Edge Currents Research Articles

A new Control Volume Finite Element Method for the stable and accurate solution of the drift–diffusion equations on general unstructured grids

We present a new Control Volume Finite Element Method with multi-dimensional Scharfetter–Gummel upwinding (CVFEM-SG) for the drift–diffusion equations. The method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one-dimensional Scharfetter–Gummel edge currents into curl-conforming elemental currents. These elemental currents combine the upwind effect from all element edges and enable accurate computation of the flux on arbitrary surfaces inside the elements. In so doing, we obtain a formulation that is stable and accurate on general unstructured finite element grids. This approach sets our formulation apart from other methods, which require the control volumes to be topologically dual to the primal grid. Numerical studies of the CVFEM-SG for a suite of scalar advection–diffusion test problems confirm the accuracy and the robustness of the new formulation. Simulations of a PN diode and an n-channel MOSFET device demonstrate the performance of the method for the fully coupled drift–diffusion system.

Anomalous Hall effects of light and chiral edge modes on the Kagomé lattice

We theoretically investigate a photonic Kagom\'e lattice which can be realized in microwave cavity arrays using current technology. The Kagom\'e lattice exhibits an exotic band structure with three bands, one of which can be made completely flat. The presence of artificial gauge fields makes it possible to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial. By tuning the artificial fluxes or in the presence of disorder, the flat band can also acquire a bandwidth in energy allowing the coexistence between chiral edge modes and bulk extended states; in this case the chiral modes become fragile towards scattering into the bulk. The photonic system then exhibits equivalents of both a quantum Hall effect without Landau levels and an anomalous Hall effect characterized by a nonquantized Chern number. We discuss experimental observables such as local density of states and edge currents. We show how synthetic uniform magnetic fields can be engineered, which allows an experimental probe of Landau levels in the photonic Kagom\'e lattice. We then draw on semiclassical Boltzmann equations for transport to devise a method to measure Berry's phases around loops in the Brillouin zone. The method is based solely on wave-packet interference and can be used to determine band Chern numbers or the photonic equivalent of the anomalous Hall response. We demonstrate the robustness of these measurements towards on-site and gauge-field disorder. We also show the stability of the anomalous quantum Hall phase for nonlinear cavities and for (artificial) atom-photon interactions.

Topological Invariants of Edge States for Periodic Two-Dimensional Models

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z_2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.

Use of quantum quenches to probe the equilibrium current patterns of ultracold atoms in an optical lattice

Atomic bosons and fermions in an optical lattice can realize a variety of interesting condensed matter states that support equilibrium current patterns in the presence of synthetic magnetic fields or non-abelian gauge fields. As a route to probing such mass currents, we propose a nonequilibrium quantum quench of the Hamiltonian that dynamically converts the current patterns into experimentally measurable real-space density patterns. We illustrate how a specific such "unidirectional" quench of the optical lattice can be used to uncover checkerboard and stripe current orders in lattice Bose superfluids and Fermi gases, as well as chiral edge currents in an integer quantum Hall state.

Field-Inducedp-Wave Superconducting State of Mesoscopic Systems

By using Bogoliubov-de Gennes equations, we study superconducting (SC) states in a quasi-two-dimensional system of radius R. It is shown that no vortices exist in s-wave SC samples with R < R(c) ~ ξ(0), the T = 0 coherence length. We predict that chiral p-wave states exhibit superconductivity for R < R(c) only in the presence of a vortex with opposite chirality. This induced SC phase is a consequence of nonzero chirality of the pairing order parameter and implies the presence of chiral edge currents. Our study may be applied to sharply probing the pairing symmetry of unconventional superconductors.

