Quantum geometry plays a fundamental role across many branches of modern physics, yet its full characterization in nonequilibrium systems remains a challenge. Here, we propose a framework for quantum geometry in Floquet topological insulators by introducing a time-resolved quantum metric tensor, defined via the trace distance between micromotion operators in momentum-time space. For class A in two spatial dimensions, we find a general inequality linking the Floquet quantum metric tensor and the Floquet topology: the associated quantum volume is bounded below by the Floquet topological invariant. This relation is found to also hold in class AIII in one dimension, where the Floquet geometric tensor may be notably reduced due to time-reflection symmetry. This work will be useful in digesting the general aspects of quantum geometry in periodically driven systems in connection with their topological characterization.
We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially filled version of Thouless's topologically quantized adiabatic pump. The corresponding single-particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless and is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, op…
We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34}, 3379 (2000)]. We discuss that the dependence on the d…
We discuss the effect of dissipation on heating which occurs in periodically driven quantum many body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states ap…
The dynamic localization in energy space -- suppression of the absorption of energy from an external microwave field due to quantum interference -- was analyzed recently for a closed quantum dot in the absence of electron-electron interactions. Here a weak interaction is shown to lead to a finite absorption and heating, which may be viewed as hopping between localized Floquet states. The heating rate grows together with the electronic temperature, eventually destroying the localization.
The Floquet eigenvalue problem is analyzed for periodically driven Friedrichs models on discrete and continuous space. In the high-frequency regime, there exists a Floquet bound state consistent with the Floquet-Magnus expansion in the discrete Friedrichs model, while it is not the case in the continuous model. In the latter case, however, the bound state predicted by the Floquet-Magnus expansion appears as a metastable state whose lifetime diverges in the limit of large frequencies. We obtain the lifetime by evaluating the imaginary part of the quasi-energy of the Floquet resonant state. In t…
The Su-Schrieffer-Heeger model of polyacetylene is a paradigmatic Hamiltonian exhibiting non-trivial edge states. By using Floquet theory we study how the spectrum of this one-dimensional topological insulator is affected by a time-dependent potential. In particular, we evidence the competition among different photon-assisted processes and the native topology of the unperturbed Hamiltonian to settle the resulting topology at different driving frequencies. While some regions of the quasienergy spectrum develop new gaps hosting Floquet edge states, the native gap can be dramatically reduced and …
We report on the theoretical investigation of the topological properties of a periodically quenched one-dimensional dimerized lattice where a piece-wise constant Hamiltonian switches from $h_1$ to $h_2$ at a partition time $t_p$ within each driving period $T$. We examine different dimerization patterns for $h_1$ and $h_2$ and the interplay with the driving parameters that lead to the emergence of topological states both at zero energy and at the edge of the Brillouin-Floquet quasi-energy zone. We illustrate different phenomena, including the occurrence of both edge states in a semimetal spectr…
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
Floquet higher order topological insulators (FHOTIs) are a novel topological phase that can occur in periodically driven lattices. An appropriate experimental platform to realize FHOTIs has not yet been identified. We introduce a periodically-driven bipartite (two-band) system that hosts FHOTI phases, and predict that this lattice can be realized in experimentally-realistic optical waveguide arrays, similar to those previously used to study anomalous Floquet insulators. The model exhibits interesting phase transitions from first-order to second-order topological matter by tuning a coupling str…
Higher-order topological phases are characterized by protected states localized at the corners or hinges of the system. By applying time-periodic quenches to a two-dimensional lattice with balanced gain and loss, we obtain a rich variety of non-Hermitian Floquet second order topological insulating phases. Each of the phases is characterized by a pair of integer topological invariants, which predict the numbers of Floquet corner modes at zero and $π$ quasienergies. We establish the topological phase diagram of the model, and find a series of non-Hermiticity induced transitions between different…
The nontrivial topology of {\it p}-wave superfluids make these systems attractive candidate in information technology. In this work we report on the topological state of a {\it p}-wave nonequilibrium excitonic insulator (NEQ-EI) and show how to steer a nontopological band-insulator with bright $p$-excitons toward this state by a suitable laser pulse, thus achieving a dynamical topological phase transition. The underlying mechanism behind the transition is the broken gauge-symmetry of the NEQ-EI which causes self-sustained persistent oscillations of the excitonic condensate and hence a Floquet …
