Edge Currents Research Articles

Magnetic edge states and edge current in honeycomb zigzag nanoribbons by Kane–Mele–Hubbard model

We investigate spin-dependent edge states of honeycomb zigzag nanoribbons with a focus on electron–electron interaction as the origin of the initial edge magnetism which is assumed to be anti-ferromagnetism order as a stable form. We study the effect of intrinsic spin–orbit interaction (SOI) and also applied in-plane transverse electric field on low energy spectrum and edge spin density. Tight-binding method in the framework of the self-consistent Kane–Mele–Hubbard model has been utilized for exploring electronic properties. Edge currents and electric dipole moments are also calculated. Results show electric field and SOI can dramatically affect the edge states and energy gaps. A transition from a magnetic edge state to a non-magnetic one occurs at critical values of SOI and electric field. Furthermore, the system goes into the topological insulator phase at sufficiently large SOI strengths. The results of edge spin density, electric dipole moment, and spin currents indicate that one can reach the favorite spin-dependent transport by manipulating the electric field and SOI in a zigzag nanoribbon. The outcome may pave the way to further control of spin-based transport in future devices.

Fast Electrically Switchable Large Gap Quantum Spin Hall States in MGe2Z4

AbstractSpin‐polarized conducting edge currents counterpropagate in quantum spin Hall (QSH) insulators and are protected against disorder‐driven localizations by the time‐reversal symmetry. Using these spin‐currents for device applications requires materials with a large bandgap and fast switchable QSH states. By means of in‐depth first‐principles calculations, this study demonstrates the large bandgap and fast switchable QSH state in a newly introduced 2D material family with 1T′‐MGe2Z4 (M = Mo or W and Z = P or As). These Ge‐based compounds show superior properties with respect to other members of the same family. For the WGe2As4 monolayer it can stabilize the 1T′‐phase, while for the other members of the family, this study needs an appropriate strain. The dynamically stable 1T′‐MGe2Z4 monolayers have a large energy gap up to 237 meV for WGe2As4. These materials undergo a phase transition from a QSH insulator to a trivial insulator with a Rashba‐like spin splitting under the influence of an out‐of‐plane electric field, demonstrating a fast tunability of the bandgap and its band topology for the Ge‐based compounds. Fast topological phase switching in a large gap 1T′‐MGe2Z4 QSH insulators have potential applications in low‐power devices, quantum computation, and quantum communication.

Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

Giant nonlocal edge conduction in the axion insulator state of MnBi2Te4

The recently discovered antiferromagnetic (AFM) topological insulator (TI) MnBi2Te4 represents a versatile material platform for exploring exotic topological quantum phenomena in nanoscale devices. It has been proposed that even-septuple-layer (even-SL) MnBi2Te4 can host helical hinge currents with unique nonlocal behavior, but experimental confirmation is still lacking. In this work, we report transport studies of exfoliated MnBi2Te4 flakes with varied thicknesses down to the few-nanometer regime. We observe giant nonlocal transport signals in even-SL devices when the system is in the axion insulator state but vanishingly small nonlocal signal in the odd-SL devices at the same magnetic field range. In conjunction with theoretical calculations, we demonstrate that the nonlocal transport is via the helical edge currents mainly distributed at the hinges between the side and top/bottom surfaces. The helical edge currents in the axion insulator state may find unique applications in topological quantum devices.

Collective Flows Drive Cavitation in Spinner Monolayers.

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced.

Steering edge currents through a Floquet topological insulator

Periodic driving may cause topologically protected, chiral transport along edges of a two-dimensional (2D) lattice that, without driving, would be topologically trivial. We study what happens if one adds a different on-site potential along the diagonal of such a 2D grid. In addition to the usual bulk and edge states, the system then also exhibits doublon states, analogous to two interacting particles in one dimension. A particle initially located at an edge propagates along the system's boundary. Its wave function splits when it hits the diagonal and continues propagating simultaneously along the edge and the diagonal. The strength of the diagonal potential determines the ratio between both parts. We show that for specific values of the diagonal potential, hopping onto the diagonal is prohibited so that the system effectively separates into two triangular lattices. For other values of the diagonal potential, we find a temporal delay between the two contributions traveling around and through the system. This behavior could enable the steering of topologically protected transport of light along the edges and through the bulk of laser-inscribed photonic waveguide arrays.

Chiral edge dynamics and quantum Hall physics in synthetic dimensions with an atomic erbium Bose-Einstein condensate

Quantum Hall physics is at the heart of research on both matter and artificial systems, such as cold atomic gases, with nontrivial topological order. We report on the observation of a chiral edge current by transferring atomic wave packets simultaneously to opposite edges of a synthetic Hall system realized in the two-dimensional state space formed by one spatial and one synthetic dimension encoded in the $J=6$ electronic spin of erbium atoms. To characterize the system, the Hall drift of the employed atomic Bose-Einstein condensate in the lowest Landau-like level is determined. The topological properties are verified by determining the local Chern marker, and upon performing low-lying excitations both cyclotron and skipping orbits are observed in the bulk and edges, respectively. Future prospects include studies of novel topological phases in cold-atom systems.

