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 study the quantum Hall effect (QHE) in bilayer graphene using the Kubo-Greenwood formula. At zero temperature the Hall conductivity sigma(yx) is given by sigma(yx) – 4(N + 1)e(2)/h with N the index of the highest occupied Landau level (LL). Including the dispersion of the LLs and their width, due to e. g. scattering by impurities, produces the plateau of the n = 0 LL in agreement with experimental results on doped samples and similar theoretical results on single-layer graphene plateaus widen with impurity concentration. Further, the evaluated resistivity rho(xx) exhibits a strong, oscillatory dependence on the electron concentration. Explicit results are obtained for delta-function impurities.

Abstract: Artificial molecular states of double quantum dots defined in bilayer graphene are studied with the atomistic tight-binding method and its low-energy continuum approximation. We indicate that the extended electron wave functions have opposite parities on sublattices of the layers and that the ground-state wave-function components change from bonding to antibonding with the interdot distance. In the weak-coupling limit, the one most relevant for quantum dots defined electrostatically, the signatures of the interdot coupling include, for the two-electron ground state, formation of states with symmetric or antisymmetric spatial wave functions split by the exchange energy. In the high-energy part of the spectrum the states with both electrons in the same dot are found with the splitting of energy levels corresponding to simultaneous tunneling of the electron pair from one dot to the other.

Abstract: We numerically investigate the spin-orbit (SO) coupling effect on the magnetic flux evolution of energy and supercurrent in mesoscopic d-wave superconducting loops by solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. It is found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the [100] edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent. Moreover, in the case of rectangular loops with SO coupling, the jumps of the ground-state energy gradually disappear by increasing the ratio of length to height of the sample, and a paramagnetic response with opposite direction of the screening current around zero flux value can occur in such systems.

Abstract: The Majorana zero modes and persistent spin current in mesoscopic d-wave-superconducting loops with spin-orbit (SO) interaction are investigated by numerically solving the spin-generalized Bogoliubov-de Gennes equations self-consistently. For some appropriate strength of the SO coupling, Majorana zero-energy states and sharp jumps of the spin-polarized currents can be observed when the highest energy levels cross the Fermi energy in the spectrum, leading to spin currents with opposite chirality flowing near the inner and outer edges of the sample. When the threaded magnetic flux turns on, four flux-dependent patterns of the persistent spin current with step-like features show up, accompanied by Majorana edge modes at flux values where the energy gap closes. Moreover, the Majorana zero mode is highly influenced by the direction of the Zeeman field. A finite in-plane field can lead to the gap opening since the inversion symmetry is broken. Remarkably, multiple Majorana zero-energy states occur in the presence of an out-of-plane field h(z), and the number of steps in the spin current evolution can be effectively tuned by the field strength due to the shift of Majorana zero modes. Finally, when the loop sample contains surface indentation defects, zero-energy modes can always show up in the presence of an appropriate h(z). Interestingly, multiple Majorana states may be present in the system with a corner defect even if h(z) = 0.

Abstract: We investigated the magnetic flux dependence of the supercurrent in mesoscopic d-wave superconducting loops, containing impurities and surface defects, by numerically solving the Bogoliubovde Gennes equations self-consistently. In the presence of impurities, bound states arise close to the Fermi energy. In the case of a single impurity, the flux-induced current is found to be suppressed. This can be different when more impurities are introduced in the sample due to the quantum interference effect, which depends sensitively on the relative position between the impurities. We further analyze the effect of small surface defects at the inner or outer edge of the loop, and show that indentation and bulge defects have pronounced and different effects on the supercurrent.

