Disordered Quantum Wires Research Articles

Non-linear conductance of disordered quantum wires

The self-consistent electron potential in a current-carryingdisordered quantum wire is spatially inhomogeneous due to theformation of resistivity dipoles across scattering centres. In thispaper it is argued that these inhomogeneities in the potentialresult in a suppression of the differential conductance of such awire at finite applied voltage. A semi-classical argument allowsthis suppression, quadratic in the voltage, to be related directlyto the amount of intrinsic defect scattering in the wire. Thisresult is then tested against numerical calculations.

Partially Coherent Conductance of Laterally Quantized Quantum Wires

The transmission of partially coherent disordered quantum wires with few conducting modes is investigated. A wire is modeled as a system of interconnected scatterers within Landauer-B�ttiker theory, implementing a finite phase coherence length by fictitious, momentum-conserving reservoirs. The average logarithmic transmission and the damping of conductance fluctuations can be understood analytically, what may be relevant for the estimation of the phase coherence length in the nonuniversal regime.

Quantum dot to disordered wire crossover: A complete solution in all length scales for systems with unitary symmetry

We present an exact solution of a supersymmetric nonlinear sigma model describing the crossover between a quantum dot and a disordered quantum wire with unitary symmetry. The system is coupled ideally to two electron reservoirs via perfectly conducting leads sustaining an arbitrary number of propagating channels. We obtain closed expressions for the first three moments of the conductance, the average shot-noise power and the average density of transmission eigenvalues. The results are complete in the sense that they are nonperturbative and are valid in all regimes and length scales. We recover several known results of the recent literature by taking particular limits.

“One-Sided” Log-Normal Distribution of Conductances for a Disordered Quantum Wire

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically for the first time the full distribution of conductance P(g) for a quasi one dimensional wire in the absence of electron-electron interaction. We show that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by an essentially `one sided' log-normal distribution. For larger disorder, the tail of the log-normal distribution for g > 1 is cut off by a Gaussian.

Random magnetic flux problem in a quantum wire

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\epsilon=0$ plays a special role. Away from $\epsilon=0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\epsilon=0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.

Effect of electron correlations and disorder on mobility and localization in quasi-one-dimensional wires

A self-consistent method for determining electron correlations and electron scattering from disorder is used to calculate electron mobilities in disordered quantum wires of finite diameter. We look at electron localization in terms of mean free paths. We find cases where the mobility drops toward zero, and the mean free path is of the order of the average electron spacing, corresponding to strong localization. We determine the peak mobility as a function of impurity density and wire diameter.

Electron correlations in thin disordered quantum wires

We calculate self-consistently the dependence of electron-electron correlations on electron-defect scattering processes in quantum wires with only the lowest subband occupied. We use the Singwi-Tosi-Land-Sj\olander approach to calculate the many-body electron-electron correlations. The effect of electron scattering from randomly distributed Coulombic impurities and off surface roughness of the wire is treated using self-consistent current-relaxation theory. Electron correlations can become very strong even at relatively high electron densities if the wire diameter is made sufficiently small. For a fixed disorder level the electron-defect scattering rate increases with increasing electron correlations. The plasmon dispersion depends on electron correlations and on the level of disorder. Electron-electron correlations transfer spectral weight at finite wave number from the plasmon to the single-particle excitations.

On the conductance and the conductivity of disordered quantum wires

We present a model, based on the Keldysh formalism, to study the transport properties of disordered quantum wires of finite lengths. Unlike the phenomenological models, we estimate the electron in- and out-scattering rates using the local density of states of various transverse modes that allow electrons to change their directions. The formulation, therefore, guarantees the conservation of both the charge and the current at any cross section of the device. Using the model we calculate the average two-probe conductances of quantum wires that are terminated at nonideal contacts.

Conductance and conductance fluctuations of narrow disordered quantum wires.

In this paper we present and discuss our results for the conductance and conductance fluctuations of narrow quantum wires with two types of disorder: boundary roughness (hard wall confining potential) and islands of strongly scattering impurities within the bulk of the wire. We use a tight--binding Hamiltonian to describe the quantum wire, infinite perfect leads, a two--terminal Landauer--type formula for the conductance, and the recursive single-particle Green's function technique. We find that conductance quantization is easily destroyed by strong scattering. We also find that Anderson localization poses a serious restriction on the high carrier mobility predicted in quantum wires. Conductance fluctuations in narrow quantum wires are not, in general, universal (as in the metallic regime), but can be independent of the wire length over a short range of lengths.

