Random Site Energies Research Articles

Finite temperature phase transition in the two-dimensional Coulomb glass at low disorders

We present numerical evidence using Monte Carlo simulations of finite temperature phase transition in two dimensional Coulomb Glass lattice model with random site energies at half-filling. For the disorder strengths (W) studied in this paper, we find the existence of charge-ordered phase (COP) below the critical temperature (Tc(W)). Also, the probability distribution of staggered magnetization calculated at each W shows a two-peak structure at their respective critical temperature. Thus the phase transition from fluid to COP as a function of temperature is second order for all W. We find no evidence of a spin glass phase between a fluid and the COP. Further, we have used finite-size scaling analysis to calculate the critical exponents. The critical exponents at zero disorder are different from the one found at finite disorders, which indicates that the disorder is a relevant parameter here. The critical exponent for correlation length ν increases and Tc decreases with increasing disorder. Similar behaviour for ν was seen in the work of Overlin et al. for three dimensional Coulomb Glass model with a positional disorder. Our study also shows that other critical exponents are also a function of disorder.

Normal and anomalous diffusion in random potential landscapes

A relation between the effective diffusion coefficient in a lattice with random site energies and random transition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous diffusion in random potential models. We show that subdiffusion is only possible either if the mean Boltzmann factor in the corresponding potential diverges or if the percolation concentration in the system is equal to unity (or both), and that superdiffusion is impossible in our system under any condition. We show also other useful applications of this relation.

Interplay of superconductivity and spin-dependent disorder

The finite temperature phase diagram for the 2D attractive fermion Hubbard model with spin-dependent disorder is considered within Bogoliubov-de Gennes mean field theory. Three types of disorder are studied. In the first, only one species is coupled to a random site energy; in the second, the two species both move in random site energy landscapes which are of the same amplitude, but different realizations; and finally, in the third, the disorder is in the hopping rather than the site energy. For all three cases we find that, unlike the case of spin-symmetric randomness, where the energy gap and average order parameter do not vanish as the disorder strength increases, a critical disorder strength exists separating distinct phases. In fact, the energy gap and the average order parameter vanish at distinct transitions, $V_{c}^{\rm gap}$ and $V_{c}^{\rm op}$, allowing for a gapless superconducting (gSC) phase. The gSC phase becomes smaller with increasing temperature, until it vanishes at a temperature $T^{\ast}$.

ASPECTS OF LOCALIZATION ACROSS THE 2D SUPERCONDUCTOR-INSULATOR TRANSITION

It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of Vc ~ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of single-particle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.

Effects of disorder on superconductivity of systems with coexisting itinerant electrons and local pairs

We study the influence of diagonal disorder (random site energy) of local pair (LP) site energies on the superconducting properties of a system of coexisting local pairs and itinerant electrons described by the (hard-core) boson-fermion model. Our analysis shows that the properties of such a model with s-wave pairing can be very strongly affected by the diagonal disorder in LP subsystem (the randomness of the LP site energies). This is in contrast with the conventional s-wave BCS superconductors, which according to the Anderson's theorem are rather insensitive to the diagonal disorder (i.e. to nonmagnetic impurities). It has been found that the disorder effects depend in a crucial way on the total particle concentration n and the LP level position DELTA_o and depending on the parameters the system can exhibit various types of superconducting behaviour, including the LP-like, intermediate (MIXED)and the 'BCS'-like. In the extended range of {n,DELTA_o} the superconducting ordering is suppressed by the randomness of the LP site energies and the increasing disorder induces a changeover from the MIXEDlike behaviour to the BCS-like one, connected with abrupt reduction of T_c and energy gap to zero. However, there also exist a definite range of {n,DELTA_o} in which the increasing disorder has a quite different effect: namely it can substantially enhance T_c or even lead to the phenomenon which can be called disorder induced superconductivity. Another interesting effect is a possibility of a disorder induced bound pair formation of itinerant electrons, connected with the change-over to the LP-like regime.

Electron mobility in liquid isomeric pentanes: Rationalization based on Anderson localization

The vast difference between electron mobilities in isomeric pentane liquids is explained on the basis of Anderson localization followed by trapping. Random site energy fluctuation is modeled on electron-anisotropic polarizability interaction with the molecules. Connectivity and intermolecular separation are obtained from X-ray scattering data. Together, these parameters determine the fraction of initially delocalized states, computed to be 0%, 61.4%, and 100%, respectively, for n-, iso-, and neo-pentane. Trap depths and densities are phenomenologically rationalized with observed mobilities. The values for trap depths are 0.17, 0.11, and 0.02 eV for n-, iso-, and neo-pentane, while the corresponding trap densities are 0.45 × 10 19, 0.70 × 10 19, and 0.23 × 10 19 cm −3, respectively.

Superuid and insulator of dirty Bose-Fermi mixture

One-dimensional Bose-Fermi mixture systems in a random potential are numerically investigated with focus on their superfluidity and localization properties. It is known that one-dimensional bosons and fermions behave differently in a weak random potential: Interacting bosons in a weak random potential exhibit superfluidity if the interactions are repulsive and not too strong, while interacting fermions with repulsive forces are localized in the presence of randomness. So the question is what happens if weakly interacting bosons and fermions are mixed in a random potential, which might be actually realized by the technique of trapping atoms on a random optical lattice. To answer this question we performed quantum Monte Carlo simulations of bosons and fermions on a one-dimensional lattice with random site energies. The result showed that when the boson-fermion interactions were attractive, both bosons and fermions tended to be localized. However when the boson- fermion interactions were repulsive and relatively weak, the superfluidity of bosons was enhanced and the fermions were delocalized.

Enhancement of persistent current in metal rings by correlated disorder

We study analytically the effect of a correlated random potential on thepersistent current in a one-dimensional ring threaded by a magnetic fluxϕ, using an Anderson tight-binding model. In our model, the system ofN = 2M atomic sites of the ring is assumed to be partitioned intoM pairs of nearest-neighbour sites (dimers). While the individual atomic site energies areassumed to be identically distributed Gaussian variables with autocorrelation parameterε02, the dimer site energies are chosen to be correlated with a Gaussian strengthα2<ε02. For this system we obtain the exact flux-dependent energy levels to second order inthe random site energies, using an earlier exact transfer matrix perturbationtheory. These results are used to study the mean persistent current generated byNe≤N spinless electronsoccupying the Ne lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses arecarried out in the case of low filling of the energy band () and for a half-filled band (Ne = N/2), for magnetic fluxes −1/2<ϕ/ϕ0<1/2. In the half-filled band case, the uncorrelated part of the disorder reduces thepersistent current while the correlated part enhances it, in such a way that forα2<ε02/2 the current decreases with the disorder, while forα2>ε02/2 it increases with it. Also, while showing a specific dependence onthe flux, the disorder effect has the same dependence on the parity ofNe as the pure system-free electron current. In contrast, at low filling of the energy band, thedisorder-induced effect in the persistent current depends critically on the parity: due toa peculiar dependence on the flux, it yields a reduction of the current for oddNe and an enhancementof it for even Ne. The observability of the effects of weak correlated disorder on persistent current in thehalf-filled band case is restricted to ring sizes in the nanoscale range, for which nomeasurements presently exist.

The Coulomb gap and low energy statistics for Coulomb glasses

We study the statistics of local energy minima in the configuration space oftwo-dimensional lattice Coulomb glasses with site disorder and the behavior of theCoulomb gap depending on the strength of random site energies. At intermediatedisorder, i.e., when the typical strength of the disorder is of the same order as thenearest-neighbor Coulomb energy, the high energy tail of the distribution of the localminima is exponential. We furthermore analyze the structure of the local minima andshow that most sites of the system have the same occupation numbers in all ofthese states. The density of states (DOS) shows a transition from the crystallinestate at zero disorder (with a hard gap) to an intermediate, probably glassy statewith a Coulomb gap. We analyze this Coulomb gap in some detail and showthat the DOS deviates slightly from the traditional linear behavior in 2D. Forfinite systems these intermediate Coulomb gap states disappear for large disorderstrengths and only a random localized state in which all electrons are in the minimaof the random potential exists.Dedication: This paper is dedicated to ThomasNattermann, our dearest friend, brilliant colleague, and outstanding teacher.

