The manipulation of the helical edge states of two-dimensional topological insulators is crucial for the development of technological applications. Recently, an important step forward, namely, the experimental realization of a quantum point contact between helical edges, has been accomplished. We theoretically predict that such a quantum point contact, in the presence of a time periodic applied electric field, is characterized by a topological quantum phase transition in the Floquet spectrum. Moreover, we show that it is possible to detect this dynamical topological quantum phase transition by a bare conductance measurements.
We show how quantized transport can be realized in Floquet chains through encapsulation of a chiral or helical shift. The resulting transport is immutable rather than topological in the sense that it neither requires a band gap nor is affected by arbitrarily strong perturbations. Transport is still characterized by topological quantities but encapsulation of the shift prevents topological phase transitions. To explore immutable transport we introduce the concept of a shiftbox, explain the relevant topological quantities both for momentum-space dispersions and real-space transport, and study mo…
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 consider a Floquet triple-layer setup composed of a two-dimensional electron gas with spin-orbit interactions, proximity coupled to an s-wave superconductor and to a ferromagnet driven at resonance. The ferromagnetic layer generates a time-oscillating Zeeman field which competes with the induced superconducting gap and leads to a topological phase transition. The resulting Floquet states support a second-order topological superconducting phase with a pair of localized zero-energy Floquet Majorana corner states. Moreover, the phase diagram comprises a Floquet helical topological superconduct…
Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, k_F \approx k_{SO}. We show that this regime is characterized by a strongly anisotropic electron spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low frequency spin fluctuations along this direction. Since the spin response in the gapless regime k_F \not \approx k_{SO} has a power law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insens…
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport …
Time-periodic external drives have emerged as a powerful tool to artificially create topological phases of matter. Prime examples are Floquet topological insulators (FTIs), where a gapped bulk supports in-gap edge states, protected against symmetry-preserving local perturbations. Similar to an ordinary static topological insulator, the robustness of an edge state in a one-dimensional (1D) FTI shows up as a pinning of its quasienergy level, but now inside one of two distinct bulk gaps. Here we propose a scheme for probing this unique feature by observing transport characteristics of a 1D finite…
We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagat…
Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is a fundamental goal of nanoscale spintronics and an important prerequisite for the formation of Majorana bound states. Such a helical state is predicted in one-dimensional (1D) nanowires subject to strong Rashba SOC and spin-mixing, its hallmark being a characteristic reentrant behaviour in the conductance. Here, we report the first direct experimental observations of the reentrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingl…
We consider the superconducting proximity effect in a helical Luttinger liquid at the edge of a 2D topological insulator, and derive the low-energy Hamiltonian for an edge state tunnel-coupled to a s-wave superconductor. In addition to correlations between the left and right moving modes, the coupling can induce them inside a single mode, as the spin axis of the edge modes is not necessarily constant. This can be induced controllably in HgTe/CdTe quantum wells via the Rashba spin-orbit coupling, and is a consequence of the 2D nature of the edge state wave function. The distinction of these two…
Floquet Majorana fermions are steady states of equal superposition of electrons and holes in a periodically driven superconductor. We study the experimental signatures of Floquet Majorana fermions in transport measurements and show, both analytically and numerically, that their presence is signaled by a quantized conductance sum rule over discrete values of lead bias differing by multiple absorption or emission energies at drive frequency. We also study the effects of static disorder and find that the quantized sum rule is robust against weak disorder. Thus, we offer a unique way to identify t…
Time-resolved, angle-resolved photoemission spectroscopy (TR-ARPES) is a one-particle spectroscopic technique that can probe excitons (two-particle excitations) in momentum space. We present an ab initio, time-domain GW approach to TR-ARPES and apply it to monolayer MoS$_2$. We show that photoexcited excitons may be measured and quantified as satellite bands, as well as leading to the renormalization of the quasiparticle bands. These features are explained in terms of an exciton- Floquet phenomenon induced by an exciton time-dependent bosonic field, which is orders of magnitude stronger than l…
