We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multi-terminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at $\pm\,\hbarΩ/2$ lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, where two terms cancel out exactly. More interestingly, we show that near the Dirac point changing the laser polarization (circular right or circular left) controls the Hall conductance, by allowing to switch it on or off, or even by flipping its sign, thereby reversing the chirality of the edge states. This might lead to new avenues to fully control topologically protected transport.
The interplay between magnetic vortex polarity, chirality and the curvature of the underlying surface results in a dependence of the vortex polarity switching efficiency on the vortex chirality. The switching is studied numerically by applying a short Gauss pulse of the external magnetic field to a spherical cap within its cut plane. The minimum field intensity required for the switching essentially depends on the vortex chirality and it does not depend on the initial vortex polarity. This effect decreases with the curvature radius increasing and it vanishes in the planar limit.
In conventional domain wall systems the aim of a high domain wall velocity may be hindered by the occurrence of a Walker breakdown at comparably low current density. We show how a Rashba interaction can stabilize the domain wall dynamics and thereby shift the Walker breakdown to higher current densities. The Rashba interaction creates a field like spin torque, which breaks the symmetry of the system and modifies the internal structure of the domain wall. Besides a shift of the Walker breakdown it can additionally induce a chirality switch of the domain wall at sufficient Rashba fields. The pre…
The interlayer van der Waals interaction in twisted bilayer graphene (tBLG) induces both in-plane and out-of-plane atomic displacements showing complex patterns that depend on the twist angle. In particular, for small twist angles, within each graphene layer, the relaxations give rise to a vortex-like displacement pattern which is known to affect the dispersion of the flat bands. Here, we focus on yet another structural property, the chirality of the twisted bilayer. We perform first-principles calculations based on density functional theory to investigate the properties induced by twist chira…
We theoretically study the equilibrium and dynamic properties of nanoscale magnetic tunnel junctions (MTJs) and magnetic wires, in which an electric field controls the magnetic anisotropy through spin-orbit coupling. By performing micromagnetic simulations, we construct a rich phase diagram and find that, in particular, the equilibrium magnetic textures can be tuned between Neel and Bloch domain walls in an elliptical MTJ. Furthermore, we develop a phenomenological model of a quasi-one-dimensional domain wall confined by a parabolic potential and show that, near the Neel-to-Bloch-wall transiti…
Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Neel walls and quantify the DMI induced by the Pd capp…
Magnetic vortices are characterized by the senses of in-plane magnetization chirality and by the polarity of the vortex core. The electrical control of vortex polarity and chirality is highly demanded not only for fundamental understanding on spin dynamics in nano-disks under different circumstances, but also for technological applications, such as magnetic non-volatile memories and spin torque oscillators for neuromorphic computing. Here we report a novel approach that enables one to electrically control both the vortex chirality and polarity with low energy consumption. Thorough micromagneti…
We propose a general edge index definition for two-dimensional Floquet topological phases based on a switch-function formalism. When the Floquet operator has a spectral gap the index covers both clean and disordered phases, anomalous or not, and does not require the bulk to be fully localized. It is interpreted as a non-adiabatic charge pumping that is quantized when the sample is placed next to an effective vacuum. This vacuum is gap-dependent and obtained from a Floquet Hamiltonian. The choice of a vacuum provides a simple and alternative gap-selection mechanism. Inspired by the model from R…
Motivated by recent pump-probe spectroscopies, we study the effect of phonon dissipation and potential cooling on the nonequilibrium distribution function in a Floquet topological state. To this end, we apply a Floquet kinetic equation approach to study two dimensional Dirac fermions irradiated by a circularly polarized laser, a system which is predicted to be in a laser induced quantum Hall state. We find that the initial electron distribution shows an anisotropy with momentum dependent spin textures whose properties are controlled by the switching-on protocol of the laser. The phonons then s…
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…
