Abstract: Using the quasiclassical formalism, we determine the low-temperature phase diagram of a quasi-one-dimensional superconductor, taking into account the interchain Josephson coupling and the paramagnetic spin splitting. We show that the anisotropy of the onset of superconductivity changes in the FFLO state as compared with the conventional superconducting phase. It can result in anomalous peaks in the field-direction dependence of the upper critical field when the magnetic field length equals to the FFLO period. This regime is characterized by the lock-in effect of the FFLO modulation wave vector, which is governed by the magnetic length. Furthermore, in the FFLO phase, the anisotropy of the upper critical field is inverted at T-1(**) = 0.5T(c0), where the orbital anisotropy disappears. We suggest that an experimental study of the anisotropy of the upper critical field can provide very reach information about the parameters of the FFLO phase in quasi-1D samples.

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: The magnetic-field dependence of the hole states in a nanocup, which is composed of a ring (the nanocup rim) that surrounds a disk (the nanocup bottom), is obtained within the Luttinger-Kohn model for the unstrained GaAs/(Al,Ga) As and the strained (In,Ga) As/GaAs systems. Aharonov-Bohm oscillations due to angular momentum transitions of the hole ground state appear with periods that vary with the thickness of the disk. The strain in the (In, Ga) As/GaAs nanocup is sensitive to the disk thickness and favors the spatial localization of the heavy holes inside the disk. Therefore, the angular momentum transitions between the valence-band states disappear for much thinner disks than in the case of the unstrained GaAs/(Al, Ga) As nanocups. In both systems, the oscillations in the energy of the hole ground state are found to disappear for thinner inner layer than in the electron ground-state energy. This is due to the different confining potentials and the mixing between the heavy- and light-hole states. As a consequence, magnetization of the single hole is found to strongly depend on the bottom thickness of the strained (In, Ga) As/GaAs nanocup. Furthermore, we found that the strain can lead to a spatial separation of the electron and the hole, as in type-II band alignment, which is advantageous for the appearance of the excitonic Aharonov-Bohm effect.

Abstract: The alpha-T3 lattice model interpolates a honeycomb (graphene-like) lattice and a T3 (also known as dice) lattice via the parameter alpha. These lattices are made up of three atoms per unit cell. This gives rise to an additional dispersionless flat band touching the conduction and valence bands. Electrons in this model are analogous to Dirac fermions with an enlarged pseudospin, which provides unusual tunneling features like omnidirectional Klein tunneling, also called super-Klein tunneling (SKT). However, it is unknown how small deviations in the equivalence between the atomic sites, i.e., variations in the alpha parameter, and the number of tunnel barriers changes the transmission properties. Moreover, it is interesting to learn how tunneling occurs through regions where the energy spectrum changes from linear with a middle flat band to a hyperbolic dispersion. In this paper we investigate these properties, its dependence on the number of square barriers and the alpha parameter for either gapped and gapless cases. Furthermore, we compare these results to the case where electrons tunnel from a region with linear dispersion to a region with a bandgap. In the latter case, contrary to tunneling through a potential barrier, the SKT is no longer observed. Finally, we find specific cases where transmission is allowed due to a symmetry breaking of sublattice equivalence.

Abstract: The scattering of a Gaussian wave packet in armchair and zigzag graphene edges is theoretically investigated by numerically solving the time-dependent Schrodinger equation for the tight-binding model Hamiltonian. Our theory allows us to investigate scattering in reciprocal space, and depending on the type of graphene edge we observe scattering within the same valley, or between different valleys. In the presence of an external magnetic field, the well-known skipping orbits are observed. However, our results demonstrate that in the case of a pseudomagnetic field, induced by nonuniform strain, the scattering by an armchair edge results in a nonpropagating edge state.

Abstract: We present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types in the presence of a perpendicular magnetic field. Results are obtained within the tight-binding (TB) and Dirac models and we discuss which features of the former can be recovered by using the approximations imposed by the latter. Energy levels of graphene quantum rings obtained by diagonalizing the TB Hamiltonian are demonstrated to be strongly dependent on the rings geometry and the microscopical structure of the edges. This makes it difficult to recover those spectra by the existing theories that are based on the continuum (Dirac) model. Nevertheless, our results show that both approaches (i.e., TB and Dirac model) may provide similar results, but only for very specific combinations of ring geometry and edge types. The results obtained by a simplified model describing an infinitely thin circular Dirac ring show good agreement with those obtained for hexagonal and rhombus armchair graphene rings within the TB model. Moreover, we show that the energy levels of a circular quantum ring with an infinite mass boundary condition obtained within the Dirac model agree with those for a ring defined by a ring-shaped staggered potential obtained within the TB model.

Abstract: Within a tight binding approach we investigate the energy levels of hexagonal and triangular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We study AA- and AB-(Bernal) stacked BLG QDs and obtain the energy levels in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). Our results show that the size dependence of the energy levels is different from that of monolayer graphene QDs. The energy spectrum of AB-stacked BLG QDs with zigzag edges exhibits edge states which spread out into the opened energy gap in the presence of a perpendicular electric field. We found that the behavior of these edges states is different for the hexagonal and triangular geometries. In the case of AA-stacked BLG QDs, the electron and hole energy levels cross each other in both cases of armchair and zigzag edges as the dot size or the applied bias increases.

