Tuning the thermoelectric response of silicene nanoribbons with vacancies.

In this work, we present a thorough study of the thermoelectric properties of silicene nanoribbons in the presence of a random distribution of atomic vacancies. By using a linear approach within the Landauer formalism, we calculate phonon and electron thermal conductances, the electric conductance, the Seebeck coefficient and the figure of merit of the nanoribbons. We found a sizable reduction of the phonon thermal conductance as a function of the vacancy concentration over a wide range of temperature. At the same time, the electric properties are not severely deteriorated, leading to an overall remarkable thermoelectric efficiency. We conclude that the incorporation of vacancies paves the way for designing better and more efficient nanoscale thermoelectric devices.

Quantum nanoconstrictions fabricated by cryo-etching in encapsulated graphene.

We report on a novel implementation of the cryo-etching method, which enabled us to fabricate low-roughness hBN-encapsulated graphene nanoconstrictions with unprecedented control of the structure edges; the typical edge roughness is on the order of a few nanometers. We characterized the system by atomic force microscopy and used the measured parameters of the edge geometry in numerical simulations of the system conductance, which agree quantitatively with our low temperature transport measurements. The quality of our devices is confirmed by the observation of well defined quantized 2e2/h conductance steps at zero magnetic field. To the best of our knowledge, such an observation reports the clearest conductance quantization in physically etched graphene nanoconstrictions. The fabrication of such high quality systems and the scalability of the cryo-etching method opens a novel promising possibility of producing more complex truly-ballistic devices based on graphene.

Solitons in a nonlinear model of spin transport in helical molecules.

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

Electric control of the bandgap in quantum wells with band-inverted junctions.

In IV-VI semiconductor heterojunctions with band-inversion, such as those made of [Formula: see text] [Formula: see text]Te or [Formula: see text] [Formula: see text]Se, interface states are properly described by a two-band model, predicting the appearance of a Dirac cone in single junctions. However, in quantum wells the interface dispersion is quadratic in momentum and the energy spectrum presents a gap. We show that the interface gap shrinks under an electric field parallel to the growth direction. Therefore, the interface gap can be dynamically tuned in experiments on double-gated quantum wells based on band-inverted compounds.

Tuning the Fermi velocity in Dirac materials with an electric field.

Dirac materials are characterized by energy-momentum relations that resemble those of relativistic massless particles. Commonly denominated Dirac cones, these dispersion relations are considered to be their essential feature. These materials comprise quite diverse examples, such as graphene and topological insulators. Band-engineering techniques should aim to a full control of the parameter that characterizes the Dirac cones: the Fermi velocity. We propose a general mechanism that enables the fine-tuning of the Fermi velocity in Dirac materials in a readily accessible way for experiments. By embedding the sample in a uniform electric field, the Fermi velocity is substantially modified. We first prove this result analytically, for the surface states of a topological insulator/semiconductor interface, and postulate its universality in other Dirac materials. Then we check its correctness in carbon-based Dirac materials, namely graphene nanoribbons and nanotubes, thus showing the validity of our hypothesis in different Dirac systems by means of continuum, tight-binding and ab-initio calculations.

Lump solitons in a higher-order nonlinear equation in 2+1 dimensions.

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrödinger equation to 2+1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Binding energy of hydrogenic impurities in quantum dots under intense laser radiation.

We calculate the binding energy of on- and off-center hydrogenic impurities in a parabolic quantum dot subjected to an intense high-frequency laser field. An exactly solvable model that replaces the actual Coulomb interaction with the donor by a non-local separable potential is introduced for calculating the binding energy. The separable potential allows us to solve the problem exactly and all calculations are carried out analytically. The action of the laser irradiation results in dressed Coulomb and confinement potentials. At low laser intensity the binding energy is found to decrease when the impurity is shifted away from the origin. At high laser intensity and strong confinement the opposite behavior is observed. We propose a simple one-dimensional model that explains the observed crossover.

Graphene nanoring as a tunable source of polarized electrons.

We propose a novel spin filter based on a graphene nanoring fabricated above a ferromagnetic strip. The exchange interaction between the magnetic moments of the ions in the ferromagnet and the electron spin splits the electronic states, and gives rise to spin polarization of the conductance and the total electric current. We demonstrate that both the current and its polarization can be controlled by a side-gate voltage. This opens the possibility to use the proposed device as a tunable source of polarized electrons.

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect.

We calculate numerically the localization length critical index within the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. We report a finite-size scaling analysis using both the traditional power-law corrections to the scaling function and the inverse logarithmic ones, which provided a more stable fit resulting in the localization length critical index ν = 2.616 ± 0.014. We observe an increase of the critical exponent ν with the system size, which is possibly the origin of discrepancies with early results obtained for smaller systems.

Toward graphene-based quantum interference devices.

A new type of quantum interference device based on a graphene nanoring in which all edges are of the same type is studied theoretically. The superposition of the electron wavefunction propagating from the source to the drain along the two arms of the nanoring gives rise to interesting interference effects. We show that a side-gate voltage applied across the ring allows for control of the interference pattern at the drain. The electron current between the two leads can therefore be modulated by the side gate. The latter manifests itself as conductance oscillations as a function of the gate voltage. We study quantum nanorings with two edge types (zigzag or armchair) and argue that the armchair type is more advantageous for applications. We demonstrate finally that our proposed device operates as a quantum interference transistor with high on/off ratio.

