Abstract: We study nonlinear flux dynamics in a current-carrying type-I superconductor. The stray magnetic field of the current induces the intermediate state, where nucleation of flux domains is discretized to a single fluxoid at a time, while their final shape (tubular or laminar), size, and nucleation rate depend on applied current and edge conditions. The current induces opposite flux domains on opposite sides of the sample, and subsequently drives them to annihilation-which is also discretized, as a sequence of vortex-antivortex pairs. The discretization of both nucleation and annihilation leaves measurable traces in the voltage across the sample and in locally probed magnetization. The reported dynamic phenomena thus provide an unambiguous proof of a flux quantum being the smallest building block of the intermediate state in type-I superconductors.

Abstract: It is well known that the formation of discrete electron levels strongly influences the pairing in metallic nanograins. Here, we focus on another effect of quantum confinement in superconducting grains that was not studied previously, i.e., spatially nonuniform pairing. This effect is very significant when single-electron levels form bunches and/or a kind of shell structure. We find that, in highly symmetric grains, the order parameter can exhibit variations with position by an order of magnitude. Nonuniform pairing is closely related to a quantum-confinement-induced modification of the pairing-interaction matrix elements and size-dependent pinning of the chemical potential to groups of degenerate or nearly degenerate levels. For illustrative purposes, we consider spherical metallic nanograins and also rectangular shapes. We show that the relevant matrix elements are, as a rule, enhanced in the presence of quantum confinement, which favors spatial variations of the order parameter, compensating the corresponding energy cost. The size-dependent pinning of the chemical potential further increases the spatial variation of the pair condensate. The role of nonuniform pairing is smaller in less symmetric confining geometries and/or in the presence of disorder. However, it always remains of importance when the energy spacing between discrete electron levels δ is approaching the scale of the bulk gap ΔB, i.e., δ>0.10.2 ΔB.

Abstract: Thermal fluctuations of the order parameter in an ultrathin triangular-shaped superconducting structure are studied near Tc, in zero applied field. We find that the order parameter is prone to much larger fluctuations in the corners of the structure as compared to its interior. This geometry-induced localization of thermal fluctuations is attributed to the fact that condensate confinement in the corners is characterized by a lower effective dimensionality, which favors stronger fluctuations.

Abstract: We consider two possible mechanisms for single-vortex fluctuative entry/exit through the surface barrier in ultrathin superconducting disk-shaped nanoislands made of Pb and consisting of just a few monoatomic layers, which can be fabricated using modern techniques. We estimate tunneling probabilities and establish criteria for the crossover between these two mechanisms depending on magnetic field and system sizes. For the case of vortex entry, quantum tunneling dominates on the major part of the temperature/flux phase diagram. For the case of vortex exit, thermal activation turns out to be more probable. This nontrivial result is due to the subtle balance between the barrier height and width, which determine rates of the thermal activation and quantum tunneling, respectively.

Abstract: Quasiperiodic pinning arrays, as recently demonstrated theoretically and experimentally using a fivefold Penrose tiling, can lead to a significant enhancement of the critical current Ic as compared to traditional regular pinning arrays. However, while regular arrays showed only a sharp peak in Ic(Φ) at the matching flux Φ1 and quasiperiodic arrays provided a much broader maximum at Φ<Φ1, both types of pinning arrays turned out to be inefficient for fluxes larger than Φ1. We demonstrate theoretically and experimentally the enhancement of Ic(Φ) for Φ>Φ1 by using non-Penrose quasiperiodic pinning arrays. This result is based on a qualitatively different mechanism of flux pinning by quasiperiodic pinning arrays and could be potentially useful for applications in superconducting microelectronic devices operating in a broad range of magnetic fields.

Abstract: Electron transport through a spin-orbit-coupled quantum ring is investigated within linear response theory. We show that the finite width of the ring results in the appearance of Fano resonances in the conductance. This turns out to be a consequence of the spin-orbit interaction that leads to a breaking of the parity of the states localized in the ring. The resonances appear when the system is close to maxima of Aharonov-Casher conductance oscillations where spin transfer is heavily modified. When the spin-orbit coupling strength is detuned from the Aharonov-Casher maxima the resonances are broadened resulting in a dependence of the spin transport on the electron Fermi energy in contrast to predictions from one-dimensional models.

Abstract: The effect of the Coulomb interaction on the energy spectrum and anisotropic distribution of two electron states in a quantum ring in the presence of Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI) is investigated in the presence of a perpendicular magnetic field. We find that the interplay between the RSOI and DSOI makes the single quantum ring behaves like a laterally coupled quantum dot and the interdot coupling can be tuned by changing the strengths of the SOIs. The interplay can lead to singlet-triplet state mixing and anticrossing behavior when the singlet and triplet states meet with increasing magnetic field. The two electron ground state displays a bar-bell-like spatial anisotropic distribution in a quantum ring at a specific crystallographic direction, i.e., [110] or [11̅ 0], which can be switched by reversing the direction of the perpendicular electric field. The ground state exhibits a singlet-triplet state transition with increasing magnetic field and strengths of RSOI and DSOI. An anisotropic electron distribution is predicted which can be detected through the measurement of its optical properties.

Abstract: We numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic d-wave superconducting loops by solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Abstract: Using the tight-binding (TB) approximation with inclusion of the spin-orbit interaction, we predict a topological phase transition in the electronic band structure of phosphorene in the presence of axial strains. We derive a low-energy TB Hamiltonian that includes the spin-orbit interaction for bulk phosphorene. Applying a compressive biaxial in-plane strain and perpendicular tensile strain in ranges where the structure is still stable leads to a topological phase transition. We also examine the influence of strain on zigzag phosphorene nanoribbons (zPNRs) and the formation of the corresponding protected edge states when the system is in the topological phase. For zPNRs up to a width of 100 nm the energy gap is at least three orders of magnitude larger than the thermal energy at room temperature.

Abstract: We show that the transmission through single and double δ-function potential barriers of strength P=VWb/ℏvF in bilayer graphene is periodic in P with period π. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behavior is found for the conductance. The spectrum of a periodic succession of δ-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2π. For P smaller than a critical value Pc, the spectrum exhibits two Dirac points while for P larger than Pc an energy gap opens. These results are extended to the case of a superlattice of δ-function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period π.

Abstract: The configuration interaction method is used to obtain the magneto-optical absorption spectrum of a few-electron (Ne=1,2,,5) quantum dot containing a single magnetic ion. We find that the IR spectrum (the position, the number, and the oscillator strength of the cyclotron resonance peaks) depends on the strength of the Coulomb interaction, the number of electrons, and the position of the magnetic ion. We find that the Kohn theorem is no longer valid as a consequence of the electron-spin-magnetic-ion-spin-exchange interaction.

Abstract: A strong in-plane magnetic field drastically alters the low-energy spectrum of bilayer graphene by separating the parabolic energy dispersion into two linear Dirac cones. The effect of this dramatic change on the transport properties strongly depends on the orientation of the in-plane magnetic field with respect to the propagation direction of the charge carriers and the angle at which they impinge on the electrostatic potentials. For magnetic fields oriented parallel to the potential boundaries an additional propagating mode that results from the splitting into Dirac cones enhances the transmission probability for charge carriers tunneling through the potentials and increases the corresponding conductance. Our results show that the chiral suppression of transmission at normal incidence, reminiscent of bilayer graphene's 2 pi Berry phase, is turned into a chiral enhancement when the magnetic field increases, thus indicating a transition from a bilayer to a monolayer-like system at normal incidence. Further, we find that the typical transmission resonances stemming from confinement in a potential barrier are shifted to higher energy and are eventually transformed into antiresonances with increasing magnetic field. For magnetic fields oriented perpendicular to the potential boundaries we find a very pronounced transition from a bilayer system to two separated monolayer-like systems with Klein tunneling emerging at certain incident angles symmetric around 0, which also leaves a signature in the conductance. For both orientations of the magnetic field, the transmission probability is still correctly described by pseudospin conservation. Finally, to motivate the large in-plane magnetic field, we show that its energy spectrum can be mimicked by specific lattice deformations such as a relative shift of one of the layers. With this equivalence we introduce the notion of an in-plane pseudomagnetic field.

Abstract: The energy spectrum and eigenstates of single-layer black phosphorus nanoribbons in the presence of a perpendicular magnetic field and an in-plane transverse electric field are investigated by means of a tight-binding method, and the effect of different types of edges is examined analytically. A description based on a continuum model is proposed using an expansion of the tight-binding model in the long-wavelength limit. Thewave functions corresponding to the flatband part of the spectrum are obtained analytically and are shown to agree well with the numerical results from the tight-binding method for both narrow (10 nm) and wide (100 nm) nanoribbons. Analytical expressions for the critical magnetic field at which Landau levels are formed and the ranges of wave numbers in the dispersionless flatband segments in the energy spectra are derived. We examine the evolution of the Landau levels when an in-plane lateral electric field is applied, and we determine analytically how the edge states shift withmagnetic field. For wider nanoribbons, the conductance is shown to have a characteristic staircase shape in combined magnetic and electric fields. Some of the stairs in zigzag and skewed armchair nanoribbons originate from edge states that are found in the band gap.

Abstract: The hunt for high-temperature superfluidity has received new impetus from the discovery of atomically thin stable materials. Electron-hole superfluidity in coupled MoSe2-WSe2 monolayers is investigated using a mean-field multiband model that includes band splitting caused by strong spin-orbit coupling. This splitting leads to a large energy misalignment of the electron and hole bands which is strongly modified by interchanging the doping of the monolayers. The choice of doping determines if the superfluidity is tunable from one to two components.

Abstract: The classical-map hypernetted-chain (CHNC) scheme, developed for treating fermion fluids at strong coupling and at finite temperatures, is applied to electron-electron and electron-hole double quantum wells. The pair-distribution functions and the local field factors needed in linear-response theory are determined for a range of temperatures, carrier densities, and barrier widths typical for experimental double-quantum-well systems in GaAs-GaAlAs. For electron-hole double quantum wells, a large enhancement in the pair-distribution functions is found for small carrier separations. The CHNC equations for electron-hole systems no longer hold at low densities where bound-state formation occurs.