Universality of AC conductivity: Random site-energy model with Fermi statistics

The universality of the frequency-dependent (AC) conduction of many disordered solids in the extreme-disorder limit has been demonstrated experimentally. Theoretically, this universality has been established with different techniques and for various models. A popular model that has been extensively investigated and for which AC universality was established is the symmetric random-barrier model without Fermi statistics. However, for the more realistic model of random site-energies and Fermi statistics AC universality has never been rigorously established. In the present work we perform a numerical study of the latter model for a regular lattice in two dimensions. In addition, we allow for variable-range hopping. Our main conclusion is that AC universality appears to hold for this realistic model. The obtained master curve for the conductivity and the one obtained for the random-barrier model in two dimensions appear to be the same.

Calculating charge-carrier mobilities in disordered semiconducting polymers: Mean field and beyond

We model charge transport in disordered semiconducting polymers by hopping of charges on a regular cubic lattice of sites. A large on-site Coulomb repulsion prohibits double occupancy of the sites. Disorder is introduced by taking random site energies from a Gaussian distribution. Recently, it was demonstrated that this model leads to a dependence of the charge-carrier mobilities on the density of charge carriers that is in agreement with experimental observations. The model is conveniently solved within a mean-field approximation, in which the correlation between the occupational probabilities of different sites is neglected. This approximation becomes exact in the limit of vanishing charge-carrier densities, but needs to be checked at high densities. We perform this check by dividing the lattice in pairs of neighboring sites and taking into account the correlation between the sites within each pair explicitly. This pair approximation is expected to account for the most important corrections to the mean-field approximation. We study the effects of varying temperature, charge-carrier density, and electric field. We demonstrate that in the parameter regime relevant for semiconducting polymers used in practical devices the corrections to the mobilities calculated from the mean-field approximation will not exceed a few percent, so that this approximation can be safely used.

Scaling of current distributions in variable-range hopping transport on two- and three-dimensional lattices

From extensive computer simulations of variable-range hopping (VRH) transport of charges on regular two- and three-dimensional lattices with random site energies we calculate the average contribution to the total current of hops over a certain distance and with a certain hop energy. We find that the resulting current distribution is a universal function of scaled distance and energy variables. We discuss this scaling in the light of the original arguments of Mott and percolation arguments to explain the temperature dependence of the VRH conductivity.

Delocalization of quasiparticles in quasi-two-dimensional disordered superconductors with s-wave pairing

We investigate localization behavior of quasiparticles in disordered multi-plane superconductors with s-wave pairing. By introducing disorder with random site energies, the spatial fluctuations of Bogoliubov-de Gennes pairing potential are self-consistently determined. The size dependence of rescaled localization length for a long bar is calculated by using the transfer-matrix method. From the finite-size scaling analysis we show that there exists a critical point of the disorder strength Wc which separates the extended and localized quasiparticle states in such quasi-two-dimensional systems. The associated critical behavior is studied and the relationship of the results to the number of planes is discussed.

Diffusion behavior of quasiparticles in two-dimensional disordered systems withs-wave pairing

We investigate the diffusion behavior of quasiparticles in two-dimensional (2D) disordered systems with $s$-wave pairing by using the finite-size scaling analysis and transfer-matrix method. The disorder is introduced by random site energies, and the spatial fluctuations of the pairing potential due to this randomness are determined self-consistently. From the size dependence of the Lyapunov exponents, we show that the quasiparticle state in every channel is localized in such a 2D system. The calculated size dependence of the total transmittance of quasiparticles through all possible channels, however, shows a different scaling behavior that suggests the existence of a critical point. The associated critical behavior is studied and the relationship of the results to the Meissner effect and supercurrent is discussed.

Disorder in organic charge-transfer single crystals: Dipolar disorder in ClMePD-DMeDCNQI

The unusual electronic, vibrational, and structural properties of the title compound are associated with the polar donor D=2-chloro-5-methyl-p-phenylenediamine, which is twofold disordered in single crystals. Its 3 D dipole generates random site energies with standard deviation sigma=0.35 eV that significantly alter the standard description of charge-transfer (CT) salts with nonpolar donors and acceptors. The average structure at 298 and 150 K is centrosymmetric, space group P1, and consistent with increasing degree of CT (or ionicity rho) on cooling. Vibrational spectra indicate that rho increases from approximately 0.3 at 400 K to approximately 0.6 at 80 K, with coincident Raman and infrared (IR) molecular modes in contrast with the centrosymmetric structure. Dipolar disorder is modeled by adding random site energies to Peierls-Hubbard models of CT salts, and sigma=0.35 eV is shown to suppress the Peierls instability for typical bandwidth and lattice stiffness, in agreement with the structural data. Disorder also breaks inversion symmetry and rationalizes coincident Raman and IR modes. The combination of site energies xp and the dipole operator P for systems with periodic boundary conditions leads at molecule p to (partial differentialP/ partial differentialxp)2 for the IR intensity polarized along the DA stack. The ensemble average of (partial differentialP/ partial differentialxp)2 for sigma=0.35 eV as a function of the ground-state ionicity rho accounts for the intensity variations of totally symmetric molecular modes of D and A, either on cooling at ambient pressure or on squeezing at ambient temperature.

