arXiv subjects

B. D. Simons

Publications and source records attributed to B. D. Simons.

At least 55 records · Page 3Linked to original sources

arXiv2003

Charge transport and phase transition in exciton rings

The macroscopic exciton rings observed in the photoluminescence (PL) patterns of excitons in coupled quantum wells (CQWs) are explained by a series of experiments and a theory based on the idea of carrier imbalance, transport and recombination. The rings are found to be a source of cold excitons with temperature close to that of the lattice. We explored states of excitons in the ring over a range of temperatures down to 380 mK. These studies reveal a sharp, albeit continuous, second order phase transition to a low-temperature ordered exciton state, characterized by ring fragmentation into a periodic array of aggregates. An instability at the onset of degeneracy in the cold exciton system, due to stimulated exciton formation, is proposed as the transition mechanism.

cond-mat↗

arXiv2003

Parametric Statistics of Individual Energy Levels in Random Hamiltonians

We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric velocity correlation function and the distribution of level shifts under the influence of an arbitrary external perturbation.

cond-mat↗

arXiv2003

Parametric Spectral Statistics in Unitary Random Matrix Ensembles: From Distribution Functions to Intra-Level Correlations

We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of $H$ and $H'=H+V$ for an arbitrary fixed $V$ both for finite matrix size $N$ and in the ``thermodynamic'' $N\to\infty$ limit; (ii) derive many-point parametric correlation functions of the two sets of eigenvalues and show that they are naturally parametrised by the eigenvalues of the reactance matrix for scattering off the ``potential'' $V$; (iii) prove the universality of the correlation functions in unitary ensembles with non-Gaussian non-invariant confinement potential $W(H-V)$; (iv) establish a general scheme for exact calculation of level-number-dependent parametric correlation functions and apply the scheme to the calculation of intra-level velocity autocorrelation function and the distribution of parametric level shifts.

cond-mat↗

arXiv2003

Polariton condensation and lasing in optical microcavities - the decoherence driven crossover

We explore the behaviour of a system which consists of a photon mode dipole coupled to a medium of two-level oscillators in a microcavity in the presence of decoherence. We consider two types of decoherence processes which are analogous to magnetic and non-magnetic impurities in superconductors. We study different phases of this system as the decoherence strength and the excitation density is changed. For a low decoherence we obtain a polariton condensate with comparable excitonic and photonic parts at low densities and a BCS-like state with bigger photon component due to the fermionic phase space filling effect at high densities. In both cases there is a large gap in the density of states. As the decoherence is increased the gap is broadened and suppressed, resulting in a gapless condensate and finally a suppression of the coherence in a low density regime and a laser at high density limit. A crossover between these regimes is studied in a self-consistent way analogous to the Abrikosov and Gor'kov theory of gapless superconductivity.

cond-mat↗

arXiv2002

Parametric spectral correlations in disordered and chaotic structures

We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the (n,m)-point parametric correlation function of the initial and final density of states for perturbations of arbitrary rank and strength. A further generalization of these results allows for the incorporation of short-range spatial correlations in diffusive as well as ballistic chaotic structures.

cond-mat↗

arXiv2002

Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors

The physics of low-energy quasi-particle excitations in disordered d-wave superconductors is a subject of ongoing intensive research. Over the last decade, a variety of conceptually and methodologically different approaches to the problem have been developed. Unfortunately, many of these theories contradict each other, and the current literature displays a lack of consensus on even the most basic physical observables. Adopting a symmetry-oriented approach, the present paper attempts to identify the origin of the disagreement between various previous approaches, and to develop a coherent theoretical description of the different low-energy regimes realized in weakly disordered d-wave superconductors. We show that, depending on the presence or absence of time-reversal invariance and the microscopic nature of the impurities, the system falls into one of four different symmetry classes. By employing a field-theoretical formalism, we derive effective descriptions of these universal regimes as descendants of a common parent field theory of Wess-Zumino-Novikov-Witten type. As well as describing the properties of each universal regime, we analyse a number of physically relevant crossover scenarios, and discuss reasons for the disagreement between previous results. We also touch upon other aspects of the phenomenology of the d-wave superconductor such as quasi-particle localization properties, the spin quantum Hall effect, and the quasi-particle physics of the disordered vortex lattice.

cond-mat.mes-hall↗

arXiv2001

Tail States in Disordered Superconductors with Magnetic Impurities: the Unitarity Limit

When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that `optimal fluctuations' of the random impurity potential can lead to the nucleation of `domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordered system, the aim of the present paper is to extend this analysis to the consideration of magnetic impurities in the unitarity scattering limit. This investigation reveals that the qualitative behaviour is maintained while the density of states exhibits a rich structure.