A two-dimensional topological insulator (2DTI) has an insulating bulk and helical spin-polarised edge modes robust to backscattering by non-magnetic disorder. While ballistic transport has been demonstrated in 2DTIs over short distances, larger samples show significant backscattering and a nearly temperature-independent resistance whose origin is unclear. 2DTI edges have shown a spin polarisation, however the degree of helicity is difficult to quantify from spin measurements. Here, we study 2DTI few-layer Na3Bi on insulating Al2O3. A non-local conductance measurement geometry enables sensitive…
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e. metallic bulk transport with conductivity of order $e^2/h$, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders…
Probing topological Floquet states in graphene with ultrafast terahertz scanning tunneling microscopy
University of Bremen（不来梅大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Paul Scherrer Institute（保罗谢尔研究所）；University of Fribourg（弗里堡大学）；The Flatiron Institute（_flatiron研究所）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）
We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet bandstructure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the bandstructure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anders…
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…
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…
We consider the fate of a helical edge state of a spin Hall insulator and its topological transition in presence of a circularly polarized light when coupled to various forms of environments. A Lindblad type equation is developed to determine the fermion occupation of the Floquet bands. We find by using analytical and numerical methods that non-secular terms, corresponding to 2-photon transitions, lead to a mixing of the band occupations, hence the light induced photocurrent is in general not perfectly quantized in the presence of finite coupling to the environment, although deviations are sma…
We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. The transport channels occur due to a $\mathbb Z_2$ non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. We discuss how the Floquet ladder can be implemented in a photonic waveguide lattice and show that the direction of transport in the resulting waveguide structure can be externally controlled by focu…
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…
For cold atomic systems, varying the optical lattice potential periodically provides a general and simple way to drive the system into phases with nontrivial topology. Besides its simplicity, this driving approach, compared to the usual driving approach by exerting an external electromagnetic field to the static system, has the merit that it does not break the original static system's time-reversal symmetry at any given time. Based on this approach, we find that a trivial insulator with time-reversal symmetry can be driven into a Floquet quantum spin Hall insulator. This novel state of matter …
We investigate the effects of alternating voltage on nonequilibrium quantum systems with localised phonon modes. Nonequilibrium Green's functions are utilised, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and foun…
The Lieb Lattice exhibits intriguing properties that are of general interest in both the fundamental physics and practical applications. Here, we investigate the topological Landau-Zener Bloch oscillation in a photonic Floquet Lieb lattice, where the dimerized helical waveguides is constructed to realize the synthetic spin-orbital interaction through the Floquet mechanism, rendering us to study the impacts of topological transition from trivial gaps to non-trivial ones. The compact localized states of flat bands supported by the local symmetry of Lieb lattice will be associated with other band…
We study the transport properties of a topological system coupled to an AC electric field by means of Floquet-Keldysh formalism. We consider a semi-infinite chain of dimers coupled to a semi-infinite metallic lead, and obtain the density of states and current when the system is out of equilibrium. Our formalism is non-perturbative and allows us to explore, in the thermodynamic limit, a wide range of regimes for the AC field, arbitrary values of the coupling strength to the metallic contact and corrections to the wide-band limit. We find that hybridization with the contact can change the dimeri…
Topological protection of edge state in quantum spin Hall systems relies only on time-reversal symmetry. Hence, S z conservation on the edge can be relaxed which can have an interferometric manifestation in terms of spin Berry phase. Primarily it could lead to the generation of spin Berry phase arising from a closed loop dynamics of electrons. Our work provides a minimal framework to generate and detect these effects by employing both spin-unpolarized and spin-polarized leads. We show that spin-polarized leads could lead to resonances or anti-resonances in the two-terminal conductance of the i…
Helical superconductors form a two dimensional, time-reversal invariant topological phase characterized by a Kramers pair of Majorana edge modes (helical Majorana modes). Existing detection schemes to identify this phase rely either on spin transport properties, which are quite difficult to measure, or on local charge transport, which allows only a partial identification. Here we show that the presence of helical Majorana modes can be unambiguously revealed by measuring the nonlocal charge conductance. Focusing on a superconducting ring, we suggest two experiments that provide unique and robus…