The high Chern number phases with the Chern number |C| > 1 are observed in this study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) model with a cyclic parameter. Besides the standard intra-dimer and the nearest-neighbor (NN) inter-dimer hopping of the SSH model, an additional next-nearest-neighbor (NNN) hopping is considered in the E-SSH model. The cyclic parameter, which plays the role of a synthetic dimension, is invoked as a modulation of the hopping strengths. A rigorous analysis of different phase diagrams has shown multiple Floquet topological phase transitions among th…
We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf $\mathbb{Z}$ invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet $\mathbb{Z}_2$ invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time-evolution, subject to a process in which …
We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high frequency regime. First, we consider a driving protocol relevant for experiments with frequencies smaller than the bandwidth and weak amplitudes and derive an effective Hamiltonian, which through a symmetry analysis, provides analytical insight into the rich effects of the drive. We find that circularly polarized light at low frequencies can selectively decrease the strength of AA-type interlayer hopping while leaving the AB-type unaffe…
Electrons in a lattice exhibit time-periodic motion, known as Bloch oscillation, when subject to an additional static electric field. Here we show that a corresponding dynamics can occur upon replacing the spatially periodic potential by a time-periodic driving: Floquet oscillations of charge carriers in a spatially homogeneous system. The time lattice of the driving gives rise to Floquet bands that take on the role of the usual Bloch bands. For two different drivings (harmonic driving and periodic kicking through pulses) of systems with linear dispersion we demonstrate the existence of such o…
We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in $1/ω$, with $ω$ being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck …
A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled. This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator. Here we generalize this characterization of topological phases toward periodically driven systems. We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet…
We study the interplay of strong correlations and coherent driving by considering the strong-coupling Kondo model driven by a time-periodic bias voltage. Combining a recent nonequilibrium renormalization group method with Floquet theory, we find that by the coherent dressing of the driving field side-replicas of the Kondo resonance emerge in the conductance, which are not completely washed out by the decoherence induced by the driving. We show that to accurately capture the interplay of driving and strong correlations one needs to go beyond simple phenomenological pictures, which underestimate…
Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes, and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic p…
We present a class of three dimensional (3D) two-band Floquet topological insulators constructed from two-dimensional Floquet topological insulators with a $Z$ topological index. It is shown that the 3D two-band Floquet topological insulator has a $Z_2$ topological index, whose value can be obtained by numerical calculations or by using a relation to the winding number. The classification of the 3D $Z_2$ Floquet topological insulator, however, cannot be attributed to the stable homotopy groups. Thus, it is an example outside the proposed K-theory classifications of Floquet topological insulato…
Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them been characterized by a pair of even-integer topological invariants $(w_{0},w_π)\in2\mathbb{Z}\times2\mathbb{Z}$. U…
In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from th…
Periodically driven Kitaev chains are known to exhibit novel Floquet Majorana fermions and anomalous Floquet end modes. The fact that `quasienergy in Floquet systems is periodic' poses a difficulty in defining the ground state in periodically driven systems. To overcome this problem, we start with the ground state of the undriven Kitaev chain and gradually switch on the periodic driving in chemical potential over a timescale $τ$. The extent to which the single particle eigenstates of the undriven system get distributed among the Floquet states upon driving can be characterized by inverse parti…
Time-periodic (Floquet) drive can give rise to novel symmetry breaking and topological phases of matter. Recently, we showed that a quintessential Floquet topological phase known as the anomalous Floquet-Anderson insulator is stable to noise on the timing of its Floquet drive. Here, we perturb the anomalous Floquet-Anderson insulator at a single incommensurate frequency, resulting in a quasiperiodic 2-tone drive. Our numerics indicate that a robust topological phase survives at weak noise with topological pumping that is more stable than the case of white noise. Within the topological phase, w…
Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system. We illustrate the applications of this formalism by giving general expressions for optical conductivity of Floquet systems, including its homodyne and heterodyne components and beyond. We obtain the Floquet optical conductivity of specific driven models, including two-dimensional Dirac material such as the surface of a topological insulator, graphene, and the Haldane model irradiated with circularly or linearly polariz…
Chirally stacked $N$-layer graphene is a semimetal with $\pm p^N$ band-touching at two nonequivalent corners in its Brillioun zone. We predict that an off-resonant circularly polarized light (CPL) drives chirally stacked $N$-layer graphene into a Floquet Chern Insulators (FCIs), a.k.a. quantum anomalous Hall insulators, with tunable high Chern number $C_F=\pm N$ and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number $C_v=\pm N$ induced by a voltage gate can be engineered by the parameters of the CPL and voltage gate. We …
We propose a general framework to solve tight binding models in D dimensional lattices driven by ac electric fields. Our method is valid for arbitrary driving regimes and allows to obtain effective Hamiltonians for different external fields configurations. We establish an equivalence with time independent lattices in D+1 dimensions, and analyze their topological properties. Further, we demonstrate that non-adiabaticity drives a transition from topological invariants defined in D+1 to D dimensions. Our approach provides a theoretical framework to analyze ac driven systems, with potential applic…
We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graph…
After extensive investigation on the Floquet second-order topological insulator (FSOTI) in two dimension (2D), here we propose two driving schemes to systematically engineer the hierarchy of Floquet first-order topological insulator, FSOTI, and Floquet third-order topological insulator in three dimension (3D). Our driving protocols allow these Floquet phases to showcase regular $0$, anomalous $π$, and hybrid $0$-$π$-modes in a unified phase diagram, obtained for both 2D and 3D systems, while staring from the lower order topological or non-topological phases. Both the step drive and the mass ki…
Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an "anomalous" two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologicall…
We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-Stückelberg-Majorana models. We reproduce some known expressions for transition probabilities in a simpl…
We investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a periodic magnetic field and elliptically polarized light, are discussed respectively. By use of the Floquet theory, we find that both the two periodic drives can resonantly induce the topological transitions from normal insulator (NI) phases to Floquet topological insulator (FTI) phases. The Floquet topological transitions are characterized by variation of Chern number. Moreover, we show that the Floquet topological transitions can be explained by…
Fractional Chern insulators are the proposed phases of matter mimicking the physics of fractional quantum Hall states on a lattice without an overall magnetic field. The notion of Floquet fractional Chern insulators refers to the potential possibilities to generate the underlying topological bandstructure by means of Floquet engineering. In these schemes, a highly controllable and strongly interacting system is periodically driven by an external force at a frequency such that double tunneling events during one forcing period become important and contribute to shaping the required effective ene…
We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy g ap of the bulk. The phase diagram of th…
We study two-terminal transport through two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We focus on the Anomalous Floquet-Anderson Insulator (AFAI) phase, a topologically-nontrivial phase within this class, which hosts topologically protected chiral edge modes coexisting with its fully localized bulk. We show that the unique properties of the AFAI yield remarkable far-from-equilibrium transport signatures: for a large bias between leads, a quantized amount of charge is transported through the system each driving period. Upon increasi…
Results are presented for the entanglement entropy and spectrum of half-filled graphene following the switch on of a circularly polarized laser. The laser parameters are chosen to correspond to several different Floquet Chern insulator phases. The entanglement properties of the unitarily evolved wavefunctions are compared with the state where one of the Floquet bands is completely occupied. The true states show a volume law for the entanglement, whereas the Floquet states show an area law. Qualitative differences are found in the entanglement properties of the off-resonant and on-resonant lase…
Topological states require the presence of extended bulk states, as usually found in the picture of energy bands and topological states bridging the bulk gaps. But in driven systems this can be circumvented, and one can get topological states coexisting with fully localized bulk states, as in the case of the anomalous Floquet-Anderson insulator. Here, we show the fingerprints of this peculiar topological phase in the transport properties and their dependence on the disorder strength, geometrical configuration (two-terminal and multiterminal setups) and details of the driving protocol.
