Volume 58, Issue 2
February 2002, pages 147-442
pp 147-147 February 2002 Special Issue on Mesoscopic and Disordered Systems
pp 149-153 February 2002
Some problems in the physics of disordered systems are pointed out; most of these arise from experiments.
pp 155-172 February 2002
We recall some basic aspects of the pinning of flux lines in a superconducting cylindrical shell subjected to a depinning magnetic field, as well as its description by the quantum mechanics of a disordered ring with an imaginary vector potential proportional to the depinning field (N Hatano and D R Nelson, Phys. Rev.B56, 8651 (1997)). We then discuss our recent analysis of the pinning-depinning transition in terms of an explicit solution for the inverse localization length of the eigenstates of the non-hermitian quantum system for weak disorder. Our results as to the nature of the non hermitian quantum states, differ qualitatively from earlier studies which did not examine the detailed properties of the localization length. Nevertheless we obtain a well-defined simple picture for the pinning-depinning transition of flux lines. We discuss furthermore a new exact calculation of localized state eigenenergies for weak disorder, which we compare with previous analytic and numerical results.
pp 173-181 February 2002
We present a simple model of transmission across a metallic mesoscopic ring. In one of its arm an electron interacts with a single magnetic impurity via an exchange coupling. We show that entanglement between electron and spin impurity states leads to reduction of Aharonov-Bohm oscillations in the transmission coefficient. The spin-conductance is asymmetric in the flux reversal as opposed to the two-probe electrical conductance which is symmetric. In the same model, in contradiction to the naive expectation of a current magnification effect, we observe enhancement as well as suppression of this effect depending on the system parameters. The limitations of this model to the general notion of dephasing or decoherence in quantum systems are pointed out.
pp 183-193 February 2002
It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field the dc conductance fluctuations are much stronger for the periodic pumping than in the case of the noise ac field of the same intensity. The reduction factor r in a static magnetic field takes the universal value of 2 only for the white-noise pumping. In general r may deviate from 2 thus signalling on the time-reversal breaking by the ac field. For the bi-harmonic ac field of the form A(t) = A0[cos(ω1t) − cos(ω2t)] we predict the enchancement of effects of T-symmetry breaking at commensurate frequencies ω2/ω1 = P/Q. In the high-temperature limit there is also the parity effect; the enchancement is only present if either P or Q is even.
pp 195-203 February 2002
We numerically study the effect of non-symmetry dictated nodes (NSDN) on electron correlation effects for spinless electrons. We find that repulsive interaction between electrons can enhance the overlap between nearest neighbors in the tight binding Hamiltonian, in the presence of NSDN. Normally, in the absence of NSDN, attractive interaction between electrons give such an effect and repulsive interaction gives the opposite effect.
pp 205-216 February 2002
With a brief introduction to one-dimensional channels and conductance quantization in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantized conductances and an interesting odd-even effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the odd-even effect. We end with a brief summary and discussion of future projects.
pp 217-224 February 2002
This paper summarizes some work that I have been doing on eigenvalue correlators of random matrix models which show some interesting behavior. First we consider matrix models with gaps in their spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the Hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems.
pp 225-231 February 2002
We study a new type of long-range correlations for waves propagating in a random medium. These correlations originate from scattering events which take place close to a point source. The scattered waves propagate by diffusion to distant regions. In this way long range correlations, between any pair of distant points, are established.
pp 233-239 February 2002
In doped polyaniline (PANI), the charge transport properties are determined by mesoscopic morphology, which in turn is controlled by the molecular recognition interactions among polymer chain, dopant and solvent, Molecular recognition plays a significant role in chain conformation and charge delocalization. The resistivity of PANI doped by camphor sulfonic acid (CSA)/2-acrylo-amido-1-propane sulfonic acid (AMPSA)/dodecyl benzene sulfonic acid (DBSA) is around 0.02 Ω cm. PANI-CSA and PANI-AMPSA show a metallic positive temperature coefficient of resistivity above 150 K. with a finite value of conductivity at 1.4 K; whereas, PANI-DBSA shows hopping transport at low temperatures. The magnetoresistance is positive (negative) for PANI-CSA (PANI-AMPSA); and PANI-DBSA has a large positive MR. The behavior of MR suggests subtle variations in mesoscopic morphology between PANI-CSA and PANI-AMPSA.