Pure magnon valley currents in a patterned ferromagnetic thin film

We propose a new method to generate pure magnon valley currents in ferromagnetic thin films with triangular antidot lattices. We find that inhomogeneous distortions can generate pseudomagnetic fields which can be up to 60 $\mathrm{T}$ for magnons, and give rise to well-defined Landau levels. The pseudomagnetic fields push magnons at different valleys $\mathrm{K}$ and ${\mathrm{K}}^{\ensuremath{'}}$ transversely to opposite directions and accumulate at opposite edges, leading to magnon valley Hall effect and forming pure magnon valley edge currents. We also find that the oppositely directed pseudomagnetic fields result in magnon snake states at the center of the ribbon, forming pure magnon valley currents. Our work might pave a new way to manipulate magnon transport by using artificial designed structures.

Edge Currents Induced by AC Electric Field in Two-Dimensional Dirac Structures

Edges in two-dimensional structures are the source of nonlinear transport and optical phenomena which are particularly important in small-size flakes. We present a microscopic theory of the edge photogalvanic effect, i.e., the formation of DC electric current flowing along the sample edges in response to AC electric field of the incident terahertz radiation, for two-dimensional Dirac materials including the systems with massive and massless charge carriers. The edge current direction is controlled by the AC field polarization. The spectral dependence of the current is determined by the carrier dispersion and the mechanism of carrier scattering, as shown for single-layer and bilayer graphene as examples.

Gauge invariance and anomalies in condensed matter physics

This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called “gauge theory of states/phases of matter.” The chiral anomaly, which plays quite a prominent role in that formalism, is recalled. I then sketch an application of the chiral anomaly in 1 + 1 dimensions to quantum wires. Subsequently, some elements of the quantum Hall effect in two-dimensional (2D) gapped (“incompressible”) electron liquids are reviewed. In particular, I discuss the role of anomalous chiral edge currents and of the anomaly inflow in 2D gapped electron liquids with explicitly or spontaneously broken time reversal, i.e., in Hall and Chern insulators. The topological Chern–Simons action yielding transport equations valid in the bulk of such systems and the associated anomalous edge action are derived. The results of a general classification of “Abelian” Hall insulators are outlined. After some remarks on induced Chern–Simons actions, I sketch results on certain 2D chiral photonic wave guides. I then continue with an analysis of chiral edge spin-currents and bulk response equations in time-reversal invariant 2D topological insulators of electron gases with spin–orbit interactions. The “chiral magnetic effect” in 3D systems and axion-electrodynamics are reviewed next. This prepares the ground for an outline of a general theory of 3D topological insulators, including “axionic insulators.” Some remarks on Weyl semi-metals, which exhibit the chiral magnetic effect, and on Mott transitions in 3D systems with dynamical axion-like degrees of freedom conclude this review.

Evaluation of MR ratio and reliability of MTJ device having SiN sidewall by modifying reference layer thickness

For high-performance magnetic tunnel junction devices, the ion beam etching (IBE) process is improved by including the fabrication of a SiN sidewall around the MgO tunnel barrier layer. This sidewall prevents the redeposition from lower metal layers on the edge of the MgO layer. The magnetoresistance (MR) ratio at an IBE angle of 20° is larger than that at 60°. Edge current by the redeposition is suppressed by the SiN sidewall, and etching damage is reduced by decreasing the IBE angle. The dependence of the MR ratio on the reference layer thickness is investigated using an FeB reference layer with thicknesses of 0.7, 0.9 and 1.05 nm. The MR ratio increases with the reference layer thickness, and an MR ratio of 180% is achieved at a layer thickness of 1.05 nm. A resistance variability of under 0.5% confirms the high resistance stability of the tested device.

Staggered pseudo magnetic field in twisted transition metal dichalcogenides: Physical origin and experimental consequences

In systems comprised of two layers of certain semiconductors stacked with a certain twist angle, the quantum mechanics of electron transfer between layers is believed to give rise to a ``staggered flux'' physics in which electrons move as though exposed to an extremely strong, but rapidly spatially varying, magnetic field. This staggered flux, heretofore thought of as a theoretical construct, is shown to give rise to dramatic, observable behavior, including ``Hofstadter butterfly'' structures in the electron spectrum, sign reversals in the Hall effect, and edge currents in systems with junctions or spatially varying interlayer potentials.

Floquet Superradiance Lattices in Thermal Atoms.