Localization on a two-channel model with cross-correlated disorder.

We study the wavepacket dynamics in a two-channel Anderson model with correlated diagonal disorder. To impose correlations in the disorder distribution we construct the on-site energy landscape following both symmetric and antisymmetric rules. Our numerical data show that symmetric cross-correlations have a small impact on the degree of localization of the one-particle eigenstates. In contrast, antisymmetric correlations lead to a reduction of the effective degree of disorder, thus resulting in a substantial increase of the wavepacket spread. A finite-size scaling analysis shows that the antisymmetric cross-correlations, in spite of weakening the localization, do not promote ballistic transport. The present results shed light on recent findings concerning an apparent delocalization transition in a correlated DNA-like ladder model.

Stable BLOCH oscillations of cold atoms with time-dependent interaction.

We investigate Bloch oscillations of interacting cold atoms in a mean-field framework. In general, atom-atom interaction causes dephasing and destroys Bloch oscillations. Here we show that Bloch oscillations are persistent if the interaction is modulated harmonically with suitable frequency and phase. For other modulations, Bloch oscillations are rapidly damped. We explain this behavior in terms of collective coordinates whose Hamiltonian dynamics permits one to predict a whole family of stable solutions. In order to describe also the unstable cases, we carry out a stability analysis for Bogoliubov excitations. Using Floquet theory, we are able to predict the unstable modes as well as their growth rate, found to be in excellent agreement with numerical simulations.

Trapping and motion of polarons in weakly disordered DNA molecules.

Polaron effects for charge migration in DNA molecules have been previously considered within the Peyrard-Bishop-Holstein model. When a uniform electric field is applied, the polaron moves asymptotically at a constant velocity, provided dissipative effects are taken into account, and then current flows through DNA. Disorder originating from interactions with a random environment of solute molecules and ions surrounding the DNA molecule could prevent charge migration due to the localization of the carrier wavefunction. We studied numerically the Peyrard-Bishop-Holstein model when the disordered DNA molecule is subjected to a uniform electric field. We found the threshold value of the electric field to observe polaron motion when disorder is present. We also calculated the fluctuations of the electric current and found that they provide valuable information about the polaron dynamics.

Effects of the environment on the electric conductivity of double-stranded DNA molecules.

We present a theoretical analysis of the effects of the environment on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to static disorder and (ii) phonon-induced scattering of the carriers between the localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the I-V characteristics becomes wider. A simple physical explanation of this effect is provided.

Fano-Rashba effect in quantum dots.

We consider the electronic transport through a Rashba quantum dot coupled to ferromagnetic leads. We show that the interference of localized electron states with resonant electron states leads to the appearance of the Fano-Rashba effect. This effect occurs due to the interference of bound levels of spin-polarized electrons with the continuum of electronic states with an opposite spin polarization. We investigate this Fano-Rashba effect as a function of the applied magnetic field and Rashba spin-orbit coupling.

A solvable model of hydrogenic impurities in quantum dots.

A solvable model is developed for electronic structure calculations of shallow hydrogenic impurities in two-dimensional quantum dots. We replace the actual Coulomb interaction (local potential) between the electron and the hydrogenic impurity by a projective operator (non-local separable potential) to determine the resulting electronic states in closed form. It is shown that non-local separable potentials may be used to accurately calculate the energy shift of the electronic levels as a function of the size of the quantum dot and the impurity position.

Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder.

We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum S(k) approximately 1/k(alpha) with alpha>0. de Moura and Lyra [Phys. Rev. Lett. 81, 3735 (1998)]] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided alpha>2. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.

Anderson transition in low-dimensional disordered systems driven by long-range nonrandom hopping.

The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically, using a supersymmetric method combined with a renormalization group analysis, as well as numerically that extended states may occur in the one- and two-dimensional Anderson model with a nonrandom hopping falling off as some power of the distance between sites. The different size scaling of the bare level spacing and the renormalized magnitude of the disorder seen by the quasiparticles finally results in the delocalization of states at one of the band edges of the quasiparticle energy spectrum.

Multiparticle biased diffusion-limited aggregation with surface diffusion: A comprehensive model of electrodeposition

We present a complete study of the multiparticle biased diffusion-limited aggregation (MBDLA) model supplemented with surface diffusion (SD), focusing on the relevance and effects of the latter transport mechanism. By comparing different algorithms, we show that MBDLA + SD is a very good qualitative model for electrodeposition in essentially the whole range of current intensities provided one introduces SD in the model in the proper fashion. We have found that the correct procedure involves simultaneous bulk diffusion and SD, introducing a time scale arising from the ratio of the rates of the two processes. We discuss in detail the different morphologies obtained and compare them to the available experimental data with very satisfactory results. We also characterize the aggregates thus obtained by means of the dynamic scaling exponents of the interface height, allowing us to distinguish several regimes in the mentioned interface growth. Our asymptotic scaling exponents are again in good agreement with recent experiments. We conclude by discussing a global picture of the influence and consequences of SD in electrodeposition.