F.A.B.F. de Moura

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.

Wave-packet dynamics in chains with delayed electronic nonlinear response.

We study the dynamics of one electron wave packet in a chain with a nonadiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schrödinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the bandwidth. We show that a weaker nonlinearity is required to produce self-trapping in the regime of short delay times. However, this trend is reversed for slow nonlinear responses, resulting in a reentrant phase diagram. In slowly responding media, self-trapping only takes place for very strong nonlinearities.

Critical behavior of the two-dimensional Anderson model with long-range correlated disorder

We describe the critical behavior of the Anderson-like transition predicted to occur in the 2D tight-binding model with isotropic scale-free long-range correlated disorder characterized by a power-law spectral density. We explore the scale invariance of the participation function relative fluctuation at the critical point to locate the mobility edge as a function of the power-law spectral density exponent α2D. The states near the band center, which exhibit power-law localization for uncorrelated disorder, become delocalized for α2D>2. In addition, we consider the finite-size scaling hypothesis to estimate the correlation length critical exponent. We find that the critical exponent ν depends on α2D, thus indicating that correlations in the disorder distribution are indeed relevant in this regime, in agreement with the extended Harris criterion.

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

Abstract.We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.

Dynamics of one electron in a nonlinear disordered chain

In this paper we report new numerical results on the disordered Schrödinger equation with nonlinear hopping. By using a classical harmonic Hamiltonian and the Su-Schrieffer-Heeger approximation we write an effective Schrödinger equation. This model with off-diagonal nonlinearity allows us to study the interaction of one electron and acoustical phonons. We solve the effective Schrödinger equation with nonlinear hopping for an initially localized wavepacket by using a predictor-corrector Adams-Bashforth-Moulton method. Our results indicate that the nonlinear off-diagonal term can promote a long-time subdiffusive regime similar to that observed in models with diagonal nonlinearity.

Absence of localization on the 2d model with long-range correlated off-diagonal disorder

Abstract We study the one-electron eigenstates in a two-dimensional (2d) Anderson model with long-range correlated off-diagonal disorder, generated by a 2d discrete Fourier method. The dynamics of an initially localized wave packet is investigated by numerically solving the 2d time-dependent Schrödinger equation. In additional the participation number and its scaling behavior was obtained through direct diagonalization. Our numerical data suggest that the system exhibits a ballistic dynamics in the strongly correlated disorder regime. Moreover, the scaling analysis of mean participation number around the band center also indicates the presence of extended states for high degree of correlations.

Electronic transport in poly(CG) and poly(CT) DNA segments with diluted base pairing

We present a model for describing electrical conductivity along poly(CG) and poly(CT) DNA segments with diluted base pairing within a tight-binding Hamiltonian approach. The base pairing is restricted to occurring at a fraction p of the cytosine (C) nucleotides at which a guanine (G) nucleotide is attached. We show that the Schrodinger equation can be mapped exactly onto that of the one-dimensional Anderson model with diluted disorder. Using a Green function formalism as well as exact diagonalization of the full one-dimensional Hamiltonian of finite segments, we compute the density of states, the wavefunction of all energy eigenstates and their corresponding localization lengths. We show that the effective disorder introduced by the diluted base pairing is much stronger in poly(CG) than in poly(CT) segments, with significant consequences for the electronic transport properties. The electronic wavepacket remains localized in the poly(CT) case, while it acquires a diffusive spread for the poly(CG)-based sequence.

Finite-size scaling and disorder effect on the transmissivity of multilayered structures with metamaterials

We investigate the influence of metamaterials on the scaling laws of the transmission on multilayered structures composed of random sequences of ordinary dielectric and metamaterial layers. The spectrally averaged transmission in a frequency range around the fully transparent resonant mode is shown to decay with the total number of layers as 1/N. Such thickness dependence is faster than the 1/N(1/2) decay recently reported to take place in random sequences of ordinary dielectric slabs. The interplay of strong localization and the emergence of resonant modes within the gap leads to a non-monotonous disorder dependence of the transmission that reaches a minimum at an intermediate disorder strength.

Coherent electron dynamics in a two-dimensional random system with mobility edges

We study numerically the dynamics of a one-electron wavepacket in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schrodinger equation is used for this purpose. We find that the wavepacket displays Bloch-like oscillations associated with the appearance of a phase of delocalized states in the strong correlation regime. The amplitude of oscillations directly reflects the bandwidth of the phase and allows us to measure it. The oscillations reveal two main frequencies whose values are determined by the structure of the underlying potential in the vicinity of the wavepacket maximum.

Electron–soliton dynamics in chains with cubic nonlinearity

In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron-soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling.