Abstract: It is well known that, in bulk, the solution of the Bogoliubovde Gennes equations is the same whether or not the HartreeFock term is included. Here the HartreeFock potential is position independent and so gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. This is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position-dependent HartreeFock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubovde Gennes equations with the HartreeFock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.

Abstract: he properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (δ-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a finite number of barriers. The results are contrasted with those for electrons described by the Schrödinger equation. In addition, a collimation of an incident beam of electrons is obtained along the direction perpendicular to that of the SL. We also highlight an analogy with optical media in which the refractive index varies in space.

Abstract: The dynamics of electrons and holes propagating through the nano-scaled channels of modern semiconductor devices can be seen as a widespread manifestation of non-equilibrium statistical physics and its ruling principles. In this respect both the devices that are pushing conventional CMOS technology towards the final frontiers of Moores law and the upcoming set of alternative, novel nanostructures grounded on entirely new concepts and working principles, provide an almost unlimited playground for assessing physical models and numerical techniques emerging from classical and quantum mechanical non-equilibrium theory. In this paper we revisit the Boltzmann as well as the WignerBoltzmann equation which offers a valuable platform to study transport of charge carriers taking part in drive currents. We focus on a numerical procedure that regained attention recently as an alternative tool to solve the time-dependent Boltzmann equation for inhomogeneous systems, such as the channel regions of field-effect transistors, and we discuss its extension to the WignerBoltzmann equation. Furthermore, we pay attention to the calculation of tunneling leakage currents. The latter typically occurs in nano-scaled transistors when part of the carrier distribution sustaining the drive current is found to tunnel into the gate due the presence of an ultra-thin insulating barrier separating the gate from the channel region. In particular, we discuss the paradox related to the very existence of leakage currents established by electrons occupying quasi-bound states, while the (real) wave functions of the latter cannot carry net currents. Finally, we describe a simple model to resolve the paradox as well as to estimate gate currents provided the local carrier generation rates largely exceed the tunneling rates.

Abstract: The time evolution of a wave packet injected into a semiconductor quantum ring is investigated in order to obtain the transmission and reflection probabilities. Within the effective-mass approximation, the time-dependent Schrödinger equation is solved for a system with nonzero width of the ring and leads and finite potential-barrier heights, where we include smooth lead-ring connections. In the absence of a magnetic field, an analysis of the projection of the wave function over the different subband states shows that when the injected wave packet is within a single subband, the junction can scatter this wave packet into different subbands but remarkably at the second junction the wave packet is scattered back into the subband state of the incoming wave packet. If a magnetic field is applied perpendicularly to the ring plane, transmission and reflection probabilities exhibit Aharonov-Bohm (AB) oscillations and the outgoing electrons may end up in different subband states from those of the incoming electrons. Localized impurities, placed in the ring arms, influence the AB oscillation period and amplitude. For a single impurity or potential barrier of sufficiently strong strength, the period of the AB oscillations is halved while for two impurities localized in diametrically opposite points of the ring, the original AB period is recovered. A theoretical investigation of the confined states and time evolution of wave packets in T wires is also made, where a comparison between this system and the lead-ring junction is drawn.

Abstract: We study the effect of electron confinement on the superconducting-to-normal phase transition driven by a magnetic field and/or on the current-carrying state of the superconducting condensate in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We show that in a parallel magnetic field and/or in the presence of supercurrent the transition from superconducting to normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magnetic field exhibits quantum-size oscillations with pronounced resonant enhancements.

Abstract: We theoretically investigate resonant tunneling through S- and U-shaped nanostructured graphene nanoribbons. A rich structure of resonant tunneling peaks is found emanating from different quasi-bound states in the middle region. The tunneling current can be turned on and off by varying the Fermi energy. Tunability of resonant tunneling is realized by changing the width of the left and/or right leads and without the use of any external gates.

Abstract: In this study we investigate the effect of device topology on the ballistic current in n-channel metal-oxide-semiconductor field-effect transistors. Comparison of the nanoscale planar and double-gate devices reveals that, down to a certain thickness of the double gate film, the ballistic current flowing in the double gate device is twice as large compared to its planar counterpart. On the other hand, further thinning of the film beyond this threshold is found to change noticeably the confinement and transport characteristics, which are strongly depending on the film material and the surface orientation. For double gate Ge and Si devices there exists a critical film thickness below which the transverse gate field is no longer effectively screened by the inversion layer electron gas and mutual inversion of the two gates is turned on. In the case of GaAs and other similar IIIV compounds, a decrease in the film thickness may drastically change the occupation of the L-valleys and therefore amend the transport properties. The simulation results show that, in both cases, the ballistic current and the transconductance are considerably enhanced.