Recent advances on the stabilization and manipulation of chiral magnetization configurations in systems consisting in alternating atomic layers of ferromagnetic and non-magnetic materials hold promise of innovation in spintronics technology. The low dimensionality of the systems promotes spin orbit driven interfacial effects like antisymmetric Dzyaloshinskii-Moriya interactions (DMI) and surface magnetic anisotropy, whose relative strengths may be tuned to achieve stable nanometer sized magnetic objects with fixed chirality. While in most of the cases this is obtained by engineering complex mu…
Results are presented for the occupation probabilities and current densities of bulk and edge states of half-filled graphene in a cylindrical geometry, and irradiated by a circularly polarized laser. It is assumed that the system is closed, and that the laser has been switched on as a quench. Laser parameters corresponding to some representative topological phases are studied: one where the Chern number of the Floquet bands equals the number of chiral edge modes, a second where anomalous edge states appear in the Floquet Brillouin zone boundaries, and a third where the Chern number is zero, ye…
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）
The Dzyaloshinskii-Moriya interaction (DMI) has drawn great attention as it stabilizes magnetic chirality, with important implications in fundamental and applied research. This antisymmetric exchange interaction is induced by the broken inversion symmetry at interfaces or in non-centrosymmetric lattices. Significant interfacial DMI was found often at magnetic / heavy-metal interfaces with large spin-orbit coupling. Recent studies have shown promise of induced DMI at interfaces involving light elements such as carbon (graphene) or oxygen. Here we report direct observation of induced DMI by chem…
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…
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…
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…
The valley-polarized quantum anomalous Hall (VQAH) state, which forwards a strategy for combining valleytronics and spintronics with nontrivial topology, attracts intensive interest in condensed-matter physics. So far, the explored VQAH states have still been limited to magnetic systems. Here, using the low-energy effective model and Floquet theorem, we propose a different mechanism to realize the Floquet VQAH state in nonmagnetic heterobilayers under light irradiation. We then realize this proposal via first-principles calculations in transition metal dichalcogenide heterobilayers, which init…
Fu and Kane have discovered that a topological insulator with induced s-wave superconductivity (gap $Δ_0$, Fermi velocity $v_{\rm F}$, Fermi energy $μ$) supports chiral Majorana modes propagating on the surface along the edge with a magnetic insulator. We show that the direction of motion of the Majorana fermions can be inverted by the counterflow of supercurrent, when the Cooper pair momentum along the boundary exceeds $Δ_0^2/μv_{\rm F}$. The chirality inversion is signaled by a doubling of the thermal conductance of a channel parallel to the supercurrent. Moreover, the inverted edge can tran…
We study the transport properties of a monolayer transition metal dichalcogenide (TMDC) ribbon subject to a time periodic circularly polarized laser field. First, we calculate the quasienergy spectrum within the framework of the Floquet theory and analyze the nontrivial topology of the Floquet bulk gaps. The later is revealed by the presence of chiral edge states inside the bulk gaps in finite samples, in agreement with the calculation of the appropriate winding numbers as a function of both the energy and the amplitude of the laser field. The effect of the time dependent perturbation on the e…
The spin mixing conductance (SMC) is a key quantity determining efficiency of spin transport across interfaces. Thus, knowledge of its precise value is required for accurate measurement of parameters quantifying numerous effects in spintronics, such as spin-orbit torque, spin Hall magnetoresistance, spin Hall effect and spin pumping. However, the standard expression for SMC, provided by the scattering theory in terms of the reflection probability amplitudes, is inapplicable when strong spin-orbit coupling (SOC) is present directly at the interface. This is the precisely the case of topological…
We report on the emergence of laser-induced chiral edge states in graphene ribbons. Insights on the nature of these Floquet states is provided by an analytical solution which is complemented with numerical simulations of the transport properties. Guided by these results we show that graphene can be used for realizing non-equilibrium topological states with striking tunability: While the laser intensity can be used to control their velocity and decay length, changing the laser polarization switches their propagation direction.
