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The transition dynamics of two-state systems with time-dependent energy levels, first considered by Landau, Zener, Majorana, and St\"uckelberg, is one of the basic models in quantum physics and has been used to describe various physical systems. We propose here a generalization of the Landau-Zener (LZ) problem characterized by distinct paths of the instantaneous eigenstates as the system evolves in time, while keeping the instantaneous eigenenergies exactly as in the standard LZ model. We show that these paths play an essential role in the transition probability $P$ between the two states, and can lead to superadiabatic transitions, i.e., to a substantial reduction of $P$. As an instructive extreme case, we identify an unconditionally adiabatic regime with $P=0$ no matter how fast the system evolves in time and regardless of the energy gap between the two levels at the anticrossing point. On the other hand, large $P$ occur even in the absence of any anticrossing point. These phenomena can be explained by observing the rotation of the instantaneous eigenvectors on the Bloch sphere. The superadiabatic LZ model can describe valley transition dynamics during charge and spin shuttling in semiconductor quantum dots., Comment: 6 pages, 3 figures

The valley splitting (VS) of a silicon quantum dot plays an important role for the performance and scalability of silicon spin qubits. In this work we investigate the VS of a SiGe/Si/SiGe heterostructure as a function of the size and location of the silicon quantum dot. We use the effective mass approach to describe a realistic system, which takes into account concentration fluctuations at the Si/SiGe interfaces and also the interface roughness. We predict that the size of the quantum dot is an important parameter for the enhancement of the VS and it can also induce a transition between the disorder-dominated to deterministic-enhanced regimes. Analyzing how the VS changes when we move the quantum dot in a specific direction, we obtain that the size of the quantum dot can be used to reduce the variability of the VS, which is relevant for charge/spin shuttling.

In this work we investigate the transport properties of non-relativistic quantum particles on incommensurate multilayered structures with the thicknesses $w_n$ of the layers following an extended Harper model given by $w_n = w_0 |\cos(\pi a n^{\nu})|$. For the normal incidence case, which means an one-dimensional system, we obtained that for a specific range of energy, it is possible to see a metallic-insulator transition with the exponent $\nu$. A metallic phase is supported for $\nu<1$. We also obtained that for the specific value $\nu=1$ there is an alternation between metallic and insulator phases as we change the disorder strength $w_0$. When we integrate out all incidence angles, which means a two-dimensional system, the metallic-insulator transition can be seen for much larger range of energy compared to the normal incidence case.

The performance and scalability of silicon spin qubits depend directly on the value of the conduction band valley splitting. In this work, we investigate the influence of electromagnetic fields and the interface width on the valley splitting of a quantum dot in a Si/SiGe heterostructure. We propose a new three-dimensional theoretical model within the effective mass theory for the calculation of the valley splitting in such heterostructures that takes into account the concentration fluctuation at the interfaces and the lateral confinement. With this model, we predict that the electric field is an important parameter for valley splitting engineering, since it can shift the probability distribution away from small valley splittings for some interface widths. We also obtain a critical softness of the interfaces in the heterostructure, above which the best option for spin qubits is to consider an interface as wide as possible.

We investigate the propagation of waves in one-dimensional systems with L\'evy-type disorder. We perform a complete analysis of non-relativistic and relativistic wave transmission submitted to potential barriers whose width, separation or both follow L\'evy distributions characterized by an exponent $0 < \alpha <1$. For the first two cases, where one of the parameters is fixed, non-relativistic and relativistic waves present anomalous localization, $\langle T \rangle \propto L^{-\alpha}$. However, for the latter case, in which both parameters follow a L\'evy distribution, non-relativistic and relativistic waves present a transition between anomalous and standard localization as the incidence energy increases relative to the barrier height. Moreover, we obtain the localization diagram delimiting anomalous and standard localization regimes, in terms of incidence angle and energy. Finally, we verify that transmission fluctuations, characterized by its standard deviation, are universal, independent of barrier architecture, wave equation type, incidence energy and angle, further extending earlier studies on electronic localization., Comment: Accepted for publication as a Regular Article in Physical Review E

We study the suppression of the conductance quantization in quantum spin Hall systems by a combined effect of electronic interactions and edge disorder, that is ubiquitous in exfoliated and CVD grown 2D materials. We show that the interplay between the electronic localized states due to edge defects and electron-electron interactions gives rise to local magnetic moments, that break time-reversal symmetry and the topological protection of the edge states in 2D topological systems. Our results suggest that edge disorder leads to small deviations of a perfect quantized conductance in short samples and to a strong conductance suppression in long ones. Our analysis is based on on the Kane-Mele model, an unrestricted Hubbard mean field Hamiltonian and on a self-consistent recursive Green's functions technique to calculate the transport quantities., Comment: 6 pages, 3 figures