Abstract: By using a model Hamiltonian with competing antiferromagnetic (AFM) and d-wave superconductivity orders, the impurity-induced structures of orders in d-wave superconductors is investigated. We find that the transition between one-dimensional stripe and two-dimensional checkerboardlike modulation around a single nonmagnetic impurity can take place as the strength of the AFM interaction U or the impurity scattering strength V0 is varied. It is also found that the impurity-induced stripe can first transit to checkerboardlike modulation and then disappears with increasing the next-nearest-neighbor hopping strength |t|. Phase diagrams of V0 versus U and |t| for various modulations of the spin order are presented. In addition, the quantum interference effect on the modulations of orders due to two strong nonmagnetic impurities is briefly examined, and the checkerboardlike and quasistripe patterns can occur depending on the sites where two impurities are placed.

Abstract: We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene. These structures can be created by tuning the gap of the graphene bilayer using nanostructured gates or by position-dependent doping. The energy levels have a magnetic field (B0) dependence that is strikingly distinct from that of usual semiconductor quantum rings. In particular, the eigenvalues are not invariant under a B0 ¨ −B0 transformation and, for a fixed total angular momentum index m, their field dependence is not parabolic, but displays two minima separated by a saddle point. The spectra also display several anticrossings, which arise due to the overlap of gate-confined and magnetically confined states.

Abstract: We present a theoretical study of the optoelectronic properties of bilayer graphene. The optical conductance and transmission coefficient are calculated using the energy-balance equation derived from a Boltzmann equation for an air/graphene/dielectric-wafer system. For short wavelengths (<0.2 µm), we obtain the universal optical conductance =e2/(2). Interestingly, there exists an optical absorption window in the wavelength range 10100 µm, which is induced by different transition energies required for inter- and intra-band optical absorptions in the presence of the MossBurstein effect. As a result, the position and width of this absorption window depend sensitively on temperature, carrier density, and sample mobility of the system. These results are relevant for applications of recently developed graphene devices in advanced optoelectronics such as the infrared photodetectors.

Abstract: We studied the effect of sample geometry on the evolution of the superconducting state in nanoscale Nb circular and square loops by transport measurements. A multistage resistive transition with temperature is found for both samples, which is related to the effect of contact leads made from the same superconducting material. The H-T phase diagrams close to Tc0 show clear periodic oscillations on top of a parabolic background, i.e., Little-Parks effect. However, the amplitude of the oscillations decreases faster in the circular loop compared to the one in the square sample. Numerical simulations are conducted within the nonlinear Ginzburg-Landau theory to show the effect of sample geometry on the nucleation of superconductivity in superconducting loop structures.

Abstract: The lowest energy electronic states of a donor located near a semiconductor-insulator-metal interface are investigated within the effective mass approach. The effect of the finite thickness of the insulator between the semiconductor and the metallic gate on the energy levels is studied. The lowest energy states are obtained through a variational approach, which takes into account the influence of all image charges that arise due to the presence of the metallic and the dielectric interfaces. We compare our results with a numerical exact calculation using the finite element technique.

Abstract: From a numerical solution of the Bogoliubov-de Gennes equations, we investigate an interplay of the transverse discrete modes with a longitudinal supercurrent in a metallic cylindrical superconducting nanowire. The superconductor-to-normal transition induced by a longitudinal superflow of electrons is found to occur as a cascade of jumps in the order parameter (supercurrent and superfluid density) as a function of the superfluid velocity for diameters d<1015 nm (for Al parameters) and sufficiently low temperatures T<0.30.4Tc, with Tc the critical temperature. When approaching Tc, the jumps are smoothed into steplike but continuous drops. A similar picture occurs for d>1520 nm. Only when the diameter exceeds 5070 nm the quantum-size cascades are fully washed out, and we arrive at the mesoscopic regime. Below this regime the critical current density jc exhibits the quantum-size oscillations with pronounced resonant enhancements: the smaller the diameter, the more significant is the enhancement. Thickness fluctuations of real samples will smooth out such oscillations into an overall growth of jc with decreasing nanowire diameter.

Abstract: We apply density-functional theory to study the adsorption of water clusters on the surface of a graphene sheet and find i) graphene is highly hydrophobic and ii) adsorbed water has very little effect on the electronic structure of graphene. A single water cluster on graphene has a very small average dipole moment which is in contrast with an ice layer that exhibits a strong dipole moment.

Abstract: We study single- and two-electron parabolic quantum dots in the presence of linear Dresselhaus and Rashba spin-orbit interactions. Contributions of both types of spin-orbit coupling are investigated in the context of the spin polarization of the system at high magnetic fields. We demonstrate that for negative Landé factors the effect of the Dresselhaus coupling is suppressed at high magnetic field, which for structures without inversion asymmetry leads to a completely spin-polarized system and a strict antisymmetry of the wave functions with respect to the interchange of spatial-electron coordinates. For negative Landé factor the Rashba coupling is preserved at high field and consequently the spin polarization of the systems as well as the spatial antisymmetry of the two-electron wave function remain approximate.