pp 241-257 February 2002
We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.
pp 259-269 February 2002
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited using small square lattice models where electrons interact via a Coulomb U/r potential. From exact numerical diagonalizations, one finds that the mesoscopic electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings. The roles of a random substrate and of the spin degrees of freedom are investigated. Possible relations with the 2d metal-insulator transition observed in various field effect devices are suggested.
pp 271-283 February 2002
We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.
pp 285-292 February 2002
We discuss the possibility of spin-glass order in the vicinity of the unexpected metallic state of the two-dimensional electron gas in zero applied magnetic field. An average ferromagnetic moment may also be present, and the spin-glass order then resides in the plane orthogonal to the ferromagnetic moment. We argue that a quantum transition involving the destruction of the spinglass order in an applied in-plane magnetic field offers a natural explanation of some features of recent magnetoconductance measurements. We present a quantum field theory for such a transition and compute its mean field properties.
pp 293-311 February 2002
We present the study of spin and charge transport in nanostructures in the presence of spin-orbit (SO) interaction. Single band tight binding Hamiltonians for Elliot-Yafet and Rashba SO interaction are derived. Using these tight binding Hamiltonians and spin resolved Landauer-Büttiker formula, spin and charge transport is studied. Specifically numerical results are presented for a new method to perform magnetic scanning tunneling microscopy with non-magnetic tip but in the presence of Elliot-Yafet SO interaction. The spin relaxation phenomena in two-dimensional electron gas in the presence of Rashba SO interaction are studied and contrary to naive expectation, it is shown that disorder helps to reduce spin relaxation.
pp 313-323 February 2002
Experimental realization of mirrorless lasers in the last decade have resulted in hectic activity in this field, due to their novelty, simplicity and ruggedness and their great potential for application. In this article, I will review the various developments in this field in roughly chronological order, and discuss some possible applications of this exciting phenomenon, also termed as ‘random lasing’.
pp 325-331 February 2002
We present a maximum-entropy model for the transport of waves through a classically chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint 〈TrSS†〉 = αn: n is the dimensionality of S, and 0 ≤ α ≤ 1. For α = 1 the S-matrix distribution concentrates on the unitarity sphere and we have no absorption; for α = 0 the distribution becomes a delta function at the origin and we have complete absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential — Rayleigh statistics — even for n = 1. For n ≫ 1 Rayleigh statistics is attained even with no absorption; here we extend the study to α<1. The model is compared with random-matrixtheory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. The success of the model for strong absorption is understood in the light of a central-limit theorem. For weak absorption, some important physical constraint is missing in the construction of the model.
pp 333-341 February 2002
We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the inverse participation ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymmetry.
pp 343-359 February 2002
In this paper we report some of the important results of experimental investigations of the flicker noise near the metal-insulator (MI) transition in doped silicon single crystals. This is the first comprehensive work to study low-frequency noise in heavily doped Si over an extensive temperature range (2 K<T<500 K). The measurements of conductance fluctuations (flicker noise) were carried out in the frequency range 10−2<f<4 × 101 Hz in single crystalline Si across the MI transition by doping with phosphorous and boron. The magnitude of noise in heavily doped Si is much larger than that seen in lightly doped Si over the whole temperature range. The extensive temperature range covered allowed us to detect two distinct noise mechanisms. At low temperatures (T<100 K) universal conductance fluctuations (UCF) dominate and the spectral dependence of the noise is determined by dephasing the electron from defects with two-levels (TLS). At higher temperatures (T>200 K) the noise arises from activated defect dynamics. As the MI transition is approached, the 1/f spectral power, typical of the metallic regime, gets modified by the presence of discrete Lorentzians which arise from generation-recombination process which is the characteristic of a semiconductor.
pp 361-369 February 2002
Non-resonant microwave absorption (NRMA) studies of superconducting MgB2 and a sample containing ∼10% by weight of MgO in MgB2 are reported. The NRMA results indicate near absence of intergranular weak links in the pure MgB2 sample. A linear temperature dependence of the lower critical field Hc1 is observed indicating a non-s wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d wave symmetry is also not observed. In the MgB2 + MgO sample, much larger low field dependent absorption is observed indicating the presence of intergranular weak links. The hysteretic behavior of NRMA is compared and contrasted in the two samples. In the pure MgB2 sample, a large hysteresis is observed between the forward and the reverse scans of the magnetic field indicating strong pinning of flux lines. This hysteresis saturates a few degrees below Tc while in the MgB2 + MgO sample, a much slower increase of hysteresis with decreasing temperature is observed, a signature of weaker pinning.
