Abstract: A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method is used to describe disordered single-layer graphene Josephson junctions. Scattering by vacancies, ripples, or charged impurities is included. We compute the Josephson current and investigate the nature of multiple Andreev reflections, which induce bound states appearing as peaks in the density of states for energies below the superconducting gap. In the presence of single-atom vacancies, we observe a strong suppression of the supercurrent, which is a consequence of strong intervalley scattering. Although lattice deformations should not induce intervalley scattering, we find that the supercurrent is still suppressed, which is due to the presence of pseudomagnetic barriers. For charged impurities, we consider two cases depending on whether the average doping is zero, i.e., existence of electron-hole puddles, or finite. In both cases, short-range impurities strongly affect the supercurrent, similar to the vacancies scenario.

Abstract: Depending on the Ginzburg-Landau parameter kappa, superconductors can either be fully diamagnetic if kappa < 1/root 2 (type I superconductors) or allow magnetic flux to penetrate through Abrikosov vortices if kappa > 1/root 2 (type II superconductors; refs 1,2). At the Bogomolny critical point, kappa = kappa(c) = 1/root 2, a state that is infinitely degenerate with respect to vortex spatial configurations arises(3,4). Despite in-depth investigations of conventional type I and type II superconductors, a thorough understanding of the magnetic behaviour in the near-Bogomolny critical regime at kappa similar to kappa(c) remains lacking. Here we report that in confined systems the critical regime expands over a finite interval of kappa forming a critical superconducting state. We show that in this state, in a sample with dimensions comparable to the vortex core size, vortices merge into a multi-quanta droplet, which undergoes Rayleigh instability(5) on increasing kappa and decays by emitting single vortices. Superconducting vortices realize Nielsen-Olesen singular solutions of the Abelian Higgs model, which is pervasive in phenomena ranging from quantum electrodynamics to cosmology(6-9). Our study of the transient dynamics of Abrikosov-Nielsen-Olesen vortices in systems with boundaries promises access to non-trivial effects in quantum field theory by means of bench-top laboratory experiments.

Abstract: By considering a cylindrically symmetric generalization of a plane wave, the first-order Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of the incoming beam. In this paper, the elastic Coulomb scattering amplitude is calculated analytically for incoming Bessel beams. This reveals novel features occurring for wide-angle scattering and quantitative insights for small-angle vortex scattering. The result successfully generalizes the well-known Rutherford formula, incorporating transverse and orbital angular momentum into the formalism.

Abstract: The recent experimental realization of electron vortex beams opens up a wide research domain previously unexplored. The present paper explores the relativistic properties of these electron vortex beams, and quantifies deviations from the scalar wave theory. It is common in electron optics to use the Schrodinger equation neglecting spin. The present paper investigates the role of spin and the total angular momentum J(z) and how it pertains to the vortex states. As an application, we also investigate if it is possible to use holographic reconstruction to create novel total angular momentum eigenstates in a transmission electron microscope. It is demonstrated that relativistic spin coupling effects disappear in the paraxial limit, and spin effects in holographically created electron vortex beams can only be exploited by using specialized magnetic apertures.

Abstract: Superconducting correlations may propagate between two superconductors separated by a tiny insulating or metallic barrier, allowing a dissipationless electric current to flow(1,2). In the presence of a magnetic field, the maximum supercurrent oscillates(3) and each oscillation corresponding to the entry of one Josephson vortex into the barrier(4). Josephson vortices are conceptual blocks of advanced quantum devices such as coherent terahertz generators(5) or qubits for quantum computing(6), in which on-demand generation and control is crucial. Here, we map superconducting correlations inside proximity Josephson junctions(7) using scanning tunnelling microscopy. Unexpectedly, we find that such Josephson vortices have real cores, in which the proximity gap is locally suppressed and the normal state recovered. By following the Josephson vortex formation and evolution we demonstrate that they originate from quantum interference of Andreev quasiparticles(8), and that the phase portraits of the two superconducting quantum condensates at edges of the junction decide their generation, shape, spatial extent and arrangement. Our observation opens a pathway towards the generation and control of Josephson vortices by applying supercurrents through the superconducting leads of the junctions, that is, by purely electrical means without any need for a magnetic field, which is a crucial step towards high-density on-chip integration of superconducting quantum devices.

Abstract: The Tomasch effect (TE) is due to quasiparticle interference (QPI) as induced by a nonuniform superconducting order parameter, which results in oscillations in the density of states (DOS) at energies above the superconducting gap. Quantum confinement in nanoscale superconductors leads to an inhomogenerous distribution of the Cooperpair condensate, which, as we found, triggers the manifestation of a new TE. We investigate the electronic structure of nanoscale superconductors by solving the Bogoliubov-de Gennes (BdG) equations self-consistently and describe the TE determined by two types of processes, involving two-or three-subband QPIs. Both types of QPIs result in additional BCS-like Bogoliubov-quasiparticles and BCS-like energy gaps leading to oscillations in the DOS and modulated wave patterns in the local density of states. These effects are strongly related to the symmetries of the system. A reduced 4 x 4 inter-subband BdG Hamiltonian is established in order to describe analytically the TE of two-subband QPIs. Our study is relevant to nanoscale superconductors, either nanowires or thin films, Bose-Einsten condensates, and confined systems such as two-dimensional electron gas interface superconductivity.

Abstract: Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Perot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

Abstract: Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant-multivortex combinations, and states comprising giant antivortices, were found as ground states and their stability was found to be very sensitive on the value of k(F)xi(0), the size of the sample W, and the magnetic flux Phi. By increasing the temperature and/or enlarging the size of the sample, quantum confinement is suppressed and the conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL) theory are recovered. However, contrary to the GL results we found that the states containing symmetry-induced vortex-antivortex pairs are stable over the whole temperature range. It turns out that the inhomogeneous order parameter induced by quantum confinement favors vortex-antivortex molecules, as well as giant vortices with a rich structure in the vortex core-unattainable in the GL domain.

Abstract: In 1976, Larkin and Ovchinnikov [Zh. Eksp. Teor. Fiz. 68, 1915 (1975) [Sov. Phys.–JETP 41, 960 (1976)]] predicted that vortex matter in superconductors driven by an electrical current can undergo an abrupt dynamic transition from a flux-flow regime to a more dissipative state at sufficiently high vortex velocities. Typically, this transition manifests itself as a large voltage jump at a particular current density, so-called instability current density J∗, which is smaller than the depairing current. By tuning the effective pinning strength in Al films, using an artificial periodic pinning array of triangular holes, we show that a unique and well-defined instability current density exists if the pinning is strong, whereas a series of multiple voltage transitions appear in the relatively weaker pinning regime. This behavior is consistent with time-dependent Ginzburg-Landau simulations, where the multiple-step transition can be unambiguously attributed to the progressive development of vortex chains and subsequently phase-slip lines. In addition, we explore experimentally the magnetic braking effects, caused by a thick Cu layer deposited on top of the superconductor, on the instabilities and the vortex ratchet effect.

Abstract: We present extensive calculations of the optical and plasmonic properties of a graphene sheet carrying a dc current. By calculating analytically the density-density response function of current-carrying states at finite temperature, we demonstrate that an applied dc current modifies the Pauli blocking mechanism and that absorption acquires a birefringent character with respect to the angle between the in-plane light polarization and current flow. Employing the random phase approximation at finite temperature, we show that graphene plasmons display a degree of non-reciprocity and collimation that can be tuned with the applied current. We discuss the possibility to measure these effects.

Abstract: Different allotropes of phosphorene are possible of which black and blue phosphorus are the most stable. While blue phosphorus has isotropic properties, black phosphorus is strongly anisotropic in its electronic and optical properties due to its anisotropic crystal structure. In this work, we systematically investigated the lattice thermal properties of black and blue phosphorene by using first-principles calculations based on the quasiharmonic approximation approach. Similar to the optoelectronic and electronic properties, we predict that black phosphorene has highly anisotropic thermal properties, in contrast to the blue phase. The linear thermal expansion coefficients along the zigzag and armchair direction differ up to 20% in black phosphorene. The armchair direction of black phosphorene is more expandable as compared to the zigzag direction and the biaxial expansion of blue phosphorene under finite temperature. Our comparative analysis reveals that the inclusion of finite-temperature effects makes the blue phase thermodynamically more stable over the black phase above 135 K.

Abstract: Recently it was found that bilayer graphene may exhibit regions with and without van der Waals coupling between the two layers. We show that such structures can exhibit a strong layer selectivity when current flows through the coupled region and that this selectivity can be tuned by means of electrostatic gating. Analysing how this effect depends on the type of bilayer stacking, the potential on the gates and the smoothness of the boundary between the coupled and decoupled regions, we show that nearly perfect layer selectivity is achievable in these systems. This effect can be further used to realise a tunable layer switch.