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By using angle-resolved photoemission spectroscopy (ARPES), we study the electronic structure of highly oriented pyrolytic graphite (HOPG). In contrast to the pristine HOPG, band gap opening of approximately 100 meV is directly observed at the surface of nano-scale HOPG square pattern. Our Raman data and density functional theory calculations suggest that the bandgap opening is likely caused by tensile strain induced from the patterning. We believe that this surface engineering of HOPG will not only be useful for enhancing terahertz devices but also provides a route for modifying other materials/metasurfaces for optoelectronics applications.

The influence of spatial variation of Fermi velocity on the spin-polarized transport properties of massless Dirac fermions in proximity-induced ferromagnetic graphene junction was investigated. We found that the velocity ratio ξ causing the width of the spin conductance dip near the Dirac point is broadened as the Fermi velocity ratio increases. In contrast, the effect of the Fermi velocity mismatch does not affect the shifting of the Dirac point. It leads to the indirect measurement of the Fermi velocity ratio that can be tuned by the spin-dependent conductance. In addition to the presence of both the exchange field and the Fermi velocity modulation, we found high spin filtering occurs when the Fermi velocity ratio ξ ≥ 1. Due to the transmission probability of electron with spin down, T↓ is blocked by the effect of Fermi velocity modulation similar to waves travelling through a different media. Moreover, we also found that the resonant transmission of the electron with spin up can be perfectly transmitted through the Fermi velocity barrier at the limit injected angle θ → π/2 for H/EF ≈ 1. The spin transport properties can be controlled by suitably modifying the strength of the ferromagnetic insulator and varying the Fermi velocity modulation, which leads to the highest spin polarization. By manipulating the behavior of spin-dependent collimation and spin beam splitting in this structure, we proposed a spin transport device for making lateral spin polarization. These interesting features will help make the development of spintronic devices in the graphene-based nanostructure.

Recently, it has been found that, with the Rényi statistics, the asymptotically flat Schwarzschild black hole can be in thermal equilibrium with infinite heat reservoir at a fixed temperature when its event horizon radius is larger than the characteristic length scale Lλ=1/πλ, where λ is the nonextensivity parameter. In the Rényi extended phase space with the PdV work term, an off shell free energy in the canonical ensemble with the thermodynamic volume as an order parameter is considered to identify a first-order Hawking-Page (HP) phase transition as a solid-liquid phase transition. It has the latent heat of fusion from solid (corresponding to thermal radiation) to liquid (corresponding to black hole) in the form of ∼1/λ; this is evident in the absence of the HP phase transition in the case of an asymptotically flat Schwarzschild black hole from the Gibbs-Boltzmann statistics (λ=0). Moreover, we investigate the generalized second law of black hole thermodynamics (GSL) in Rényi statistics by considering the black hole as a working substance in a heat engine. Interestingly, an efficiency η of the black hole in a Carnot cycle takes the form ηc=1−TC/TH. This confirms the validity of the GSL in the Rényi extended phase space.

The phase structure and critical phenomena of the 3+1 dimensional charged black holes in asymptotically flat spacetime are investigated within the Rényi statistics. As the nonextensive parameter λ above zero, a charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation and have a Hawking–Page phase transition. This gives more evidence supporting the proposed conjectured equivalence between the black hole thermodynamics in asymptotically flat spacetime via Rényi statistics and that in asymptotically anti–de Sitter (AdS) spacetime via Gibbs–Boltzmann statistics. The present work also provides another aspect of supporting evidence through exploring the extended phase space within the Rényi statistics. Working on a modified version of the Smarr formula, the thermodynamic pressure P and volume v of a charged black hole are found to be related to λ. The thermodynamics of asymptotically flat charged black holes via Rényi statistics has the Van der Waals phase structure, P−v criticality and universal constant, in a similar way as that of asymptotically AdS charged black hole via Gibbs–Boltzmann statistics. This raises an interesting question of how λ in the former system relates to |Λ| in the latter one.

The tilt-mismatch effect on resonant tunneling through an electrical potential barrier in asymmetric tilt-Dirac cone junction is investigated. By varying barrier height, the angle-selective transmission of resonant tunneling oscillates as a function of gate voltage, and the linear phase shift due to the increase in the tilt parameter. We found that the signature of the tilt parameter can be determined by measuring the tunneling transport properties across the tilt-mismatch junction. For tilt-homogeneous junction, the tilt-induced pseudo-magnetic effect can occur only when an electric potential is applied to the system. However, the asymmetric tilt-energy dispersion systems also can mimic the pseudo-magnetic barrier structure without the electric potential. This result opens the opportunity for the tilt-Dirac cone system's magnetic focusing applications in electron-optics without magnetism.

Modulation effects of alternating periodic electrostatic scalar and magnetic vector potentials on the anisotropic and the tilt characteristics of Dirac cone in a semi-infinite graphene was theoretically investigated using the transfer matrix technique. To study its anisotropic behavior, we characterized the geometry deformation of superlattice Dirac cone by introducing the tilt parameter, eccentricity, and group velocity. We found that the Dirac cone anisotropy and tilt effect depend on the amplitude of the periodically modulated scalar and/or vector potentials. As the results of tuning the coupled periodic scalar and vector potentials, four different phases of Dirac fermions emerged and were categorized through a phase diagram of the tilt parameter. For a strong coupled modulation, the tilt parameter becomes larger than one and the type-II Dirac cone phase emerged. We also found that pairs of extra Dirac points can be induced by a very high periodic scalar modulation coupled with a low periodic vector modulation. Moreover, strong modulation caused the Fermi contour to deform from a closed contour into an opened contour, introducing an electron-hole pocket on the graphene. Our results demonstrate the possibility to control the anisotropic behavior of the electronic structure of graphene, which might lead to an artificial tilted Dirac cone material and direction-dependent quantum devices.

We studied electronic properties of a two-dimensional electron gas confined on the surface of helical curved tube, specifically, curvature induced by the geometry of helically coiled carbon nanotubes. The curvature generates two types of effective couplings that are (i) Penney-Kronig potential and (ii) a periodic spin-orbit potential. The energy-momentum dispersion relations are theoretically calculated using new variables to explain the electron spiraling around the circular helix line in counterclockwise and clockwise directions. Then we have to set up the formalism for dealing with a periodic potential as Bloch’s theorem. For calculation, we rewrite the Dirac equation in curved space-time in the form of a block matrix equation. Our numerical results demonstrate that there are pseudo-Landau quantization levels and the motion of an electron in circumference direction coupling with the arc length motion coupling. In addition, the one-dimensional dispersion relation lines present characteristics of time reversal symmetry and inversion symmetry. Finally, we also investigated the differential energy of band structures for the case where the periodic spin-orbit potential increased with respect to the increase of curvature. We found that the non-linearly increase of the differential energy was due to the periodic spin-orbit potential, corresponding to Zeeman effect.

The mismatch effect of a double Fermi-velocity barrier structures NG/FG 1 /NG/FG 2 /NG junction on the electrically driven SdH-like oscillations of spin-dependent conductance is investigated, where NG is normal graphene and FG 1,2 is the ferromagnetic-gate with Fermi-velocity modulation ξ 1,2 where ξ 1,2 is the Fermi velocity ratio between NG region and FG 1,2 region. The results show that the effect of asymmetry of the double Fermi-velocity barrier structures, the difference value between ξ 1 and ξ 2 cause of the oscillations the spin-dependent quantum beating pattern. Which the beating patterns of the spin transport appeared as a result of the superposition of the two oscillatory components in the double Fermi velocity barriers. In addition, we found that the shifting of the spin-dependent quantum beats of the G ↑ and G ↓ is due to the presence of the exchange field, H, that is, the G ↑ and G ↓ are shifted in the opposite direction. By the difference value of the phase shift can be estimated to be 2H . In case of U + η σ H > > E F which electrons are collimated, the oscillations behaviors show the quantum beating with holding constant amplitude and the period of the beating amplitude depend on the Fermi velocity ratio mismatch in FG regions. These interesting characteristic of spin-dependent quantum transport may identify the effect of Femi-velocity asymmetry on double proximity-induced ferromagnetic graphene structure for making spintronic devices.