Difference of scattering geometrical optics components and line integrals of currents in modified edge representation

Equivalent edge currents (EECs) are widely used to asymptotically extract and express the diffraction from the periphery of the scatterers, as in the concept suggested by Young. Authors proposed novel EECs based on the unique concept named as Modified Edge Representation (MER), for surface to line integral reduction of Physical Optics (PO) radiation integral. MER is based upon not only asymptotic approximation but also Stokes' theorem, and it has remarkable accuracy even for small scatterers and is uniformly applicable at the geometrical boundaries. Moreover MER‐EECs are clearly defined not only at the edges but also everywhere on the scatterer surface, with the singularity at the stationary phase point (SPP) if any. It comes that the radiation integral in general, consisting of both the diffraction and the Geometrical Optics (GO) components, could be reduced into two sets of line integration of MER‐EECs along the periphery and the indentation at SPPs. In this paper, the GO reflection is numerically compared with the MER indentation integral around the reflected point for the dipole scattering from an ellipsoid; the error is empirically derived in analytical form.

Properties of edge states in a spin-triplet two-band superconductor

Motivated by Sr2RuO4 the magnetic properties of edge states in a two-band spin-triplet superconductor with electron- and hole-like Fermi surfaces are investigated assuming chiral p-wave pairing symmetry. The two bands correspond to the alpha-beta-bands of Sr2RuO4 and are modeled within a tight-binding model including inter-orbital hybridization and spin-orbit coupling effects. Including superconductivity the quasiparticle spectrum is determined by means of a self-consistent Bogolyubov-de Gennes calculation. While a full quasiparticle excitation gap appears in the bulk, gapless states form at the edges which produce spontaneous spin and/or charge currents. The spin current is the result of the specific band structure while the charge current originates from the superconducting condensate. Together they induce a small spin polarization at the edge. Furthermore onsite Coulomb repulsion is included to show that the edge states are unstable against the formation of a Stoner-like spin polarization of the edge states. Through spin-orbit coupling the current- and the correlation-induced magnetism are coupled to the orientation of the chirality of the superconducting condensate. We speculate that this type of phenomenon could yield a compensation of the magnetic fields induced by currents and also explain the negative result in the recent experimental search for chiral edge currents.

Electron transport in suspended semiconductor structures with two-dimensional electron gas

We study electron transport in suspended semiconductor microstructures fabricated from AlAs/GaAs membranes containing a high mobility two-dimensional electron gas. In quantizing magnetic fields, a reflection of edge current channels from the border of suspended area is observed resulting in the absence of vanishing magnetoresistance in the quantum Hall effect (QHE) regime. Relocation of this border out of the Hall bar revives the QHE. We have also found that the critical current of the breakdown of QHE in suspended samples is three times lower than in non-suspended samples due to the peculiarity of heat transport in the membranes.

Self-consistent diverted tokamak equilibria with nonzero edge current

The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equilibria (Bingren Shi, Plasma Phys. Control Fusion 50 (2008) 085006, 51 (2009) 105008, Nucl. Fusion 51 (2011) 023004), is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch-Schlüter(PS) current. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad—Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separatrix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.

Effect of magnetic field on electron transport in HgTe/CdTe quantum wells: Numerical analysis

The effect of magnetic field on electron transport in the inverted band structure of HgTe/CdTe quantum well is investigated. Although magnetic field breaks the time-reversal symmetry, the quantum spin Hall effect can still survive at large magnetic field up to 10 T. Moreover, two quantum anomalous Hall-like phases emerge, in which the system only has a spin-up or spin-down edge state at a given sample edge and the edge current is spin polarized. By tuning the Fermi energy, the system can transit between the quantum spin Hall phase and two quantum anomalous Hall-like phases, so the polarized direction of the edge current is well controllable. Thus the spin selectivity can be realized for potential applications of spintronics. Due to the quantum spin and anomalous Hall-like effects, the longitudinal and Hall resistances exhibit quantum plateaus. In addition, at certain magnetic field, some exotic plateaus like $\frac{2}{3}$ fractional quantum Hall effect are also observed, where edge states with the same spin counterpropagate at the one edge. At last, these plateaus are hardly affected by Rashba spin-orbit interaction, Zeeman effect, and Anderson disorder.