Abstract: In the framework of the time-dependent Ginzburg-Landau formalism, we study the dynamics of vortex-antivortex (V-Av) pairs in mesoscopic symmetric and asymmetric superconducting loops under an applied ac current. In contrast to the case of a constant biasing dc current, the process of the V-Av collision and annihilation is strongly affected by the time-periodic ac signal. As the direction of the applied ac current is reversed, the existed V-Av pair moves backward and then collides with a new created Av-V pair in a symmetric loop. In the presence of an appropriate external magnetic field, a novel sinusoidal-like oscillatory mode of the magnetization curve is observed, and the periodic dynamical process of the V-Av annihilation occurs in both branches of the sample. Moreover, for the asymmetric sample with an off-centered hole the creation point of the V-Av pair shifts away from the center of the sample, and the creation and annihilation dynamics of V-Av pairs turns out to be very different from the symmetric case. Copyright (C) EPLA, 2014

Abstract: Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement-leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multivortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different from those predicted by the Ginzburg-Landau theory. These unconventional states are relevant for high-T-c nanograins, confined Bose-Einstein condensates, and graphene flakes with proximity-induced superconductivity.

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: Tunable transport properties and Fano resonances are predicted in a circular bilayer phosphorene nanoring. The conductance exhibits Fano resonances with varying incident energy and applied perpendicular magnetic field. These Fano resonance peaks can be accurately fitted with the well known Fano curves. When a magnetic field is applied to the nanoring, the conductance oscillates periodically with magnetic field which is reminiscent of the Aharonov-Bohm effect. Fano resonances are tightly related to the discrete states in the central nanoring, some of which are tunable by the magnetic field.

Abstract: We study the mobility of Dirac fermions in monolayer graphene on a GaAs substrate, limited by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (PA) and of the intrinsic deformation potential of acoustical phonons in graphene (DA). In the high-temperature (T) regime, the momentum relaxation rate exhibits the same linear dependence on T but different dependencies on the carrier density n, corresponding to the mobility mu proportional to 1 root n and 1/n, respectively for the PA and DA scattering mechanisms. In the low-T Bloch-Gruneisen regime, the mobility shows the same square-root density dependence mu proportional to root n, but different temperature dependencies mu proportional to T-3 and T-4, respectively for PA and DA phonon scattering. DOI: 10.1103/PhysRevB.87.075443

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: We present a theoretical investigation of the plasmon-polariton modes in grating coupled graphene inside a Fabry-Perot cavity. The cavity or photon modes of the device are determined by the Finite Difference Time Domain (FDTD) simulations and the corresponding plasmon-polariton modes are obtained by applying a many-body self-consistent field theory. We find that in such a device structure, the electric field strength of the incident electromagnetic (EM) field can be significantly enhanced near the edges of the grating strips. Thus, the strong coupling between the EM field and the plasmons in graphene can be achieved and the features of the plasmon-polariton oscillations in the structure can be observed. It is found that the frequencies of the plasmon-polariton modes are in the terahertz (THz) bandwidth and depend sensitively on electron density which can be tuned by applying a gate voltage. Moreover, the coupling between the cavity photons and the plasmons in graphene can be further enhanced by increasing the filling factor of the device. This work can help us to gain an in-depth understanding of the THz plasmonic properties of graphene-based structures.

Abstract: We present a theoretical study of the electrical generation of acoustic-phonon emission from graphene at room temperature. The drift velocity (v(x)) and temperature of electrons driven by dc electric field (F-x) are determined by solving self-consistently the momentum-and energy-balance equations derived from the Boltzmann equation. We find that in the presence of impurity, acoustic-and optic-phonon scattering, v(x) can be much larger than the longitudinal (v(l)) and transverse (v(t)) sound velocities in graphene even within the linear response regime. As a result, although the acoustic Cerenkov effect cannot be obviously seen in the analytical formulas, the enhanced acoustic-phonon emission can be observed with increasing F-x when v(x) > v(l) and v > v(t). The frequency of acoustic-phonon emission from graphene can be above 10 THz, which is much higher than that generated from conventional semiconductor systems. This study is pertinent to the application of graphene as hypersonic devices such as terahertz sound sources. (C) 2013 AIP Publishing LLC.