We theoretically study the thermoelectric transport properties of strained HgTe in the topological insulator phase. We developed a model for the system using a Dirac Hamiltonian including the effect of strain induced by the interface between HgTe and the CdTe substrate. The conductivity tensor was explored assuming the electrons are scattered by charge impurities, while the thermopower tensor was addressed using the Mott relation. Seebeck and Nernst responses exhibit remarkable enhancements in comparison with other two-dimensional Dirac materials, such as graphene, germanane, prosphorene and stanene. The intensity of these termoeletric responses, their dependencies with the external perpendicular magnetic field and temperature are also addressed.

We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-B\"uttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to local equilibrium spin currents, that we analyze in the quantum spin Hall regime., Comment: 16 pages, 11 figures

The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons., Comment: The following article has been accepted by J. of Applied Physics

The search for new materials is a very intense task in many technological areas. In 2015, a new variant of graphene was proposed, the pentagraphene, which was followed by the propose of a pentagonal boron nitride structure called penta-BN$_2$. Based on these structures, we investigated the electronic, magnetic, and optical properties of penta-BN$_2$ nanoribbons (p-BNNRs) considering four different kinds of edges, carefully closing the valence shells with H atoms to prevent dangling bonds. To achieve this goal, we used first-principles calculations in a density functional theory framework. Our findings showed that the p-BNNRs have a rich magneto-electronic behavior, varying from semiconductor to half-metal. We obtained that they are ferrimagnetic, having an intrinsic magnetism, which allow potential applications in spintronic or spinwaves. From an optical absorption point of view, they mainly absorb at ultraviolet region of the spectrum, especially at UV-B region, which could indicate a potential application as a UV filter.

In 2015, a new two dimensional (2D) carbon allotrope, called phagraphene, was theoretically proposed. Based on this structure, we propose here a new boron nitride structure called phaBN. It is composed by three types of rings: pentagons, hexagons and heptagons. We investigate the electronic, optical, vibrational and thermodynamic properties of phaBN using first-principles calculations in a density functional theory (DFT) framework. Our calculations revealed that the phaBN has an energy gap of 2.739 eV, which is almost half of the energy gap of the hexagonal boron nitride (h-BN), thus being a semiconductor material. By means of the optical, vibrational and thermodynamic properties, it was possible to observe the absorption interval, the stability of the structure and its formation process, respectively.

A transfer matrix approach is used to study the electronic transport in graphene superlattices with long-range correlated barrier spacements. By considering the low-energy electronic excitations as massless Dirac fermions, we compute by transmission spectra of graphene superlattices with potential barriers having spacements randomly distributed with long-range correlations governed by a power-law spectral density $S(k)\propto 1/k^{\alpha}$. We show that at large incidence angles, the correlations in the disorder distribution do not play a significant role in the electronic transmission. However, long-range correlations suppress the Anderson localization as normal incidence is approached and a band of transmitting modes sets up reminiscent of Klein tunneling.

In this work we investigate theoretically the influence of a Fermi velocity modulation in the electronic and transport properties of magnetic graphene superlattices. We solve the effective Dirac equation for graphene with a position dependent vector potential and Fermi velocity and use the transfer matrix method to obtain the transmission coefficient for the finite cases and the dispersion relation for a periodic superlattice. Our results reveals that the Fermi velocity modulation can control the resonance peaks of the transmittance and also works as a switch, turning on/off the transmission through the magnetic barriers. The results obtained here can be used for the fabrication of graphene-based electronic devices.

We study the quantum dynamics of ballistic electrons in rotating carbon nanotubes in the presence of a uniform magnetic field. When the field is parallel to the nanotube axis, the rotation-induced electric field brings about the spin-orbit interaction which, together with the kinetic, inertial, and Zeeman terms, compose the Schr\"odinger-Pauli Hamiltonian of the system. Full diagonalization of this Hamiltonian yields the eigenstates and eigenenergies leading to the calculation of the charge and spin currents. Our main result is the demonstration that, by suitably combining the applied magnetic field intensity and rotation speed, one can tune one of the currents to zero while keeping the other one finite, giving rise to a spin current generator.

