We investigate topological phases induced by a driven electric field coupled to a dimer chain (a model for polyacetylene) at high frequency regime. It is shown how the topological invariant of the system can be controlled by the field amplitude. Furthermore, in the presence of a time-periodic electric field, the effect of the next-nearest neighbour hopping amplitudes on topological properties is studied. Breaking of the inversion symmetry causes to remove the degeneracy of zero edge states. The fractional Zak phase which is now measurable by ultra-cold atoms in one dimensional optical lattice is also calculated. For calculating modified band structure, we also develop a general Floquet-Bloch approach for systems under application of a potential with lattice and time translation invariance.

We theoretically study the effect of impurity resonances on the indirect exchange interaction between magnetic impurities in the surface states of a three dimensional topological insulator. The interaction is composed of an isotropic Heisenberg, and anisotropic Ising and Dzyaloshinskii-Moriya contributions. We find that all three contributions are finite at the Dirac point, which is in stark contrast to the linear response theory which predicts a vanishing Dzyaloshinskii-Moriya contribution. We show that the spin-independent component of the impurity scattering can generate large values of the DM term in comparison with the Heisenberg and Ising terms, while these latter contributions drastically reduce in magnitude and undergo sign changes. As a result, both collinear and non-collinear configurations are allowed magnetic configurations of the impurities.

We address the electronic structure of the surface states of topological-insulator thin films with embedded local nonmagnetic and magnetic impurities. Using the T -matrix expansion of the real-space Green’s function, we derive the local density of electron states and corresponding spin-resolved densities. We show that the effects of the impurities can be tuned by applying an electric field between the surface layers. The emerging magnetic states are expected to play an important role both in the ferromagnetic mechanism of magnetic topological insulators and in its transport properties. In the case of magnetic impurities, we have categorized the possible cases for different spin directions of the impurities as well as the spin direction in which the spin-resolved density of electron states is calculated and have related them to the spin susceptibility of the system.

We investigate the effect of Rashba splitting on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a topological-insulator (TI) thin film both at finite and zero chemical potential. We show that the spin susceptibility of the TI thin film depends strongly on the direction of the distance vector between impurities. In addition to the well-known Heisenberg-, Ising-, and Dzyaloshinskii-Moria (DM)-like terms reported before in TIs, we find another term in the off-diagonal part of the spin-susceptibility tensor which is symmetric in contrast to the DM term. Furthermore, we show how one can tune the RKKY interaction by using electric field applied perpendicularly to the surface plane of the TI, where in the presence of such a field the RKKY interaction can be enhanced drastically for small chemical doping. We present our results for two different situations, namely intersurface pairing of magnetic impurities as well as intrasurface pairing. The behavior of these two situations is completely different, which we describe by mapping the density of states of each surface on the band dispersion.

The electronic transport properties in magnetically doped ultrathin films of topological insulators are
investigated by using Landauer-Buttiker formalism. The chiral selective tunneling is addressed in such systems which leads to transport gap and as a consequence current blocking. This quantum blocking of transport occurs when the magnetic states with opposite chirality are aligned energetically. This can be observed when an electron tunnels through a barrier or well of magnetic potential induced by the exchange field. It is proved and demonstrated that this chiral transition rule fails when structural inversion asymmetric potential or an in-plane magnetization is turning on. This finding is useful to interpret quantum transport through topological-insulator thin films especially to shed light on longitudinal conductance behavior of quantum anomalous Hall effect. Besides, one can design
electronic devices by means of magnetic topological-insulator thin films based on the chiral selective tunneling leading to negative differential resistance.

We derive an effective Hamiltonian at low energies for bilayer graphene when Fermi velocity manufactured on each layer is different of the velocity measured in pristine graphene. Based on the effective Hamiltonian, we investigate the influence of Fermi velocity asymmetry on the band structure of trigonally warped bilayer graphene in the presence of interlayer applied bias. In this case, the Fermi line at low energies is still preserved its threefold rotational symmetry appearing as the three pockets. Furthermore, the interlayer asymmetry in Fermi velocities leads to an indirect band gap which its value is tunable by the velocity ratio of the top to bottom layer. It is also found that one of the origins for emerging the electron-hole asymmetry in the band structure, is the velocity asymmetry which is large around the trigonal pockets.

We show how a superconducting region (S), sandwiched between two normal leads (N), in the presence of
barriers, can act as a lens for propagating electron and hole waves by virtue of the so-called crossed Andreev reflection (CAR). The CAR process, which is equivalent to Cooper pair splitting into two N electrodes, provides a unique possibility of constructing entangled electrons in solid state systems.When electrons are locally injected from an N lead, due to the CAR and normal reflection of quasiparticles by the insulating barriers at the interfaces, sequences of electron and hole focuses are established inside another N electrode. This behavior originates from the change of momentum during electron-hole conversion beside the successive normal reflections of electrons and holes due to the barriers. The focusing phenomena studied here are fundamentally different from the electron focusing in other systems, such as graphene p-n junctions. In particular, due to the electron-hole symmetry of the
superconducting state, the focusing of electrons and holes is robust against thermal excitations. Furthermore, the effects of the superconducting layer width, the injection point position, and barrier strength are investigated on the focusing behavior of the junction. Very intriguingly, it is shown that by varying the barrier strength, one can separately control the density of electrons or holes at the focuses.