Revealing Antiphase Boundaries and Defects at Atomic Resolution in NaLaMgWO&lt;SUB&gt;6&lt;/SUB&gt; Double Perovskites

The effect of magnetic field on electron transport in the inverted band structure of HgTe/CdTe quantum well is investigated. Although magnetic field breaks the time-reversal symmetry, the quantum spin Hall effect can still survive at large magnetic field up to 10 T. Moreover, two quantum anomalous Hall-like phases emerge, in which the system only has a spin-up or spin-down edge state at a given sample edge and the edge current is spin polarized. By tuning the Fermi energy, the system can transit between the quantum spin Hall phase and two quantum anomalous Hall-like phases, so the polarized direction of the edge current is well controllable. Thus the spin selectivity can be realized for potential applications of spintronics. Due to the quantum spin and anomalous Hall-like effects, the longitudinal and Hall resistances exhibit quantum plateaus. In addition, at certain magnetic field, some exotic plateaus like 2/3 fractional quantum Hall effect are also observed, where edge states with the same spin counterpropagate at the one edge. At last, these plateaus are hardly affected by Rashba spin-orbit interaction, Zeeman effect, and Anderson disorder.

Nanomagnetic skyrmions

Magnetic skyrmions and other topologically protected nanostructures are investigated. Since skyrmions are mathematical rather than physical objects, they describe a wide variety of physical systems, from simple magnetic domain walls to complicated quantum phases with long-range many-body entanglement. Important distinctions concern the skyrmions’ relativistic character, their quantum-mechanical or classical nature, and the one- or many-body character of the wave functions. As specific examples we consider magnetic nanospirals, where the topology of a vortex-like spin state is protected by magnetostatic interactions, and edge currents in dilute magnetic semiconductors and metallic nanodots. Our analysis militates against giant orbital moments created by a mesocopically enhanced spin-orbit coupling.

DNA base-specific modulation of microampere transverse edge currents through a metallic graphene nanoribbon with a nanopore.

We study two-terminal devices for DNA sequencing that consist of a metallic graphene nanoribbon with zigzag edges (ZGNR) and a nanopore in its interior through which the DNA molecule is translocated. Using the nonequilibrium Green functions combined with density functional theory, we demonstrate that each of the four DNA nucleobases inserted into the nanopore, whose edge carbon atoms are passivated by either hydrogen or nitrogen, will lead to a unique change in the device conductance. Unlike other recent biosensors based on transverse electronic transport through translocated DNA, which utilize small (of the order of pA) tunneling current across a nanogap or a nanopore yielding a poor signal-to-noise ratio, our device concept relies on the fact that in ZGNRs local current density is peaked around the edges so that drilling a nanopore away from the edges will not diminish the conductance. Inserting a nucleobase into the nanopore affects the charge density in the surrounding area, thereby modulating edge conduction currents whose magnitude is of the order of microampere at bias voltage 0.1 V. The proposed biosensors are not limited to ZGNRs and they could be realized with other nanowires supporting transverse edge currents, such as chiral GNRs or wires made of two-dimensional topological insulators.

Surface states, edge currents, and the angular momentum of chiralp-wave superfluids

The spectra of fermionic excitations, pairing correlations and edge currents confined near the boundary of a chiral p-wave superfluid are calculated to leading order in $\hbar/p_f\xi$. Results for the energy- and momentum-resolved spectral functions, including the spectral current density, of a chiral p-wave superfluid near a confining boundary are reported. The spectral functions reveal the subtle role of the chiral edge states in relation to the edge current and the angular momentum of a chiral p-wave superfluid, including the rapid suppression of $L_z(T)$ for $0 \lesssim T\ll T_c$ in the fully gapped 2D chiral superfluid. The edge current and ground-state angular momentum are shown to be sensitive to boundary conditions, and as a consequence the topology and geometry of the confining boundaries. For perfect specular boundaries the edge current accounts for the ground-state angular momentum, $L_z=(N/2)\hbar$, of a cylindrical disk of chiral superfluid with $N/2$ fermion pairs. Non-specular scattering can dramatically suppress the edge current. In the limit of perfect retro-reflection the edge states form a flat band of zero modes that are non-chiral and generate no edge current. For a chiral superfluid film confined in a cylindrical toroidal geometry the ground-state angular momentum is, in general, non-extensive, and can have a value ranging from $L_z > (N/2)\hbar$ to $L_z < -(N/2)\hbar$ depending on the ratio of the inner and outer radii and the degree of back scattering on the inner and outer surfaces. Non-extensive scaling of $L_z$, and the reversal of the ground-state angular momentum for a toroidal geometry, would provide a signature of broken time-reversal symmetry of the ground state of superfluid \Hea, as well as direct observation of chiral edge currents.