In this work we investigate the effects of a Fermi velocity modulation in a valley filter in graphene created by a combination of a magnetic and electric barrier. With the effective Dirac equation of the system, we use the transfer matrix formalism to obtain the transmittance. We verify that the valley transport in graphene is very sensitive to a Fermi velocity modulation, which is able to choose which valley will be filtered with perfect filtering. Also, it is possible to use a Fermi velocity modulation to filter both valleys or to make the valley filter transparent. It reveals that the Fermi velocity is a powerful tool that can be used to tune a graphene valley filter, since it has a total control in its transport properties.

Previous works on deformed graphene predict the existence of valley-polarized states, however, optimal conditions for their detection remain challenging. We show that in the quantum Hall regime, edge-like states in strained regions can be isolated in energy within Landau gaps. We identify precise conditions for new conducting edges-like states to be valley polarized, with the flexibility of positioning them at chosen locations in the system. A map of local density of states as a function of energy and position reveals a unique braid pattern that serves as a fingerprint to identify valley polarization.

We investigate the propagation of electronic waves described by the Dirac equation subject to a L\'evy-type disorder distribution. Our numerical calculations, based on the transfer matrix method, in a system with a distribution of potential barriers show that it presents a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schr\"odinger equation do not present such transitions. Moreover, we obtain the phase diagram delimiting anomalous and standard localization regimes, in the form of an incidence angle versus incidence energy diagram, and argue that transitions can also be characterized by the behavior of the dispersion of the transmission. We attribute this transition to an abrupt reduction in the transmittance of the system when the incidence angle is higher than a critical value which induces a decrease in the transmission fluctuations., Comment: 6 pages, 6 figures, accepted for publication in Physical Review E

We present a self-contained description of the wave-function matching (WFM) method to calculate electronic quantum transport properties of nanostructures using the Landauer-B\"uttiker approach. The method is based on a partition of the system between a central region ("conductor") containing $N_S$ sites and an asymptotic region ("leads") characterized by $N_P$ open channels. The two subsystems are linearly coupled and solved simultaneously using an efficient sparse linear solver. Invoking the sparsity of the Hamiltonian matrix representation of the central region, we show that the number of operations required by the WFM method in conductance calculations scales with $\sim N_S\times N_P$ for large $N_S$., Comment: 22 pages, 8 figures

In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We found the Schr\"odinger equation for a general surface following the da Costa approach, obtaining the geometrical potential for systems with PDM. We obtained expressions for the transmittance and reflectance for a general surface of revolution. As a first application of the general results obtained here, we investigate the transport properties of deformed nanotubes, since the variation of the effective mass with the radius of the nanotubes has been dis-considered in previous studies of this system and experimentally a change of the effective mass is observed for different radii. We found that the inclusion of the position-dependent mass, particularly a radial change in the mass distribution, can induce a significant change in the transport properties of the system, which reveals that the transport properties of two dimensional quantum systems are sensitive to the PDM and when modeling electronic transport in surfaces this effects should be considered.

In this paper we study the electronic properties of carbon nanocones with one and two nappes, with pentagonal and heptagonal defects in their lattices. We use the continuum model, which is based on a Dirac-like Hamiltonian with the topological effects described by localized non-Abelian gauge field fluxes. We develop a geometrical approach that can describe the two nappes of the double cone surface simultaneously, by extending the radial coordinate to the complete set of real numbers. We show that, for some combinations of different nanocones, forming the double conical surface, the local density of states near the apex of the cone does not vanish at the Fermi energy and presents a strong dependence on the angular momentum. We also obtain the energy spectrum for finite-sized nanocones and verify that it depends on the choice of topological defect on the surface, which suggests that a double nanocone can be used to control the electronic transport in carbon-based electronic devices.

In this paper we present a method to numerically study transverse Hall conductances using a two-terminal setup. Using nonlinear transport concepts we find that the Hall voltage dependence on the model parameters can be investigated from the difference between the injectivities from each terminal. The method is suitable to work with non-equilibrium Green's functions as well as for scattering matrix approaches. We illustrate the proposed idea by studying the quantum spin Hall effect in graphene with disordered spin-orbit scattering centers induced by adatoms. We use two distinct models, a finite difference implementation of the Dirac Hamiltonian and a tight-binding Hamiltonian combined with the scattering matrix approach and the non-equilibrium Green's functions approach, respectively., Comment: 7 pages, 5 figures