We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing…
Recent experiments showed that the surface of a three dimensional topological insulator develops gaps in the Floquet-Bloch band spectrum when illuminated with a circularly polarized laser. These Floquet-Bloch bands are characterized by non-trivial Chern numbers which only depend on the helicity of the polarization of the radiation field. Here we propose a setup consisting of a pair of counter-rotating lasers, and show that one-dimensional chiral states emerge at the interface between the two lasers. These interface states turn out to be spin-polarized and may trigger interesting applications i…
We report on simulations of the dc conductance and quantum Hall response of a Floquet topological insulator using Floquet scattering theory. Our results reveal that laser-induced edge states in graphene lead to quantum Hall plateaus once imperfect matching with the non-illuminated leads is lessened. But the magnitude of the Hall plateaus is not directly related to the number and chirality of all the edge states at a given energy as usual. Instead, the plateaus are dominated only by those edge states adding to the dc density of states. Therefore, the dc quantum Hall conductance of a Floquet top…
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find…
A comparative study of perturbative and nonequilibrium Green's function approaches for Floquet sidebands in periodically driven quantum systems
Georg-August-University Göttingen（哥廷根大学）；Paul Scherrer Institute（保罗谢勒研究所）；University of Fribourg（弗里堡大学）；University of Bremen（不来梅大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马克斯·普朗克研究所）；Philipps-Universität Marburg（马尔堡菲利普斯大学）
Recent works have demonstrated that the Floquet-Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energy-like quantity that defines the spectrum of a periodically-driven system. Here we develop a new paradigm for the topological classification of Floquet-Bloch bands, based on the time-dependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologicall…
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the light's polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity $σ_{yx}=0$ at zero Fermi energy, to a Hall ins…
The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort mid-infrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. These photon dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circ…
Floquet engineering offers tantalizing opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, this approach faces a major challenge: generic interacting Floquet systems absorb energy from the drive, leading to uncontrolled heating which washes away the sought after behavior. How to achieve and control a non-trivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting one-dimensional periodically-driven electronic system coupled to a phonon heat bath. Usi…
Second-order topological insulators (SOTI) exhibit protected gapless boundary states at their hinges or corners. In this paper, we propose a generic means to construct SOTIs in static and Floquet systems by coupling one-dimensional topological insulator wires along a second dimension through dimerized hopping amplitudes. The Hamiltonian of such SOTIs admits a Kronecker sum structure, making it possible for obtaining its features by analyzing two constituent one-dimensional lattice Hamiltonians defined separately in two orthogonal dimensions. The resulting topological corner states do not rely …
We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of k-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum nu…
Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to localized quasi-stationary states in two-dimensional systems. These states include one-dimensional interface modes at the nodes of the external potential, and fractionalized excitations at vortices of the external potential. We also propose a setup by which light can induce currents in these systems. We explain these results by showing a close analogy to px+…
Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically-driven, or Floquet systems. Due to the periodicity of the quasienergy spectrum, we find it is possible f…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists towards periodically driving parameters of these systems. In such periodically driven setups, by varying the drive sequence the effective (Floquet) Hamiltonian can be engineered to be topological: then, the principle of bulk--boundary correspondence guarantees the existence of robust edge states. It has also been realized, however, that periodically driven s…
We propose a versatile framework to dynamically generate Floquet higher-order topological insulators by multi-step driving of topologically trivial Hamiltonians. Two analytically solvable examples are used to illustrate this procedure to yield Floquet quadrupole and octupole insulators with zero- and/or $π$-corner modes protected by mirror symmetries. Furthermore, we introduce dynamical topological invariants from the full unitary return map and show its phase bands contain Weyl singularities whose topological charges form dynamical multipole moments in the Brillouin zone. Combining them with …
We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically-driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time-evolution of wavepackets on the edge of the system. We consider the optimal driving …
We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$ and $π$. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-tri…
We present a Floquet scattering theory of electron waiting time distributions in periodically driven quantum conductors. We employ a second-quantized formulation that allows us to relate the waiting time distribution to the Floquet scattering matrix of the system. As an application we evaluate the electron waiting times for a quantum point contact, modulating either the applied voltage (external driving) or the transmission probability (internal driving) periodically in time. Lorentzian-shaped voltage pulses are of particular interest as they lead to the emission of clean single-particle excit…
