhP electroluminescence shows a temperature and carrier density dependence distinct from black-body or super-Planckian thermal emission. Moreover, the carrier density dependence of HPhP electroluminescence spectra reveals that HPhP electroluminescence can arise from both inter-band transition and intra-band Cherenkov radiation of charge carriers in graphene. The HPhP electroluminescence offers fundamentally new avenues for realizing electrically-pumped, tunable mid-IR and THz phonon-polariton lasers, and efficient cooling of electronic devices.

Twisted bilayer graphene (TBG) exhibits extremely low Fermi velocities for electrons, with the speed of sound surpassing the Fermi velocity. This regime enables the use of TBG for amplifying vibrational waves of the lattice through stimulated emission, following the same principles of operation of free-electron lasers. Our Letter proposes a lasing mechanism relying on the slow-electron bands to produce a coherent beam of acoustic phonons. We propose a device based on undulated electrons in TBG, which we dub the phaser. The device generates phonon beams in a terahertz (THz) frequency range, which can then be used to produce THz electromagnetic radiation. The ability to generate coherent phonons in solids breaks new ground in controlling quantum memories, probing quantum states, realizing nonequilibrium phases of matter, and designing new types of THz optical devices.

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.

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.

Floquet engineering uses coherent time-periodic drives to realize designer band structures on-demand, thus yielding a versatile approach for inducing a wide range of exotic quantum many-body phenomena. Here we show how this approach can be used to induce non-equilibrium correlated states with spontaneously broken symmetry in lightly doped semiconductors. In the presence of a resonant driving field, the system spontaneously develops quantum liquid crystalline order featuring strong anisotropy whose directionality rotates as a function of time. The phase transition occurs in the steady state of the system achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results demonstrate that coherent driving can be used to induce non-equilibrium quantum phases of matter with dynamical broken symmetry.

Quantum interference is typically detected through the dependence of the interference signal on certain parameters (path length, Aharonov-Bohm flux, etc.), which can be varied in a controlled manner. The destruction of interference by a which-path measurement is a paradigmatic manifestation of quantum effects. Here we report on a novel measurement protocol that realizes two objectives: (i) certifying that a measured signal is the result of interference avoiding the need to vary parameters of the underlying interferometer, and (ii) certifying that the interference signal at hand is of quantum nature. In particular, it yields a null outcome in the case of classical interference. Our protocol comprises measurements of cross-correlations between the readings of which-path weakly coupled detectors positioned at the respective interferometer's arms and the current in one of the interferometer's drains. We discuss its implementation with an experimentally available platform: an electronic Mach-Zehnder interferometer (MZI) coupled electrostatically to "detectors" (quantum point contacts).

We study steady states of semiconductor nanowires subjected to strong resonant time-periodic drives. The steady states arise from the balance between electron-phonon scattering, electron-hole recombination via photoemission, and Auger scattering processes. We show that tuning the strength of the driving field drives a transition between an electron-hole metal (EHM) phase and a Floquet insulator (FI) phase. We study the critical point controlling this transition. The EHM-to-FI transition can be observed by monitoring the presence of peaks in the density-density response function, which are associated with the Fermi momentum of the EHM phase and are absent in the FI phase. Our results may help guide future studies toward inducing exotic nonequilibrium phases of matter by periodic driving.

We study the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. We solve for the bulk and edge state carrier distributions, taking into account energy and momentum relaxation through radiative recombination and electron-phonon interactions, as well as coupling to an external lead. We show that the resulting steady state resembles a topological insulator in the Floquet basis. The particle distribution in the Floquet edge modes exhibits a sharp feature akin to the Fermi level in equilibrium systems, while the bulk hosts a small density of excitations. We discuss two-terminal transport and describe the regimes where edge-state transport can be observed. Our results show that signatures of the non-trivial topology persist in the non-equilibrium steady state.

Measurements with variable system-detector interaction strength, ranging from weak to strong, have been recently reported in a number of electronic nanosystems. In several such instances many-body effects play a significant role. Here we consider the weak--to--strong crossover for a setup consisting of an electronic Mach-Zehnder interferometer, where a second interferometer is employed as a detector. In the context of a conditional which-path protocol, we define a generalized conditional value (GCV), and determine its full crossover between the regimes of weak and strong (projective) measurement. We find that the GCV has an oscillatory dependence on the system-detector interaction strength. These oscillations are a genuine many-body effect, and can be experimentally observed through the voltage dependence of cross current correlations.

Weak value (WV) protocols may lead to extreme expectation values that are larger than the corresponding orthodox expectation values. Recent works have proposed to implement this concept in nano-scale electronic systems. Here we address the issue of how one calibrates the setup in question, maximizes the measurement’s sensitivity, and extracts distinctly large WVs. Our concrete setup consists of two Mach–Zehnder interferometers: the “system” and the “detector”. Such setups have already been implemented in experiment.