Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices

We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for quasiballistic samples to obtain Majorana fermions. Moreover, we find that the total phase space area of the topological state is conserved for long disordered Rashba wires, and can even be increased in an appropriately engineered superlattice potential.Comment: 5 pages, 3 figs, RevTe

Mesoscopic Spin Hall Effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is large compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. For a fixed sample configuration, the transverse spin current has a finite typical value ~e^2 V/h, proportional to the longitudinal bias V on the sample, and corresponding to about one excess open channel for one of the two spin species. Our analytical results are in agreement with numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97, 066603 (2006)] and are further confirmed by numerical simulation in a chaotic cavity.Comment: 4 pages, 2 figure

Topologically Protected Loop Flows in High Voltage AC Power Grids

Geographical features such as mountain ranges or big lakes and inland seas often result in large closed loops in high voltage AC power grids. Sizable circulating power flows have been recorded around such loops, which take up transmission line capacity and dissipate but do not deliver electric power. Power flows in high voltage AC transmission grids are dominantly governed by voltage angle differences between connected buses, much in the same way as Josephson currents depend on phase differences between tunnel-coupled superconductors. From this previously overlooked similarity we argue here that circulating power flows in AC power grids are analogous to supercurrents flowing in superconducting rings and in rings of Josephson junctions. We investigate how circulating power flows can be created and how they behave in the presence of ohmic dissipation. We show how changing operating conditions may generate them, how significantly more power is ohmically dissipated in their presence and how they are topologically protected, even in the presence of dissipation, so that they persist when operating conditions are returned to their original values. We identify three mechanisms for creating circulating power flows, (i) by loss of stability of the equilibrium state carrying no circulating loop flow, (ii) by tripping of a line traversing a large loop in the network and (iii) by reclosing a loop that tripped or was open earlier. Because voltage angles are uniquely defined, circulating power flows can take on only discrete values, much in the same way as circulation around vortices is quantized in superfluids.Comment: 12 pages 6 figures + Supplementary Material, Accepted for publication in New Journal of Physic

Universal features of spin transport and breaking of unitary symmetries

When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry, while in the opposite limit of a single exit transport channel, spin currents vanish identically in the presence of time-reversal symmetry but can be turned on by breaking it with an orbital magnetic field

Weyl-Majorana solenoid

A Weyl semimetal wire with an axial magnetization has metallic surface states (Fermi arcs) winding along its perimeter, connecting bulk Weyl cones of opposite topological charge (Berry curvature). We investigate what happens to this "Weyl solenoid" if the wire is covered with a superconductor, by determining the dispersion relation of the surface modes propagating along the wire. Coupling to the superconductor breaks up the Fermi arc into a pair of Majorana modes, separated by an energy gap. Upon variation of the coupling strength along the wire there is a gap inversion that traps the Majorana fermions.Comment: 6 pages, 6 figures; V2: added discussion of charge operator, updated figures; V3: added a section on analytical mode-matching calculations, an appendix, and three new figures. To be published in the Focus Issue on "Topological semimetals" of New Journal of Physic

Theory of anomalous magnetic interference pattern in mesoscopic SNS Josephson junctions

The magnetic interference pattern in mesoscopic SNS Josephson junctions is sensitive to the scattering in the normal part of the system. In this paper we investigate it, generalizing Ishii's formula for current-phase dependence to the case of normal scattering at NS boundaries in an SNS junction of finite width. The resulting flattening of the first diffraction peak is consistent with experimental data for S-2DEG-S mesoscopic junctions.Comment: 6 pages, 5 figures. Phys. Rev. B 68, 144514 (2003

Superconductivity provides access to the chiral magnetic effect of an unpaired Weyl cone

Article / Letter to editorLeids Instituut Onderzoek Natuurkund

Scattering Theory of Current-Induced Spin Polarization

We construct a novel scattering theory to investigate magnetoelectrically induced spin polarizations. Local spin polarizations generated by electric currents passing through a spin-orbit coupled mesoscopic system are measured by an external probe. The electrochemical and spin-dependent chemical potentials on the probe are controllable and tuned to values ensuring that neither charge nor spin current flow between the system and the probe, on time-average. For the relevant case of a single-channel probe, we find that the resulting potentials are exactly independent of the transparency of the contact between the probe and the system. Assuming that spin relaxation processes are absent in the probe, we therefore identify the local spin-dependent potentials in the sample at the probe position, and hence the local current-induced spin polarization, with the spin-dependent potentials in the probe itself. The statistics of these local chemical potentials is calculated within random matrix theory. While they vanish on spatial and mesoscopic average, they exhibit large fluctuations, and we show that single systems typically have spin polarizations exceeding all known current-induced spin polarizations by a parametrically large factor. Our theory allows to calculate quantum correlations between spin polarizations inside the sample and spin currents flowing out of it. We show that these large polarizations correlate only weakly with spin currents in external leads, and that only a fraction of them can be converted into a spin current in the linear regime of transport, which is consistent with the mesoscopic universality of spin conductance fluctuations. We numerically confirm the theory.Comment: Final version; a tunnel barrier between the probe and the dot is considered. To appear in 'Nanotechnology' in the special issue on "Quantum Science and Technology at the Nanoscale

Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator

We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll \Delta_0$.Comment: 4 pages, 3 figures, RevTe

Anomalous power law of quantum reversibility for classically regular dynamics

The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ~ t^{-d} for the decay of classical phase space densities