Topological insulators on a Mobius strip

We study the two dimensional Chern insulator and spin Hall insulator on a non-orientable Riemann surface, the Mobius strip, where the usual bandstructure topological invariant is not defined. We show that while the flow pattern of edge currents can detect the twist of the Mobius strip in the case of Chern insulator, it can not do so in spin Hall insulator.

Manipulating fully spin-polarized edge currents in graphene ribbon

Electron fully spin-polarized edge states in graphene emerged at the interfaces of a nonuniform magnetic field are studied numerically in a tight-binding model, with both the orbital and Zeeman-splitting effects of magnetic field considered. We show that the fully spin-polarized currents can be manipulated by a gate voltage. In order to make use of the fully spin-polarized currents in the spin-related transport, a three-terminal experiment is designed and expected to export the fully spin-polarized currents. This may have important applications in spin-based nanodevices.

Tokamak startup using outboard current injection on the Pegasus Toroidal Experiment

Localized current injection near the outboard midplane is used to form 0.1 MA plasma discharges with no induction supplied from a central solenoid in the ultra-low aspect ratio Pegasus Toroidal Experiment. The discharges are initiated by driving open-field-line currents that perturb the vacuum magnetic field such that the magnetic topology transitions to a tokamak-like configuration. The plasma is subsequently driven via helicity injection from the edge current sources and poloidal field induction. Intermittent n = 1 MHD activity is observed during periods of strong edge current drive and each event leads to a rapid inward expansion of the plasma volume and a drop in the plasma inductance. The plasmas are sufficiently turbulent such that the equilibrium approaches the lowest energy state described by Taylor relaxation theory. In agreement with that theory, the maximum Ip scales with (ITFIinj/w)1/2, where ITF is the toroidal field rod current, Iinj is the injected edge current and w is the radial width of the average poloidal magnetic flux in the driven open flux region.

Edge states and distributions of edge currents in semi-infinite graphene

The distributions of edge currents in semi-infinite graphene under a uniform perpendicular magnetic field are investigated. We show unambiguously that the edge current is finite at the armchair edge but vanishes at the zigzag edge. It is shown that the current density oscillates with the distance away from the boundary and tends to zero deep inside the graphene. The study shows that the total current is independent of edge configurations. The interplay of the bulk and edge contributions to the total current is presented. The quantized plateaus of Hall conductivity at (4e 2/h)(n+1/2) provide a direct evidence of the connection between the edge states and topological properties of relativistic fermions in a magnetic field.

Majorana-Weyl fermions in the chiral superconductor Sr2RuO4

We found parity-violating Majorana fermions in a chiral superconductor Sr2RuO4. The current-voltage curves show an anomalous behavior: The induced voltage is an even function of the bias current. The magnetic field dependent results suggest the excitation of the Majorana fermions along the closed chiral edge current of the single domain under bias current. We also discuss the relationship between a change of the chirality and spontaneous magnetization of the single domain Sr2RuO4.

Quantization of Edge Currents along Magnetic Barriers and Magnetic Guides

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove quantization of the edge conductance. Next, we consider magnetic perturbations of such magnetic barriers or guides, and prove stability of the quantized value of the edge conductance. Further, we establish a sum rule for edge conductances. Regularization within the context of disordered systems is discussed as well.