We present a multiprobe recursive Green's function method to compute the transport properties of mesoscopic systems using the Landauer-B\"uttiker approach. By introducing an adaptive partition scheme, we map the multiprobe problem into the standard two-probe recursive Green's function method. We apply the method to compute the longitudinal and Hall resistances of a disordered graphene sample, a system of current interest. We show that the performance and accuracy of our method compares very well with other state-of-the-art schemes., Comment: 9 pages, 9 figures

In this work we investigate the influence of a Fermi velocity modulation on the Fano factor of periodic and quasi-periodic graphene superlattices. We consider the continuum model and use the transfer matrix method to solve the Dirac-like equation for graphene where the electrostatic potential, energy gap and Fermi velocity are piecewise constant functions of the position x. We found that in the presence of an energy gap, it is possible to tune the energy of the Fano factor peak and consequently the location of the Dirac point, by a modulations in the Fermi velocity. Hence, the peak of the Fano factor can be used experimentally to identify the Dirac point. We show that for higher values of the Fermi velocity the Fano factor goes below 1/3 in the Dirac point. Furthermore, we show that in periodic superlattices the location of Fano factor peaks is symmetric when the Fermi velocity $v_A$ and $v_B$ is exchanged, however by introducing quasi-periodicity the symmetry is lost. The Fano factor usually holds a universal value for a specific transport regime, which reveals that the possibility of controlling it in graphene is a notable result., Comment: 7 pages, 8 figures. Accepted for publication in Physica E: Low-dimensional Systems and Nanostructures

Inverted HgTe/CdTe quantum wells have been used as a platform for the realization of 2D topological insulators, bulk insulator materials with spin-helical metallic edges states protected by time-reversal symmetry. This work investigates the spectrum and the charge transport in HgTe/CdTe quantum well junctions both in the topological regime and in the absence of time-reversal symmetry. We model the system using the BHZ effective Hamiltonian and compute the transport properties using recursive Green's functions with a finite differences' method. Specifically, we have studied the material's spatially-resolved conductance in a set-up with a gated central region, forming monopolar (n-n$^{\prime}$-n) and heteropolar (n-p-n, n-TI-n) double junctions, which have been recently realized in experiments. We find regimes in which the edge states carry spin-polarized currents in the central region even in the presence of a small magnetic field, which breaks TRS. More interestingly, the conductance displays spin-dependent, Fabry-Per\'ot-like oscillations as a function of the central gate voltage producing tunable, fully spin-polarized currents through the device., Comment: 9 pages, 12 figures

We study the heat transport due to phonons in nanomechanical structures using a phase space representation of non-equilibrium Green's functions. This representation accounts for the atomic degrees of freedom making it particularly suited for the description of small (molecular) junctions systems. We show that for the steady state limit our formalism correctly recovers the heuristic Landauer-like heat conductance for a quantum coherent molecular system coupled to thermal reservoirs. We find general expressions for the non-stationary heat current due to an external periodic drive. In both cases we discuss the quantum thermodynamic properties of the systems. We apply our formalism to the case of a diatomic molecular junction., Comment: 20 pages, 6 figures

We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS$_2$ bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain energies independent of the nanoribbon width. We also study the effects of disorder in these systems using the recursive Green's function technique. We show that for the zigzag nanoribbons, the conductance due to the edge states is strongly suppressed by short-range disorder such as vacancies. In contrast, the local density of states still shows edge localization. We also show that long-range disorder has a small effect on the transport properties of nanoribbons within the bulk gap energy window., Comment: 10 pages, 9 figures

Based on the investigation of the multi-terminal conductance of a system composed of two graphene nanoribbons, in which one is on top of the other and rotated by 60 degrees, we propose a setup for a 50/50 electronic beam splitter that neither requires large magnetic fields nor ultra low temperatures. Our findings are based on an atomistic tight-binding description of the system and on the Green's function method to compute the Landauer conductance. We demonstrate that this system acts as a perfect 50/50 electronic beam splitter, in which its operation can be switched on and off by varying the doping (Fermi energy). We show that this device is robust against thermal fluctuations and long range disorder, as zigzag valley chiral states of the nanoribbons are protected against backscattering. We suggest that the proposed device can be applied as the fundamental element of the Hong-Ou-Mandel interferometer, as well as a building block of many devices in electron optics., Comment: 7 pages, 4 figures

