Abstract: The strain-induced pseudomagnetic field in supported graphene deposited on top of a nanostructured substrate is investigated by using atomistic simulations. A step, an elongated trench, a one-dimensional barrier, a spherical bubble, a Gaussian bump, and a Gaussian depression are considered as support structures for graphene. From the obtained optimum configurations we found very strong induced pseudomagnetic fields which can reach up to similar to 1000 T due to the strain-induced deformations in the supported graphene. Different magnetic confinements with controllable geometries are found by tuning the pattern of the substrate. The resulting induced magnetic fields for graphene on top of a step, barrier, and trench are calculated. In contrast to the step and trench the middle part of graphene on top of a barrier has zero pseudomagnetic field. This study provides a theoretical background for designing magnetic structures in graphene by nanostructuring substrates. We found that altering the radial symmetry of the deformation changes the sixfold symmetry of the induced pseudomagnetic field.

Abstract: Structural phase transitions in two vertically or horizontally coupled channels of strongly interacting particles are investigated. The particles are free to move in the x direction but are confined by a parabolic potential in the y direction. They interact with each other through a screened power-law potential (r(-n)e(-r/lambda)). In vertically coupled systems, the channels are stacked above each other in the direction perpendicular to the (x, y) plane, while in horizontally coupled systems both channels are aligned in the confinement direction. Using Monte Carlo (MC) simulations we obtain the ground-state configurations and the structural transitions as a function of the linear particle density and the separation between the channels. At zero temperature, the vertically coupled system exhibits a rich phase diagram with continuous and discontinuous transitions. On the other hand, the horizontally coupled system exhibits only a very limited number of phase transitions due to its symmetry. Further, we calculated the normal modes for the Wigner crystals in both cases. From MC simulations, we found that in the case of vertically coupled systems, the zigzag transition is only possible for low densities. A Ginzburg-Landau theory for the zigzag transition is presented, which predicts correctly the behavior of this transition from which we interpret the structural phase transition of the Wigner crystal through the reduction of the Brillouin zone.

Abstract: To date, several experimental groups reported measurements of the thickness dependence of T-c of atomically uniform single-crystalline Pb nanofilms. The reported amplitude of the T-c oscillations varies significantly from one experiment to another. Here we propose that the reason for this unresolved issue is an interplay of the quantum-size variations in the single-electron density of states with thickness-dependent oscillations in the phonon-mediated electron-electron coupling. Such oscillations in the coupling depend on the substrate material, the quality of the interface, the protection cover, and other details of the fabrication process, changing from one experiment to another. This explains why the available data do not exhibit one-voice consistency about the amplitude of the T-c oscillations. Our analyses are based on a numerical solution of the Bogoliubov-de Gennes equations for a superconducting slab.

Abstract: Thermal fluctuations of single layer hydrogenated graphene (graphane) are investigated using large scale atomistic simulations. By analyzing the mean square value of the height fluctuations < h(2)> and the height-height correlation function H(q) for different system sizes and temperatures, we show that hydrogenated graphene is an unrippled system in contrast to graphene. The height fluctuations are bounded, which is confirmed by a H(q) tending to a constant in the long wavelength limit instead of showing the characteristic scaling law q(4-eta)(eta similar or equal to 0.85) predicted by membrane theory. This unexpected behavior persists up to temperatures of at least 900 K and is a consequence of the fact that in graphane the thermal energy can be accommodated by in-plane bending modes, i.e., modes involving C-C-C bond angles in the buckled carbon layer, instead of leading to significant out-of-plane fluctuations that occur in graphene.

Abstract: We derive the extended Ginzburg-Landau (GL) formalism for a clean s-wave two-band superconductor by employing a systematic expansion of the free-energy functional and the corresponding matrix gap equation in powers of the small deviation from the critical temperature tau = 1 – T/T-c. The two lowest orders of this expansion produce the equation for T-c and the standard GL theory. It is shown that in agreement with previous studies, this two-band GL theory maps onto the single-band GL model and thus fails to describe the difference in the spatial profiles of the two-band condensates. We prove that this difference appears already in the leading correction to the standard GL theory, which constitutes the extended GL formalism. We derive linear differential equations that determine the leading corrections to the band order parameters and magnetic field, discuss the validity of these equations, and consider examples of an important interplay between the band condensates. Finally, we present numerical results for the thermodynamic critical magnetic field and temperature-dependent band gaps for recent materials of interest, which are in very good agreement with those obtained from the full BCS approach in a wide temperature range. To this end, we emphasize the advantages of our extended GL theory in comparison with the often used two-component GL-like model based on an unreconstructed two-band generalization of the Gor'kov derivation.