Floquet modulation has been widely used in optical lattices for coherent control of quantum gases, in particular for synthesizing artificial gauge fields and simulating topological matters. However, such modulation induces heating which can overwhelm the signal of quantum dynamics in ultracold atoms. Here we report that the thermal motion, instead of being a noise source, provides a new control knob in Floquet-modulated superradiance lattices, which are momentum-space tight-binding lattices of collectively excited states of atoms. The Doppler shifts combined with Floquet modulation provide effective forces along arbitrary directions in a lattice in frequency and momentum dimensions. Dynamic localization, dynamic delocalization, and chiral edge currents can be simultaneously observed from a single transport spectrum of superradiance lattices in thermal atoms. Our Letter paves a way for simulating Floquet topological matters in room-temperature atoms and facilitates their applications in photonic devices.

Effect of external fields in high Chern number quantum anomalous Hall insulators

A quantum anomalous Hall state with a high Chern number has so far been realized in multilayer structures consisting of alternating magnetic and undoped topological insulator (TI) layers. However, in previous proposals, the Chern number can only be tuned by varying the doping concentration or the width of the magnetic TI layers. This drawback largely restricts the applications of dissipationless chiral edge currents in electronics since the number of conducting channels remains fixed. In this paper, we propose a way of varying the Chern number at will in these multilayered structures by means of an external electric field applied along the stacking direction. In the presence of an electric field in the stacking direction, the inverted bands of the unbiased structure coalesce and hybridize, generating new inverted bands and collapsing the previously inverted ones. In this way, the number of Chern states can be tuned externally in the sample, without the need for modifying the number and width of the layers or the doping level. We showed that this effect can be uncovered by the variation of the transverse conductance as a function of the electric field at constant injection energy at the Fermi level.

Observing the quantum topology of light.

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

Linear simulation of kinetic Peeling-Ballooning mode with bootstrap current under the BOUT++ gyro landau fluid code

The kinetic peeling-ballooning mode (KPBM) plays a crucial role in the edge turbulence and transport in a tokamak plasma. However, the impact of the bootstrap current on KPBM is still unclear. Simulations of KPBM using the BOUT++ gyro-Landau-fluid code are presented in this study. To investigate the KPBM in a real tokamak equilibrium, the global equilibrium solver CORSICA was employed to generate a set of realistic equilibria of shifted circular geometry, including the Shafranov shift, elongation effects and bootstrap current. The linear instability property of the KPBM is observed in a wide range of pressure gradient and parallel current density in the pedestal region. Our results indicate that the bootstrap current has a stabilizing effect on the high-n KPBM over the entire pedestal region. Here, n is the toroidal mode number. In comparison with the ideal magnetohydrodynamic peeling-ballooning mode stability diagram, the unstable KPBM region shrinks and shifts to low ( where denotes the pressure at the peak pressure gradient position) with the increase of the bootstrap current. Moreover, we find that the low-n kink modes are driven unstable by the bootstrap current in the second stable region. With an additional external current drive on top of the bootstrap current, the low-n KPBMs can be stabilized when the total edge current is sufficiently large, although the low-n kink mode is still unstable in the region with .

Cavity-induced chiral edge currents and spontaneous magnetization in two-dimensional electron systems

We consider a laterally confined two-dimensional electron gas (2DEG), placed inside a gyrotropic cavity. Splitting of the circularly polarized electromagnetic modes leads to the emergence of the ground state spontaneous magnetization, anomalous Hall effect and chiral edge currents in 2DEG. We examine the dependence of the magnetization and edge current density on the system size for two particular cases of the confining potential: infinite wall and parabolic potentials. We show that paramagnetic and diamagnetic contributions to the edge currents have qualitatively different dependence on the system size. These findings pave the route to the design quantum electrodynamic engineering of the material properties of the mesoscopic electron systems.

Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows

Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension.

Higher angular momentum pairing states in Sr2RuO4 in the presence of longer-range interactions

The superconducting symmetry of Sr$_2$RuO$_4$ remains a puzzle. Time-reversal symmetry breaking $d_{x^2-y^2} + ig_{xy(x^2-y^2)}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random phase approximation. We show that the inclusion of second nearest neighbor repulsions, together with non-local SOC in the $B_{2g}$ channel or orbital-anisotropy of the non-local interactions, can have a significant impact on the stability of both $d_{x^2-y^2}$- and $g$-wave pairing channels. We analyze the properties, such as Knight shift and spontaneous edge current, of the realized $d_{x^2-y^2} + ig$, $s^{\prime}+id_{xy}$ and mixed helical pairings in different parameter spaces and find that the $d_{x^2-y^2} + ig$ solution is in better agreement with the experimental data.

Electrical control of spin-polarized topological currents in monolayer WTe2

We evidence the possibility for coherent electrical manipulation of the spin orientation of topologically protected edge states in a low-symmetry quantum spin Hall insulator. By using a combination of ab initio simulations, symmetry-based modeling, and large-scale calculations of the spin Hall conductivity, it is shown that small electric fields can efficiently vary the spin textures of edge currents in monolayer 1T'-${\mathrm{WTe}}_{2}$ by up to a 90-degree spin rotation, without jeopardizing their topological character. These findings suggest a new kind of gate-controllable spin-based device, topologically protected against disorder and of relevance for the development of topological spintronics.