Abstract: within the Kubo formalism. We show that the anisotropic Rashba effect caused by an external field significantly changes the magnitude of the spin splitting. Furthermore, we obtain an analytical expression for the longitudinal optical conductivity associated with interband transitions as a function of the frequency for arbitrary polarization angle. We find that the diagonal components of the optical conductivity tensor are direction dependent and the optical absorption spectrum exhibits a strongly anisotropic absorption window. The height and width of this absorption window are very sensitive to the anisotropy of the system. While the height of absorption peak increases with increasing effective mass anisotropy ratio, the peak intensity is larger when the light polarization is along the armchair direction. Moreover, the absorption peak width becomes broader as the density-of-states mass or Rashba interaction is enhanced. These features in the optical absorption spectrum can be used to determine parameters relevant for spintronics.

Abstract: Using the tight-binding approach, we investigate the electronic properties of bilayer phosphorene (BLP) quantum dots (QDs) in the presence of perpendicular electric and magnetic fields. Since BLP consists of two coupled phosphorene layers, it is of interest to examine the layer-dependent electronic properties of BLP QDs, such as the electronic distributions over the two layers and the so-produced layer-polarization features, and to see how these properties are affected by the magnetic field and the bias potential. We find that in the absence of a bias potential only edge states are layer polarized while the bulk states are not, and the layer-polarization degree (LPD) of the unbiased edge states increases with increasing magnetic field. However, in the presence of a bias potential both the edge and bulk states are layer polarized, and the LPD of the bulk (edge) states depends strongly (weakly) on the interplay of the bias potential and the interlayer coupling. At high magnetic fields, applying a bias potential renders the bulk electrons in a BLP QD to be mainly distributed over the top or bottom layer, resulting in layer-polarized bulk Landau levels (LLs). In the presence of a large bias potential that can drive a semiconductor-to-semimetal transition in BLP, these bulk LLs exhibit different magnetic-field dependences, i.e., the zeroth LLs exhibit a linearlike dependence on the magnetic field while the other LLs exhibit a square-root-like dependence.

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: A magnetic moment inside an extreme type II superconductor can have three, but not one or two, confined vortex loops near to the core. For a sub-micron superconducting particle the confined vortex loops eventually break up and reach the surface turning into external vortex pairs.

Abstract: Merged, or giant, multi-quanta vortices (GVs) appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters/GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Abstract: Using the tight-binding approach, we investigate the energy spectrum of square, triangular, and hexagonal MoS2 quantum dots (QDs) in the presence of a perpendicular magnetic field. Novel edge states emerge in MoS2 QDs, which are distributed over the whole edge which we call ring states. The ring states are robust in the presence of spin-orbit coupling (SOC). The corresponding energy levels of the ring states oscillate as a function of the perpendicular magnetic field which are related to Aharonov-Bohm oscillations. Oscillations in the magnetic field dependence of the energy levels and the peaks in the magneto-optical spectrum emerge (disappear) as the ring states are formed (collapsed). The period and the amplitude of the oscillation decrease with the size of the MoS2 QDs.

Abstract: Defects are almost inevitably present in realistic materials and defective materials are expected to exhibit very different properties than their nondefective (perfect) counterparts. Here, using a combination of the tight-binding approach and the scattering matrix formalism, we investigate the electronic transport properties of defective phosphorene nanoribbons (PNRs) containing atomic vacancies. We find that for both armchair PNRs (APNRs) and zigzag PNRs (ZPNRs), single vacancies can create quasilocalized states, which can affect their conductance. With increasing vacancy concentration, three different transport regimes are identified: ballistic, diffusive, and Anderson localized ones. In particular, ZPNRs that are known to be metallic due to the presence of edge states become semiconducting: edge conductance vanishes and transport gap appears due to Anderson localization. Moreover, we find that for a fixed vacancy concentration, both APNRs and ZPNRs of narrower width and/or longer length are more sensitive to vacancy disorder than their wider and/or shorter counterparts, and that for the same ribbon length and width, ZPNRs are more sensitive to vacancy disorder than APNRs.

Abstract: The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson's equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed.

Abstract: By taking account of the electric-field-induced charge screening, a self-consistent calculation within the framework of the tight-binding approach is employed to obtain the electronic band structure of gated multilayer phosphorene and the charge densities on the different phosphorene layers. We find charge density and screening anomalies in single-gated multilayer phosphorene and electron-hole bilayers in dual-gated multilayer phosphorene. Due to the unique puckered lattice structure, both intralayer and interlayer charge screenings are important in gated multilayer phosphorene. We find that the electric-field tuning of the band structure of multilayer phosphorene is distinctively different in the presence and absence of charge screening. For instance, it is shown that the unscreened band gap of multilayer phosphorene decreases dramatically with increasing electric-field strength. However, in the presence of charge screening, the magnitude of this band-gap decrease is significantly reduced and the reduction depends strongly on the number of phosphorene layers. Our theoretical results of the band-gap tuning are compared with recent experiments and good agreement is found.

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: Excitonic superfluidity in double phosphorene monolayers is investigated using the BCS mean-field equations. Highly anisotropic superfluidity is predicted where we found that the maximum superfluid gap is in the Bose-Einstein condensate (BEC) regime along the armchair direction and in the BCS-BEC crossover regime along the zigzag direction. We estimate the highest Kosterlitz-Thouless transition temperature with maximum value up to similar to 90 K with onset carrier densities as high as 4 x 10(12) cm(-2). This transition temperature is significantly larger than what is found in double electron-hole few-layers graphene. Our results can guide experimental research toward the realization of anisotropic condensate states in electron-hole phosphorene monolayers.

Abstract: Edge functionalization of graphene nanoribbons with nitrogen atoms for various adatom configurations at armchair and zigzag edges are investigated. We provide comprehensive information on the electronic and magnetic properties and investigate the stability of the various systems. Two types of rippling of the nanoribbons, namely edge and bulk rippling depending on the sign of edge stress induced at the edge, are found. They are found to play the decisive role for the stability of the structures. We also propose a type of edge decoration in which every third nitrogen adatom at the zigzag edges is replaced by an oxygen atom. In this way, the electron count is compatible with a full aromatic structure, leading to additional stability and a disappearance of magnetism that is usually associated with zigzag nanoribbons.

Abstract: We investigate theoretically the transport properties of Dirac fermions on the surface of a three-dimensional topological insulator. Dirac electrons can be totally reflected in front of a magnetic/electric p-n junction. For a p-n-p structure, multiple total internal reflections at the interfaces result in the bound states in the channel, which behaves like an electronic waveguide. This p-n-p like structure exhibits spin and momentum filtering features and could be used as a spin and/or charge diode.

Abstract: We use a variational technique to study the many-body phase diagram of electrons and holes in n-doped and p-doped monolayer transition metal dichalcogenides (TMDs). We find a total of four different phases. (i) A fully spin polarized and valley polarized ferromagnetic state. (ii) A state with no global spin polarization but with spin polarization in each valley separately, i.e., spin-valley locking. (iii) A state with spin polarization in one of the valleys and little to no spin polarization in the other valley. (iv) A paramagnetic state with no valley polarization. These phases are separated by first-order phase transitions and are determined by the particle density and the dielectric constant of the substrate. We find that in the presence of a perpendicular magnetic field the four different phases persist. In the case of n-doped MoS2, a fifth phase, which is completely valley polarized but not spin polarized, appears for magnetic fields larger than 7 T and for magnetic fields larger than 23 T completely replaces the second phase.