We propose a magnetization reversal model to explain the perpendicular switching of a single ferromagnetic layer induced by an in-plane current. Contrary to previously proposed reversal mechanisms that such magnetic switching is directly from the Rashba or spin Hall effects, we suggest that this type of switching arises from the current-induced chirality dependent domain wall motion. By measuring the field dependent switching behaviors, we show that such switching can also be achieved between any two multidomain states, and all of these switching behaviors can be well explained by this model. …
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…
Photonic Floquet lattices provide an excellent platform for manipulating different topologically protect-ed edge states. However, anti-chiral edge states have not been discussed much in Floquet lattices. Here, we propose a waveguide structure by combining two honeycomb Floquet photonic lattices with oppo-site rotation directions. In this structure, we find that the anti-chiral edge states have the same trans-mission direction on two parallel body edges. With an increasing modulation phase difference between the two sublattices in one direction, the width of the band gap becomes smaller and the…
The anomalous Floquet Anderson insulator (AFAI) is a two dimensional periodically driven system in which static disorder stabilizes two topologically distinct phases in the thermodynamic limit. The presence of a unit-conducting chiral edge mode and the essential role of disorder induced localization are reminiscent of the integer quantum Hall (IQH) effect. At the same time, chirality in the AFAI is introduced via an orchestrated driving protocol, there is no magnetic field, no energy conservation, and no (Landau level) band structure. In this paper we show that in spite of these differences th…
Topological charges and parity selection at Floquet quasienergy degeneracies
Quantum Advanced Research Center, CSIC（西班牙科学研究中心量子先进研究中心）；Instituto de Ciencia de Materiales de Madrid, CSIC（西班牙科学研究中心马德里材料科学研究所）；Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, Université de Toulouse, CNRS（图卢兹大学FERMI碰撞聚合反应实验室（UMR 5589，CNRS））
We report gate-induced enhancement of intrinsic charge rectification without p-n junctions in chiral semiconductor Te under magnetic field B. As gating shifts the chemical potential to the valence band maximum of Te, the charge rectification efficiency is enhanced hundredfold. By integrating model calculations, we attribute the charge rectification to the B-induced asymmetry of the chiral band structure. We also show that the carrier density subject to this asymmetry is augmented by a saddle-point structure near the valence band maximum, which further enhances the gate-tunable charge rectifica…
Floquet engineering is one of the most vigorous fields in periodically driven (Floquet) systems, with which we can control phases of matter usually by high-frequency drives. In this paper, with Floquet engineering by a combination of high-frequency drives and resonant drives, we propose a way to realize nontrivial topological phases protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry only in the presence of a $\mathbb{Z}_2$ symmetry, using a robust emergent $\mathbb{Z}_2$ symmetry induced by the resonant drives. Moreover, the symmetry protected topological (SPT) phases are switchable be…
Periodically driven non-Hermitian systems can exhibit rich topological band structure and non-Hermitian skin effect, without analogs in their static or Hermitian counterparts. In this work we investigate the exceptional band-touching points in the Floquet quasi-energy bands, the topological characterization of such exceptions points and the Floquet non-Hermitian skin effect (FNHSE). Specifically, we exploit the simplicity of periodically quenched two-band systems in one dimension or two dimensions to analytically obtain the Floquet effective Hamiltonian as well as locations of the many excepti…
The effect of noise on the process of high-speed remagnetization of vortex state of a pentagonal array of five circular magnetic nanoparticles is studied by means of computer simulation of Landau-Lifshits model. The mean switching time and its standard deviation of the reversal between the counterclockwise and clockwise vorticities have been computed. It has been demonstrated that with the reversal by the pulse with sinusoidal shape, the optimal pulse duration exists, which minimizes both the mean switching time (MST) and the standard deviation (SD). Besides, both MST and SD significantly depe…
Universal driving protocol for symmetry-protected Floquet topological phasesWe propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$ dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters…
We propose an ultrafast way to generate spin chirality and spin current in a class of multiferroic magnets using a terahertz circularly polarized laser. Using the Floquet formalism for periodically driven systems, we show that it is possible to dynamically control the Dzyaloshinskii-Moriya interaction in materials with magnetoelectric coupling. This is supported by numerical calculations, by which additional resonant phenomena are found. Specifically, when a static magnetic field is applied in addition to the circularly polarized laser, a large resonant enhancement of spin chirality is observe…
Exploiting the possibility of temporal variation of the winding number, we have prepared a SSH chain in its {\it stroboscopic} topological state, starting from the trivial one, by application of a periodic perturbation. The periodic driving, we employ here, is adiabatically switched on to break the particle-hole symmetry and generate a chiral mass term in the effective Floquet Hamiltonian; consequently the Floquet Hamiltonian also gets deformed without crossing the gapless quantum critical point. The particle hole symmetry is subsequently restored in the Floquet Hamiltonian by adiabatically sw…