The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunction of collective excitations of such states, accompanied by peculiar spin patterns in their magnetization. Both effect…
We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin …
One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial electronic bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in se…
In the heterostructure composed of a topological insulator sandwiched by two s-wave superconductors, the time reversal invariant topological superconducting phase, possessing helical Majorana edge modes, is found to exist when the two s-wave superconductors form a Josephson junction with a pi phase shift. Based on such a heterostructure, a helical Dirac-Majorana interferometer is proposed to directly measure a unique transport signature of the helical Majorana modes. Furthermore, we envision how our proposal can be realized on the basis of existing materials such as Bi2Se3 or Bi2Te3 thin films…
We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are non-contractible loops in the spectrum of the Floquet propagator that are separated by an imaginary gap. Such loops occur exclusively in non-Hermitian Floquet systems. We define the corresponding topological invariant as the winding number of the Floquet propagator relative to the imaginary gap. To relate topology to transport, we introduce the concept of regularized dynamics of non-Hermitian chains. We establish that, under the…
We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase induced by a small magnetic field threading the junction known as Doppler shift (DS), combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely non-local thermoelectric effect …
Simulating multi-node Weyl semimetals in a Mixed Floquet lattice
Indian Institute of Science Education and Research (IISER) Tirupati（印度科学教育研究所提鲁帕蒂分校）；Indian Institute of Science Education and Research Bhopal（印度科学教育研究所博帕尔分校）
Helical Anomaly from Concurrent $\mathbb{Z}$ and $\mathbb{Z}_2$ Topology in an Acoustic Semimetal
Department of Materials Science and Engineering, Nanjing University（南京大学材料科学与工程系）；School of Physics, Nanjing University（南京大学物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University（南京大学江苏省人工功能材料重点实验室）；Jiangsu Physical Science Research Center, Nanjing University（南京大学江苏省物理科学研究中心）
Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological…
Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems
Université Libre de Bruxelles（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Collège de France（法兰西公学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Sorbonne Université（索邦大学）；Centro Atómico Bariloche（巴里洛切原子能中心）；Instituto Balseiro（巴尔塞罗研究所）；Comisión Nacional de Energía Atomica (CNEA)（国家原子能委员会）；Universidad Nacional de Cuyo (UNCUYO)（门多萨国立大学）；Instituto de Nanociencia y Nanotecnología (INN-Bariloche)（纳米科学与技术研究所）；Consejo Nacional de Investigaciones Científicas y Tecnicas (CONICET)（国家科学研究委员会）
Circularly polarised light opens a gap in the Dirac spectrum of graphene and topological insulator (TI) surfaces, thereby inducing a quantum Hall-like phase. We propose to detect the accompanying edge states and their current by the magnetic field they produce. The topological nature of the edge states is reflected in the mean orbital magnetization of the sample, which shows a universal linear dependence as a function of a generalized chemical potential - independent of the driving details and the properties of the material. The proposed protocol overcomes several typically encountered problem…
Akin to zero-mode anomalies, such as the chiral anomaly of edge states in quantum Hall effect, in this work, a pi-mode anomaly is proposed in a 1+1 dimensional periodically-driven topological/normal insulator (TI/NI) heterostructure. Usually, when coupling in a background gauge field, the zero modes on domain walls would provide an anomalous current term that is eventually canceled by additional boundary contributions from the topological bulk, via the Callan-Harvey mechanism. This anomaly cancellation associated with the generalization of bulk-boundary correspondence is called anomaly inflow.…
We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4Pi-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that signatures of this effect can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestatio…
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 …
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 th…
Helical symmetry of massive Dirac fermions is broken explicitly in the presence of electric and magnetic fields. Here we present two equations for the divergence of helical and axial-vector currents following the Jackiw-Johnson approach to the anomaly of the neutral axial vector current. We discover the contribution from the helical symmetry breaking is attributed to the occupancy of the two states at the top of the valence band and the bottom of the conduction band. The explicit symmetry breaking fully cancels the anomalous correction from the quantum fluctuation in the band gap. The chiral a…