We investigate the contribution of charge puddles to the non-vanishing conductivity minimum in disordered graphene flakes at the charge neutrality point. For that purpose, we study systems with a geometry that suppresses the transmission due to evanescent modes allowing to single out the effect of charge fluctuations in the transport properties. We use the recursive Green's functions technique to obtain local and total transmissions through systems that mimic vanishing density of states at the charge neutrality point in the presence of a local disordered local potential to model the charge puddles. Our microscopic model includes electron-electron interactions via a spin resolved Hubbard mean field term. We establish the relation between the charge puddle disorder potential and the electronic transmission at the charge neutrality point. We discuss the implications of our findings to high mobility graphene samples deposited on different substrates and provide a qualitative interpretation of recent experimental results., Comment: 12 figures, 10 pages

The electronic structure of a graphene superlattice composed by two periodic regions with different Fermi velocity, energy gap and electrostatic potential is investigated by using an effective Dirac-like Hamiltonian. It must be expected that the change of the Fermi velocity in one region of the graphene superlattice is equivalent to changing the width of this region keeping the Fermi velocity unchanged, provided that the time taken to charge carriers cross the region is the same. However, it is shown here that these two systems are not equivalent. We found extra Dirac points induced by the periodic potential and their location in the \textbf{k} space. It is shown that the Fermi velocity modulation breaks the symmetry between the electron and hole minibands and that it is possible to control the behavior of the extra Dirac points. The results obtained here can be used in the fabrication of graphene-based electronic devices.

Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. In this paper, we consider a rotating non-interacting planar two-dimensional electron gas with a perpendicular uniform magnetic field and investigate the effects of the rotation in the Hall conductivi

We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a substrate that opens an energy gap of $2\Delta$ in its electronic structure. We find that extra Dirac points appear in the electronic band structure under certain conditions, so it is possible to close the gap between the conduction and valence minibands. We show that the energy gap $E_g$ can be tuned in the range $0\leq E_g \leq 2\Delta$ by changing the periodic potential. We analyze the low energy electronic structure around the contact points and find that the effective Fermi velocity in very anisotropic and depends on the energy gap. We show that the extra Dirac points obtained here behave differently compared to previously studied systems.

We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field $B_\parallel$. Due to the irregular local curvature found at graphene sheets deposited over a substrate, $B_\parallel$ can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudo magnetic fields originated from deformations and strain. We find that the competition between these mechanisms gives rise to a strong anisotropy in the conductivity tensor. This result provides a new strategy to quantitatively infer the strength of pseudo-magnetic fields in rippled graphene flakes., Comment: 11 pages, 7 figures. Submitted to Physical Review B

The electronic structure of a single-layer graphene with a periodic Fermi velocity modulation is investigated by using an effective Dirac-like Hamiltonian. In a gapless graphene or in a graphene with a constant energy gap the modulation of the Fermi velocity, as expected, only changes the dispersion between energy and moment, turning the minibands narrower or less narrow than in the usual graphene depending on how the Fermi velocity is modulated and the energy gap remains the same. However, with a modulated energy gap it is possible to control the energy gap of graphene by Fermi velocity engineering. This is based on a very simple idea that has never been reported so far. The results obtained here reveal a new way of controlling the energy gap of graphene, which can be used in the fabrication of graphene-based devices.

In this work we study theoretically the electronic properties of a sheet of graphene grown on a periodic heterostructure substrate. We write an effective Dirac equation, which includes a dependence of both the band gap and the Fermi velocity on the position, due to the influence of the substrate. This way, both bandgap and Fermi velocity enter the Dirac equation as operators. The Dirac equation is solved exactly and we find the superlattice minibands with gaps due to the breaking of translational symmetry induced by the underlying heterostructure. The spatial dependence of the Fermi velocity makes the band gap be indirect, bringing about interesting possibilities for applications in the design of nanoelectronic devices. In the limit of constant Fermi velocity we obtain a band structure, with direct band gap, very close to the one previously found in the literature, obtained using the transfer matrix method.

In this paper, motivated by the experimental evidence of rapidly rotating $C_{60}$ molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static $C_{60}$ are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

Numerical calculations based on the recursive Green's functions method in the tight-binding approximation are performed to calculate the dimensionless conductance $g$ in disordered graphene nanoribbons with Gaussian scatterers. The influence of the transition from short- to long-ranged disorder on $g$ is studied as well as its effects on the formation of a perfectly conducting channel. We also investigate the dependence of electronic energy on the perfectly conducting channel. We propose and calculate a backscattering estimative in order to establish the connection between the perfectly conducting channel (with $g=1$) and the amount of intervalley scattering., Comment: 7 pages, 9 figures. To be published on Phys. Rev. B