Abstract: Using the tight-binding approach, we investigate confined states in two different hybrid monolayer-bilayer systems: (i) a hexagonal monolayer area surrounded by bilayer graphene in the presence of a perpendicularly applied electric field and (ii) a hexagonal bilayer graphene dot surrounded by monolayer graphene. The dependence of the energy levels on dot size and external magnetic field is calculated. We find that the energy spectrum for quantum dots with zigzag edges consists of states inside the gap which range from dot-localized states, edge states, to mixed states coexisting together, whereas for dots with armchair edges, only dot-localized states are observed.

Abstract: Water inside a nanocapillary exhibits unconventional structural and dynamical behavior due to its ordered structure. The confining walls, density, and lateral pressures control profoundly the microscopic structure of trapped water. Here we study the electrostriction of confined water subjected to pressures of the order of GPa for two different setups: (i) a graphene nanochannel containing a constant number of water molecules independent of the height of the channel, (ii) an open nanochannel where water molecules can be exchanged with those in a reservoir. For the former case, a square-rhombic structure of confined water is formed when the height of the channel is d = 6.5 angstrom having a density of rho = 1.42 g cm(-3). By increasing the height of the channel, a transition from a flat to a buckled state occurs, whereas the density rapidly decreases and reaches the bulk density for d congruent to 8.5 angstrom. When a perpendicular electric field is applied, the water structure and the lateral pressure change. For strong electric fields (similar to 1 V/angstrom), the square-rhombic structure is destroyed. For an open setup, a solid phase of confined water consisting of an imperfect square-rhombic structure is formed. By applying a perpendicular field, the density and phase of confined water change. However, the density and pressure inside the channel decrease as compared to the first setup. Our study is closely related to recent experiments on confined water, and it reveals the sensitivity of the microscopic structure of confined water to the size of the channel, the external electric field, and the experimental setup.

Abstract: We investigate scattering of the topological surface state of a three-dimensional time-reversal invariant topological insulator when graphene is deposited on the topological-insulator surface. Specifically, we consider the (111) surface of a Bi2Se3-like topological insulator. We present a low-energy model for the graphene-topological insulator heterostructure and we calculate the transmission probability at zigzag and armchair edges of the deposited graphene, and the conductance through graphene nanoribbon barriers, and show that its features can be understood from antiresonances in the transmission probability.

Abstract: Amorphous semiconductors are usually characterized by a low charge carrier mobility, essentially related to their lack of long-range order. The development of such material with higher charge carrier mobility is hence challenging. Part of the issue comes from the difficulty encountered by first-principles simulations to evaluate concepts such as the electron effective mass for disordered systems since the absence of periodicity induced by the disorder precludes the use of common concepts derived from condensed matter physics. In this paper, we propose a methodology based on first-principles simulations that partially solves this problem, by quantifying the degree of delocalization of a wave function and of the connectivity between the atomic sites within this electronic state. We validate the robustness of the proposed formalism on crystalline and molecular systems and extend the insights gained to disordered/amorphous InGaZnO4 and Si. We also explore the properties of p-type oxide semiconductor candidates recently reported to have a low effective mass in their crystalline phases [G. Hautier et al., Nat. Commun. 4, 2292 (2013)]. Although in their amorphous phase none of the candidates present a valence band with delocalization properties matching those found in the conduction band of amorphous InGaZnO4, three of the seven analyzed materials show some potential. The most promising candidate, K2Sn2O3, is expected to possess in its amorphous phase a slightly higher hole mobility than the electron mobility in amorphous silicon.

Abstract: We calculate the spectrum of states that are localized at the interface between two regions of opposite bias in trilayer graphene (TLG). These potential profiles, also known as potential kinks, have been predicted to support two different branches of localized states for the case of bilayer graphene, and show similarities to the surface states of topological insulators. On the other hand, we found that ABC stacked TLG exhibits three different unidimensional branches of states in each valley that are confined to the kink interface. They have the property E(k(y)) = -E(-k(y)) when belonging to the same valley and E-K(k(y)) = -E-K' (-k(y)). A kink-antikink potential profile opens a gap in the spectrum of these one-dimensional states.

Abstract: The effects of external electric and magnetic fields on the energy spectrum of quantum rings made out of a bidimensional semiconductor material with anisotropic band structures are investigated within the effective-mass model. The interplay between the effective-mass anisotropy and the radial confinement leads to wave functions that are strongly localized at two diametrically opposite regions where the kinetic energy is lowest due to the highest effective mass. We show that this quantum phenomenon has clear consequences on the behavior of the energy states in the presence of applied in-plane electric fields and out-of-plane magnetic fields. In the former, the quantum confined Stark effect is observed with either linear or quadratic shifts, depending on the direction of the applied field. As for the latter, the usual Aharonov-Bohm oscillations are not observed for a circularly symmetric confining potential, however they can be reinstated if an elliptic ring with an appropriate aspect ratio is chosen.

Abstract: Experiments have confirmed that double monolayer graphene does not generate finite-temperature electron-hole superfluidity, because of very strong screening of the pairing attraction. The linear dispersing energy bands in monolayer graphene block any attempt to reduce the strength of the screening. We propose a hybrid device with two sheets of monolayer graphene in a modulated periodic perpendicular magnetic field. The field preserves the isotropic Dirac cones of the original monolayers but reduces the slope of the cones, making the monolayer Fermi velocity v(F) smaller. We demonstrate that with current experimental techniques, the reduction in vF can weaken the screening sufficiently to allow electron-hole superfluidity at measurable temperatures.