Abstract Modern time-resolved spectroscopy experiments on quantum materials raise the question, how strong electron-electron interactions, in combination with periodic driving, form unconventional transient states. Here we show using numerically exact methods that in a driven strongly interacting charge-density-wave insulator a band-like resonance in the gap region is formed. We associate this feature to the so-called Villain mode in quantum-magnetic materials, which originates in moving domain walls induced by the interaction. We do not obtain the in-gap band when driving a non-interacting charge density wave model. In contrast, it appears in the interacting system also in equilibrium at intermediate temperatures and in the short-time evolution of the system after a quantum quench to the lowest-order high-frequency effective Floquet Hamiltonian. Our findings connect the phenomenology of a periodically driven strongly correlated system and its quench dynamics to the finite-temperature dynamical response of quantum-magnetic materials and will be insightful for future investigations of strongly correlated materials in pump-probe setups.
Abstract Modern time-resolved spectroscopy experiments on quantum materials raise the question, how strong electron-electron interactions, in combination with periodic driving, form unconventional transient states. Here we show using numerically exact methods that in a driven strongly interacting charge-density-wave insulator a band-like resonance in the gap region is formed. We associate this feature to the so-called Villain mode in quantum-magnetic materials, which originates in moving domain walls induced by the interaction. We do not obtain the in-gap band when driving a non-interacting charge density wave model. In contrast, it appears in the interacting system also in equilibrium at intermediate temperatures and in the short-time evolution of the system after a quantum quench to the lowest-order high-frequency effective Floquet Hamiltonian. Our findings connect the phenomenology of a periodically driven strongly correlated system and its quench dynamics to the finite-temperature dynamical response of quantum-magnetic materials and will be insightful for future investigations of strongly correlated materials in pump-probe setups.
We determine the exact time-resolved photoemission spectroscopy for a nesting driven charge density wave (described by the spinless Falicov-Kimball model within dynamical mean-field theory). The pump-probe experiment involves two light pulses: the first is an ultrashort intense pump pulse that excites the system into nonequilibrium, and the second is a lower amplitude, higher frequency probe pulse that photoexcites electrons. We examine three different cases: the strongly correlated metal, the quantum-critical charge density wave, and the critical Mott insulator. Our results show that the quantum critical charge density wave has an ultraefficient relaxation channel that allows electrons to be de-excited during the pump pulse, resulting in little net excitation. In contrast, the metal and the Mott insulator show excitations that are closer to what one expects from these systems. In addition, the pump field produces spectral band narrowing, peak sharpening, and a spectral gap reduction, all of which rapidly return to their field free values after the pump is over.
We propose a mechanism for the photoinduced superconductinglike response recently reported in cuprates and other strongly correlated materials. This mechanism relies on quantum-fluctuating bosons consisting of electron pairs. With periodic drive, the electron pairs and vacancies of pairs form a coherent nonequilibrium condensate, different from conventional superconductors, yet showing a superconductinglike response in some regime even with dissipation. Unlike the case of driven fermionic bands, which results in the familiar Floquet bands with hybridization gaps, for driven bosons the ``gap'' opens up in the momentum direction, resulting in a resonant region in momentum space where the eigenvalues are complex. We give a simple physical argument for why this picture leads to a ``perfect conductor'' which exhibits superconductinglike frequency-dependent conductivity but no Meissner response. While our model is quite general, in the case of cuprates, a quantum-fluctuating pair density wave in the pseudogap region may serve as the origin of the quantum-fluctuating electron pairs.
The interaction of time-dependent electromagnetic fields with electrons in quantum materials can give rise to many both fundamentally interesting as well as technologically relevant phenomena like transient band structure manipulations or the emergence of prethermal states of matter, which are not a result of heating. This thesis contributes theoretical insights to both these topics: We model the interference of Floquet and Volkov side bands, which are a result of the dressing of electron states by light, in a time-resolved angle-resolved photoemission spectroscopy (ARPES) experiment. Furthermore, we analyze the emergence of a band-like feature in the non-equilibrium spectral function of a one-dimensional charge-density wave insulator upon periodic driving. Secondly, we use the fermionic truncated Wigner approximation (fTWA), a phase space method for the time evolution of interacting fermions, to study the light-induced order parameter dynamics in SU(N)-symmetric fermionic lattice models. By comparison with exact analytical results for an interaction quench in the Hubbard model, we find that dephasing-induced prethermalization is correctly described by fTWA. We discuss photoinduced prethermal transitions between competing phases of matter in the large-N Hubbard-Heisenberg model and find a pronounced frequency-dependence of the transition. This work contributes to a better understanding of photoinduced order parameter dynamics from a microscopic perspective.
We study transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. We investigate the dynamics of this gap opening process, taking into account the essential role of electron-electron interactions. Crucially, scattering due to interactions (1) induces dephasing, which erases memory of the system's prequench state and yields the intrinsic timescale for gap emergence, and (2) provides a mechanism for the system to absorb energy of the drive, leading to heating which must be mitigated to ensure the success of Floquet band engineering. We characterize the gap opening process via the system's generalized spectral function and correlators probed by photoemission experiments, and we identify a parameter regime at moderate driving frequencies where a hierarchy of timescales allows a well-defined Floquet gap to be produced and studied before the deleterious effects of heating set in.
Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude. In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models. Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition. The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.