pp 371-383 February 2002
Magnetic metal and metal oxide nanoparticles capped with alkylamines have been synthesized and characterized by transmission electron microscopy. X-ray diffraction, energy dispersive X-ray analysis and magnetization measurements. Core-shell Pd-Ni particles with composition, Pd561Ni3000, (diameter ∼3.3 nm) are superparamagnetic at 5 K and organize themselves into two-dimensional crystalline arrays. Similar arrays are obtained with Pd561Ni3000Pd1500 nanoparticles containing an additional Pd shell. Magnetic spinel particles of γ-Fe2O3, Fe3O4 and CoFe2O4 of average diameters in the 4–6 nm range coated with octylamine are all supermagnetic at room temperature and yield close-packed disordered arrays. Relatively regular arrays are formed by dodecylaminecapped Fe3O4 nanoparticles (∼8.6 nm diameter) while well-ordered hexagonal arrays were obtained with octylamine-covered Co3O4 nanoparticles (∼4.2 nm diameter).
pp 385-397 February 2002
We obtain the dynamics in number and phase difference, for Bose condensates that tunnel between two wells of a double-well atomic trap, using the (nonlinear) Gross-Pitaevskii equation. The dynamical equations are of the canonical form for the two conjugate variables, and the Hamiltonian corresponds to that of a momentum-shortened pendulum, supporting a richer set of tunneling oscillation modes than for a superconductor Josephson junction, that has a fixed-length pendulum as a mechanical model. Novel modes include ‘inverted pendulum’ oscillations with an average angle of π; and oscillations about a self-maintained population imbalance that we term ‘macroscopic quantum self-trapping’. Other systems with this phase-number nonlinear dynamics include two-component (interconverting) condensates in a single harmonic trap, and He3B superfluids in two containers connected by micropores.
pp 399-408 February 2002
We present here a set of coupled continuum equations to describe atomic deposition. We take into account evaporation due to thermal and mechanical disturbances as well as subsequent accretion at favourable grooves.
pp 409-417 February 2002
We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site k hops to its nearest neighbor with a quenched rate w(k). These rates are chosen randomly from the probability distribution f(w) ∼ (w − c)n, where c is the lower cutoff. For n>0, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on the local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, regions with a smooth density profile are described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size L as Lz with z = 2 + 1/(n + 1) for n>1 and suggests a different behavior for n<1.
pp 419-426 February 2002
This article reviews some effects of disorder in percolation systems away from the critical density pc. For densities below pc, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singularities in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biased diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.
pp 427-437 February 2002
A few billion years of evolutionary time and the complex process of ‘selection’ has given biology an opportunity to explore a variety of condensed matter phenomena and situations, some of which have been discovered by humans in the laboratory, that too only in extreme non-biological conditions such as low temperatures, high purity, high pressure etc., in the last centuries. Biology, at some level, is a complex and self-regulated condensed matter system compared to the ‘inanimate’ condensed matter systems such as liquid 4He, liquid water or a piece of graphite. In this article I propose a hypothesis that ‘all basic condensed matter physics phenomena and notions (already known and ones yet to be discovered) mirror in biology’. I explain this hypothesis by considering the idea of ‘Bose condensation’ or ‘momentum space order’ and discuss two known example of quantum magnetism encountered in biology. I also provide some new and rather speculative possibility, from light harvesting in biological photosynthesis, of mesoscopic excition condensation related phenomena at room temperature.
pp 439-442 February 2002
In this paper we present a qualitative outlook of mesoscopic biology where the typical length scale is of the order of nanometers and the energy scales comparable to thermal energy. Novel biomolecular machines, governed by coded information at the level of DNA and proteins, operate at these length scales in biological systems. In recent years advances in technology have led to the study of some of the design principles of these machines; in particular at the level of an individual molecule. For example, the forces that operate in molecular interactions, the stochasticity involved in these interactions and their spatio-temporal dynamics are beginning to be explored. Understanding such design principles is opening new possibilities in mesoscopic physics with potential applications.
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