Critical Hamiltonians on one-dimensional disordered lattices

We focus on tight-binding Hamiltonians on a regular one-dimensional lattice with non-random long-range inter-site coupling J(mn) = J/\m - n\(mu) and random uncorrelated site energies. Within the model the localization-delocalization transition occurs at one of the energy band edges provided 1 <mu <3/2. Using the model we demonstrate that the ratio of the first two momenta of the participation number distribution for the critical states is a size invariant parameter at some value of the disorder magnitude Delta(c). We claim that the invariance manifests the transition. We find that Delta(c) not equal 0 at 1 <mu <3/2, suggesting that the system undergoes the localization-delocalization transition with respect to disorder magnitude. At mu greater than or equal to 3/2, all states are localized. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Model for the pressure‐dependent permeation of small molecules through a polymer membrane

AbstractThe pressure‐dependent permeation of heavy noble gases through oriented polypropylene (OPP) is explained with a phenomenological model based on the hopping‐like migration of particles over a network of trapping sites with random site energies. The main mechanism behind the pressure dependence of the permeation is related to a decrease in the average activation energy of diffusion upon the gas sorption. This decrease is achieved because of a saturation of the deep traps, which reduces the mass transport to a network of shallow traps. In this way, fast‐diffusion channels with lower activation energy are created. The model is suitable for the description of the transient permeation of a gas through a polymer, as illustrated for the permeation of noble gases through an OPP membrane. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1308–1315, 2003

Effect of randomness on superconductivity and CDWin the (hard‐core) boson‐fermion model

AbstractWe discuss the influence of diagonal disorder (random site energy) on superconductivity (SC) and charge orderings (CDW) in a system of coexisting itinerant electrons and local pairs, described by the (hard‐core) boson‐fermion model. The evolution of the ground state properties and critical temperatures with increasing disorder is analysed. One finds that both the SC and the CDW can be substantially suppressed by the disorder effects. This is in obvious contrast with the s‐wave BCS superconductors which, according to the Anderson's theorem, are rather insensitive to the diagonal disorder (i.e. to nonmagnetic impurities).

FLUX DEPENDENCE OF PERSISTENT CURRENT IN A MESOSCOPIC DISORDERED TIGHT BINDING RING

We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux ϕ, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the eigenenergies expressed in terms of transfer matrices in the site representation is solved exactly to second order in a perturbation theory for weak disorder and fluxes differing from half-integer multiples of the flux quantum ϕ0=hc/e. From the equilibrium currents associated with the one-electron eigenstates we derive closed analytic expressions for the disorder averaged persistent current for even and odd numbers, Ne, of electrons in the ground state. Explicit discussion for the half-filled band case confirms that the persistent current is periodic with a period ϕ0, as in the absence of disorder, and that its amplitude is generally suppressed by the effect of the disorder. In comparison to previous results, based on an approximate analysis of the secular equation, the current suppression by disorder is strongly enhanced by a new periodic factor proportional to 1/ sin 2(2πϕ/ϕ0), for ϕ≠( integer )ϕ0/2.

Single-parameter scaling in one-dimensional Anderson localization: Exact analytical solution

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of the single parameter scaling in this model. According to this criterion, states with energies from the conduction band of the underlying non-random system satisfy single parameter scaling when disorder is small enough. At the same time, single parameter scaling is not valid for states close to band boundaries and those outside of the original spectrum even in the case of small disorder. The obtained results are applied to the Kronig-Penney model with the potential in the form of periodically positioned $\delta$-functions with random strengths. We show that an increase in the disorder can restore single parameter scalingbehavior for states from band-gaps of this model.