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: The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.

Abstract: We describe a semianalytic approach to the two-band Ginzburg-Landau theory, which predicts the behavior of vortices in two-band superconductors. We show that the character of the short-range vortex-vortex interaction is determined by the sign of the normal domain-superconductor interface energy, in analogy with the conventional differentiation between type I and type II superconductors. However, we also show that the long-range interaction is determined by a modified Ginzburg-Landau parameter κ*, different from the standard κ of a bulk superconductor. This opens the possibility for nonmonotonic vortex-vortex interaction, which is temperature dependent, and can be further tuned by alterations of the material on the microscopic scale.

Abstract: Using the Ginzburg-Landau theory extended to the next-to-leading order, we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that those can be different even in the strict domain of applicability of the Ginzburg-Landau theory. This justifies the use of this theory to describe relevant physics of two-gap superconductors, distinguishing them from their single-gap counterparts. The calculational degree of complexity increases only slightly with respect to the conventional Ginzburg-Landau expansion, thus the extended Ginzburg-Landau model remains numerically far less demanding compared to the full microscopic approaches.

Abstract: An analytical approach, using the Dirac-Weyl equation, is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. Results are obtained for the infinite-massand zigzag boundary conditions. We found that the energy spectrum of a dot with the zigzag boundary condition exhibits a zero-energy band regardless of the value of the magnetic field, while for the infinite-mass boundary condition, the zero-energy states appear only for high magnetic fields. The analytical results are compared to those obtained from the tight-binding model: (i) we show the validity range of the continuum model and (ii) we find that the continuum model with the infinite-mass boundary condition describes rather well its tight-binding analog, which can be partially attributed to the blurring of the mixed edges by the staggered potential.

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: Hall probe magnetometry has been used to investigate the magnetization of individual cylindrically shaped Pb nanowires grown by electrocrystallization on a highly oriented pyrolytic graphite electrode. These measurements have been interpreted by comparison with three-dimensional Ginzburg-Landau (GL) calculations for nanowires with our sample parameters. We find that the measured superheating field and the critical field for surface superconductivity are strongly influenced by the temperature-dependent coherence length, ξ(T) and penetration depth λ(T) and their relationship to the nanowire diameter. As the temperature is increased toward Tc this drives a change in the superconductor-normal transition from first order irreversible to first order reversible and finally second order reversible. We find that the geometrical flux confinement in our type-I nanowires leads to the formation of a one-dimensional row of single-quantum vortices. While GL calculations show a quite uniform distribution of vortices in thin nanowires, clear vortex bunching is found as the diameter increases, suggesting a transition to a more classical type-I behavior. Subtle changes in minor magnetization loops also indicate that slightly different flux configurations can form with the same vorticity, which depend on the sample history.

Abstract: We predict heating of quasiparticles driven by order parameter oscillations in the resistive state of short superconducting microbridges. The finite relaxation time of the magnitude of the order parameter |Δ| and the dependence of the spectral functions both on |Δ| and the supervelocity Q are the origin of this effect. Our results are opposite to those of Aslamazov and Larkin [ Zh. Eks. Teor. Fiz. 70 1340 (1976)] and Schmid et al. [ Phys. Rev. B 21 5076 (1980)] where cooling of quasiparticles was found.

Abstract: We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of a Rashba-like spin-orbit interaction. Our results corroborate previous work performed with the momentum average approximation and with weak-coupling perturbation theory. We find that spin-orbit coupling increases the effective mass in the regime with weak electron-phonon coupling, and decreases the effective mass in the regimes of intermediate and strong electron-phonon coupling. Analytical strong-coupling perturbation theory results confirm our numerical results in the small-polaron regime. A large amount of spin-orbit coupling can lead to a significant lowering of the polaron effective mass.