Monte Carlo calculation of electron relaxation times in perfect and disordered quantum wire laser structures

We calculate the electron relaxation times in GaAs quantum wires of 100×100 Å and 200×200 Å cross sections by a Monte Carlo simulation with the inclusion of electron-phonon and electron-electron interactions for the wire band structure computed by solving the one-band Schrödinger equation with and without structural disorder at the wire interface. The electron relaxation time is found to be greater than a hundred picoseconds for the 100×100 Å wire, while it is approximately 10 ps for the wire with the 200×200 Å cross section with the results converging to the case of bulk material for increased wire cross section. The influence of disorder on carrier relaxation in quantum wires is found to be negligible. The unusually slow carrier equilibration process is attributed to the combined effect of the sharply peaked one-dimensional density of states and the absence of randomizing intrasubband carrier-carrier scattering processes in quasi-one-dimensional systems. The dependence of electron relaxation times on the size of the quantum wire appears to be extremely sensitive.

Density of states and localization length in compositionally disordered quantum wires.

Electronic states in compositionally disordered quantum wires are studied using a tight-binding Hamiltonian to determine the electronic density of states and localization lengths. The quantum wires are generated using the statistics of the structural roughness extracted from the results of computer simulations of molecular-beam-epitaxy growth of quantum-well wires on a vicinal surface. For monolayer structures, interface roughness and islands strongly suppress the subband structure. The electronic states are found to be localized to within several tens of lattice spacings, which implies severely reduced mobility in narrow quantum wires. Enlargement of the cross section of the wire by depositing additional layers does not improve the subband structure of the density of states. However, the localization lengths will be longer, except for energies near the band edge. The maximum localization length is proportional to the number of layers. Characteristic features of this model in the strong scattering regime, such as a spike in the density of states at the center of the subband and the gap around it, and strong reduction in the localization length for these energies, are observed for a monolayer structure. For multilayer structures spikes also occur at E=\ifmmode\pm\else\textpm\fi{}V, but the gap has disappeared.

Magnetoconductivity in disordered quantum wires

The authors generalize the linear response theory of magnetoconductivity of disordered two-dimensional electron gases to include the case where a confinement potential is present in one of the two spatial directions. The theory allows studies of the effect of suppression of backscattering due to the existence of spatially separated edge states in high magnetic fields. Explicit calculations of the conductivity are carried out for weak scattering in two limits: the weak and the strong confinement limit.

Coherent-potential approximation calculations in compositionally disordered quantum wires: density of states

The authors have investigated the influence of different types of disorder on the electronic density of states in compositionally disordered quantum wires, using the tight-binding, coherent-potential approximation (CPA). In order to embed the correlations that are present in any wire structure the single-site CPA condition (ti')config=0, has been generalized to the matrix equation for a slice (L) of the wire as a scatterer (tL')config=0. Essentially this approximation is similar to the molecular CPA (MCPA) or the cluster CPA but due to the geometry of the system translational invariance along the effective wire is not broken. Calculations for monolayer wires reveal that the boundary roughness of a wire degrades the ideal quasi-one dimensional density of states in a characteristic way. This degradation is even stronger in the presence of islands. The subband representation reveals that the density of states in each channel is affected by the edge disorder in proportion to the Fermi energy or channel number. By contrast the effect of the presence of islands is independent of the channel number.

Electronic properties of compositionally disordered quantum wires.

Electronic states in quantum wires are studied using computer simulations of the growth to characterize the compositional disorder and a tight-binding Hamiltonian to determine the electronic densities of states. Calculations for monolayer slices of wires generated from the statistics of the simulated wires reveal the degrding effect of interface profile fluctuations and islands on the ideal quasi-one-dimensional electronic characteristics. Fixed-width fluctuations of the wire profiles, on the other hand have had a relatively minor effect on the first few subbands. Calculations of the localization length are used to characterize the mobility within the quantum wires.

Phase coherence in quantum wires in presence of scattering by acoustic phonons

We investigate the destruction of phase coherence of electrons in a disordered quantum wire by acoustic phonon scattering using non-equilibrium Green-function technique. The main subjects of our analysis are the influence of discrete subband structure, the transition to strong localization and the nature of dephasing by acoustic phonons. The results are used to discuss the temperature dependence of phase coherence length and weak localization contribution to conductance in GaAs quantum wires.