By combining Floquet theory with Green’s function formalism, we present non-adiabatic quantum spin
and charge pumping through a zigzag ferromagnetic graphene nanoribbon including a double-barriers
structure driven weakly by two local ac gate voltages operating with a phase-lag. Over a wide range of
Fermi energies, interesting quantum pumping such as (i) pure spin pumping with zero net charge
pumping, (ii) pure charge pumping and (iii) fully spin polarized pumping can be achieved by tuning and
manipulating driving frequency in the non-adiabatic regime. Spin polarized pumping which is measurable
using the current technology depends on the competition between the energy level spacing and
the driving frequency.

Coherent spin-dependent transport through a junction containing normal/ferromagnetic/normal bilayer
graphene nanoribbon with zigzag edges is investigated by using Landauer formalism. In a more realistic setup, the exchange field is induced by two ferromagnetic insulator strips deposited on the ribbon edges while a perpendicular electric field is applied by the top gated electrodes. Our results show that, for antiparallel configuration, a band gap is opened giving rise to a semiconducting behavior, while for parallel configuration, the band structure has no band gap. As a result, a giant magnetoresistance is achievable by changing the alignment of induced magnetization. Application of a perpendicular electric field on the parallel configuration results in a spin field-effect transistor where a fully spin polarization occurs around the Dirac point. To compare our results with the one for monolayer graphene, we demonstrate that the reflection symmetry and so the parity conservation fail in bilayer graphene nanoribbons with the zigzag edges.

The band structure and transport properties of massive Dirac fermions in bilayer graphene
with velocity modulation in space are investigated in the presence of a previously created band
gap. It is pointed out that velocity engineering may be considered as a factor to control the
band gap of symmetry-broken bilayer graphene. The band gap is direct and independent of
velocity value if the velocity modulated in two layers is set up equally. Otherwise, in the case
of interlayer asymmetric velocity, not only is the band gap indirect, but also the electron–hole
symmetry fails. This band gap is controllable by the ratio of the velocity modulated in the
upper layer to the velocity modulated in the lower layer. In more detail, the shift of momentum
from the conduction band edge to the valence band edge can be engineered by the gate bias
and velocity ratio. A transfer matrix method is also elaborated to calculate the four-band
coherent conductance through a velocity barrier possibly subjected to a gate bias. Electronic
transport depends on the ratio of velocity modulated inside the barrier to that for surrounding
regions. As a result, a quantum version of total internal reflection is observed for thick enough
velocity barriers. Moreover, a transport gap originating from the applied gate bias is
engineered by modulating the velocities of the carriers in the upper and lower layers.

Abstract

Abstract

Abstract:

Using the transfer matrix method, we study the conductance of the chiral particles through a monolayer graphene superlattice with long-range correlated disorder distributed on the potential of the barriers. Even though the transmission of the particles through graphene superlattice with white noise potentials is suppressed, the transmission is revived in a wide range of angles when the potential heights are long-range correlated with a power spectrum S(k) ∼ 1/kβ . As a result, the conductance increases with increasing the correlation exponent values gives rise a metallic phase. We obtain a phase transition diagram in which a critical correlation exponent depends strongly on disorder strength and slightly on the energy of the incident particles. The phase transition, on the other hand, appears in all ranges of the energy from propagating to evanescent mode regimes

Abstract

Abstract:

Using self-consistent calculations based on nonequilibrium Green’s function formalism, the origin of negative differential resistance (NDR) in molecular junctions and quantum wires is investigated. Coupling of the molecule to electrodes becomes asymmetric at high bias due to asymmetry between its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels. This causes appearance of an asymmetric potential profile due to a depletion of charge and reduction of screening near the source electrode. With increasing bias, this sharp potential drop leads to an enhanced localization of the HOMO and LUMO states in different parts of the system. The reduction in overlap, caused by localization, results in a significant reduction in the transmission coefficient and current with increasing bias. An atomic chain connected to two graphene ribbons was investigated to illustrate these effects. For a chain substituting a molecule, an even-odd effect is also observed in the NDR characteristics.

Abstract

The exact probability distributions of the resistance, the conductance and the transmission are calculated for the one-dimensional Anderson model with long-range correlated off-diagonal disorder at E = 0. It is proved that despite the Anderson transition in 3D, the functional forms of the resistance and its related variables distribution functions do not vary when there exists a metal– insulator transition induced by a correlation among disorders. Furthermore, we derive analytically all statistical moments of the resistance, the transmission and the Lyapunov exponent. The rate of growth of the resistance with the length decreases as the Hurst exponent H tends to its critical value (Hcr = 1/2) from the insulating regime. In the metallic regime H ≥ 1/2, all distributions become independent of size. Therefore, in the thermodynamic limit, the resistance and the transmission fluctuations do not diverge with the length in this regime.

Validity of the single-parameter scaling (SPS) in the one-dimensional Anderson model with purely off-diagonal disorder is studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS. Moreover, the scaling relations for the Lyapunov exponent are proposed for these two regimes. In the non-SPS regime, in addition to the localization length, there exists a new length scale which is related to the integral density of states. A physical interpretation of the new length is as the crossover length which separates regions with chiral symmetry from those with standard symmetry.

The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at the band center in terms of the pair correlation function. It is proved that for long-range correlated hopping disorder, a localization-delocalization transition occurs at the critical Hurst exponent Hc =1/2 when the variance of the logarithm of hopping “lnt” is kept fixed with system size N. Numerically, this transition can be expanded to the vicinity of the band center. Based on numerical calculations, finite-size scaling relations are postulated for the localization length near the band center E0 in terms of the system parameters E,N,H, and lnt. D