Localization of surface states in disordered step lattices

The character of the surface state wave function on regularly stepped Cu(111) is reinvestigated. It is shown that the qualitative change at terrace lengths around 17 A observed previously by Ortega et al. [Phys. Rev. Lett. 84, 6110 (2000)]] must necessarily be described as a change from a propagating superlattice state to a terrace-confined quasi-one-dimensional state. This reconciles previous, apparently contradictory experimental results and sheds new light on the behavior of nearly free electrons in nanostructures. Possible mechanisms driving the localization are discussed on the basis of the surface state bulk penetration depth, which has been measured in both regimes.     

Near band centre states for one-dimensional off-diagonal disordered systems

We study and characterize the eigenstates near the centre of the band of a one-dimensional tight binding model with off-diagonal disorderW _T . We report a new exponent for the localization length on an energy-dependent range of disorderW _T . We correlate this feature with a change of structure of the wave-function displayed by the behaviour of its density-density correlation function.     

Density of states of disordered two-dimensional crystals with half-filled band

A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P0 = +/-pi / a,pi / a for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial quantum corrections due to both nesting and elastic impurity scattering processes, and as a result the Van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is significantly changed. A small offset from the middle of the band gives rise to the disappearance of quantum corrections to the DoS.     

Localization of excitons in weakly disordered semiconductor structures: A model study

Localization of the center‐of‐mass (com) motion of an exciton in a disordered semiconductor structure is studied theoretically by focusing on nonlinear optical spectroscopy. A one‐dimensional tight‐binding model with diagonal disorder is applied and the Coulomb interaction is treated consistently. In the ordered situation the center‐of‐mass momentum (K) selection rule leads to only the lowest transition for K = 0. The break down of the com‐K‐selection rule produces the well known asymmetric excitonic lines of disordered semiconductors. The coupling between the lowest dominant transition to this modified com‐continuum yields Fano‐like features in the nonlinear spectra.     

Scaling behavior of one-dimensional weakly disordered models

The density of states and various characteristic lengths of one-dimensional tight-binding models and disordered harmonic chains are calculated in the limit of weak disorder at the band edge of the ordered system. The density of states and a localization length of the one-dimensional Anderson model were already calculated by Derrida and Gardner; we recover their results. For the tight-binding models with off-diagonal disorder our results are in agreement with numerical calculations of Krey.     

Nonexistence of localized band tail states in substitutional semiconductor alloys and some other disordered systems

A recent theory of semiconducting glasses seems to imply a substantial density of localized band tail states in substitutional semiconductor alloys, such as Sie or GaAsP, and also in homogenous strain-free amorphous Si and Ge. Experimental evidence against the existence of such states in these non-glassy disordered materials is overwhelming. The paradox is resolved by noting that if the material is in thermodynamic equilibrium, the disorder of the atomic potentials will not result in disorder of the valence or conduction band energy levels.     

Luttinger-liquid behavior in weakly disordered quantum wires

We have measured the temperature dependence of the conductance in long V-groove quantum wires fabricated in GaAs/AlGaAs heterostructures. Our data are consistent with recent theories developed within the framework of the Luttinger-liquid model, in the limit of weakly disordered wires. We show that, for the relatively low level of disorder in our quantum wires, the value of the interaction parameter g congruent with 0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Fitting such data with perturbation-theory models leads inevitably to wrong (lower) values of g.     

Aharonov-Bohm effect in one-channel weakly disordered rings

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of with a period of the flux quantum . As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime () to the ballistic one (). The analytical expression for the density of states shows the exact dependence of on the ring's circumference and on disorder strength for both regimes. Received 27 December 1999     

A derivation for the energy dependence of the density of band tail states in disordered materials

Variational arguments are employed to present the first explicit derivation of the behavior of band tail states and localization length over most of the tail region of a random alloy. Exponential tails are shown to exist near the mobility edges, in conformity with the observation in disordered systems. The character of the states forming the band tails is discussed and, for random alloys, the localization length is shown to exhibit a minimum as a function of energy between band edge and mobility edge.     

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.     

Off-perturbative states in disordered systems

The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the critical point, in the paramagnetic phase of the random temperature model, and in the ferromagnetic phase of the random field one, the free energy contains non-analytic contributions which have the form of essential singularities. It is demonstrated that these contributions appear due to localized in space instanton-like excitations.     

Quasiparticle states in disordered superfluids

A model for disordered superfluids and superconductors is considered in terms of the Bogoliubov-de Gennes equation with a random order parameter field. Two characteristic cases are distinguished: model I with a real order parameter (time reversal invariant system) and model II with a complex order parameter (broken time reversal invariance). The fluctuations of the order parameter close the gap in both models, and we investigate the states at the center of the filled gap. The two models have distinctive properties in terms of the quasiparticle states due to different symmetries. Model II exhibits only localized quasiparticle states at the band center. In contrast, the fluctuations of the real order parameter of model I can be described by a nonlinear sigma model which leads to a transition from localized to extended states for dimensionsd>2.     

Localization in a one-dimensional disordered model

Numerical investigation of a random, one dimensional Kronig-Penny-like model is performed using long chains and large ensembles. Dependence of the inverse localization length α on randomness, irreproducibility of resistance measurements and the dependence of the standard deviation of α on α and the length of the chain were studied. For energies, E=k² close to the zone boundary k=π, we have found α～(π-k).