We investigate that effect of the curvature on induced hybridization and modification of emission profiles for each chiral's index single-wall carbon nanotubes (SWCNTs). According to the Schwinger two particle pair state method, we provide an analytical expression by calculating polar of spot intensity as a function of the polar angle. The emission profiles for indirect transition have an asymmetric shape as a function of the electron wave vector of the axis direction kt and depend on the chiral index. Here we show polarization-dependent, given analytically by expanding the matrix element into the scalar product of the light polarization vector and the dipole vector. These scalar products having a maximum value depend on the summation of phase factors of spinors of electrons in the conduction band Φc and valence band Φv. In the case of direct transition, dipole vector tube axis is maximum at the phase summation of Φc and Φv is 0 or 2π. In contrast, the maximum dipole vector circumference is obtained at the phase summation of π for the case of indirect transition. We can predict a strong emission peak and emission profiles which can be used to identify optical transitions in an individual SWCNT with different chiral indices experimentally.

The ground state entanglement of the system, both in discrete-time and continuous-time cases, is quantified through the linear entropy. The result shows that the entanglement increases as the interaction between the particles increases in both time scales. It is also found that the strength of the harmonic potential affects the formation rate of the entanglement of the system. The different feature of the entanglement between continuous-time and discrete-time scales is that, for discrete-time entanglement, there is a cut-off condition. This condition implies that the system can never be in a maximally entangled state., 5 pages, 2 figures

We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain.

The influence of magnetic vector potential barrier (MVPB) on the spin-polarized transport of massless Dirac particles in ferromagnetic graphene is studied theoretically. The phenomenon of Klein tunneling of relativistic particles across a rectangular potential barrier prevents any of the massless fermions from being confined but they can be electrically confined by quantum dots with integrable dynamics (Bardarson et al., 2009) [36] . Utilization of only the in-plane exchange splitting in the ferromagnetic graphene cannot produce 100% spin polarization. This tunneling can be confined using the magnetic vector potential barrier, which leads to high degree of spin polarization. By combining the orbital effect and the Zeeman interaction in graphene junction, it is found that the junction mimics behavior of half-metallic tunneling junction, in which it acts as a metal to particles of one spin orientation but as an insulator or a semiconductor to those of the opposite orientation. The idea of the half-metallic tunneling junction can provide a source of ∼100% spin-polarized current, which is potentially very useful. Adjustment of the position of the Fermi level in ferromagnetic layer by placing a gate voltage on top of the ferromagnetic layer shows that reverse of the orientation of the completely spin-polarized current passing through the junction is controlled by adjusting the gate voltage. These interesting characteristics should lead to a practical gate voltage controlled spin filtering and spin-polarized switching devices as a perfect spin-polarized electron source for graphene-based spintronics.

The effects of the bias voltage placed on a second gate which is positioned to the left of the ferromagnetic graphene (FG) layer on the switching of the charge and spin transports in a ferromagnetic graphene junction are studied. We show that the change in the bias voltage from positive to negative (while maintaining the positive voltage on the first gate above the FG layer) can induce a switching from high to low conductance states in the junction. The voltage on the first gate is used to shift the Fermi level in the FG layer. Enhancement of the on/off conductance ratio on the switching is shown to be inversely proportional to the thickness of the second gate barrier. We show that by biasing the nanostructures with the voltage U2, the spin polarization can be increased and that as a consequence, the thickness of the FG barrier layer needed for spin-polarized transport can be reduced.