cond-mat.supr-con↗

arXiv2001

Phase coherence phenomena in superconducting films

Superconducting films subject to an in-plane magnetic field exhibit a gapless superconducting phase. We explore the quasi-particle spectral properties of the gapless phase and comment on the transport properties. Of particular interest is the sensitivity of the quantum interference phenomena in this phase to the nature of the impurity scattering. We find that films subject to columnar defects exhibit a `Berry-Robnik' symmetry which changes the fundamental properties of the system. Furthermore, we explore the integrity of the gapped phase. As in the magnetic impurity system, we show that optimal fluctuations of the random impurity potential conspire with the in-plane magnetic field to induce a band of localized sub-gap states. Finally, we investigate the interplay of the proximity effect and gapless superconductivity in thin normal metal-superconductor bi-layers.

cond-mat.supr-con↗

arXiv2001

Optimal Fluctuations and Tail States of non-Hermitian Operators

A statistical field theory is developed to explore the density of states and spatial profile of `tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified with symmetry broken, instanton field configurations of the theory, are closely related to localized sub-gap states recently identified in disordered superconductors. By focusing separately on the problems of a quantum particle propagating in a random imaginary scalar potential, and a random imaginary vector potential, we discuss the methodology of our approach and the universality of the results. Finally, we address potential physical applications of our findings.

cond-mat.dis-nn↗

arXiv2001

Quantized Adiabatic Charge Transport in a Carbon Nanotube

The coupling of a metallic Carbon nanotube to a surface acoustic wave (SAW) is proposed as a vehicle to realize quantized adiabatic charge transport in a Luttinger liquid system. We demonstrate that electron backscattering by a periodic SAW potential, which results in miniband formation, can be achieved at energies near the Fermi level. Electron interaction, treated in a Luttinger liquid framework, is shown to enhance minigaps and thereby improve current quantization. Quantized SAW induced current, as a function of electron density, changes sign at half-filling.

cond-mat.mes-hall↗

arXiv2001

Gap Fluctuations in Inhomogeneous Superconductors

Spatial fluctuations of the effective pairing interaction between electrons in a superconductor induce variations of the order parameter which in turn lead to significant changes in the density of states. In addition to an overall reduction of the quasi-particle energy gap, theory suggests that mesoscopic fluctuations of the impurity potential induce localised tail states below the mean-field gap edge. Using a field theoretic approach, we elucidate the nature of the states in the `sub-gap' region. Specifically, we show that these states are associated with replica symmetry broken instanton solutions of the mean-field equations.

cond-mat.supr-con↗

arXiv1999

Optimal Fluctuations and Tail States of non-Hermitian Operators

We develop a general variational approach to study the statistical properties of the tail states of a wide class of non-Hermitian operators. The utility of the method, which is a refinement of the instanton approach introduced by Zittartz and Langer, is illustrated in detail by reference to the problem of a quantum particle propagating in an imaginary scalar potential.

cond-mat↗

arXiv1999

Classical and Quantum Dynamics in a Random Magnetic Field

Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis begins with an investigation of the spectral properties of the purely classical evolution operator. We show that, although the kinetic equation is formally time-reversible, density relaxation is controlled by {\em irreversible} classical dynamics. In the case of a weak magnetic field, the effective kinetic operator corresponds to diffusion in the angle space, the diffusion constant being determined by the spectral resolution of the inhomogeneous magnetic field. Applying these results to the quantum problem, we demonstrate that the low-lying modes of the field theory are related to the eigenmodes of the irreversible classical dynamics, and the higher modes are separated from the zero mode by a gap associated with the lowest density relaxation rate. As a consequence, we find that the long-time properties of the system are characterised by universal Wigner-Dyson statistics. For a weak magnetic field, we obtain a description in terms of the quasi one-dimensional non-linear $σ$-model.

cond-mat.dis-nn↗

arXiv1999

Competition between zero bias anomaly and proximity effect in disordered systems

We investigate the suppression of the proximity effect in mesoscopic normal metal/superconductor systems induced by Coulomb interaction. We identify and elucidate the mechanism by which disorder leads to an amplification of this effect. In particular, for strong enough disorder, the proximity effect is shown to vanish. An expression for the tunneling density of states is obtained, and experimental applications are discussed.

cond-mat.supr-con↗

arXiv1998

Quantum Mechanics with Random Imaginary Scalar Potential

We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble averaged one-particle Green function from which we obtain the density of complex eigenvalues. Based on the connection between non-Hermitian quantum mechanics and the statistical mechanics of polymer chains, we determine the distribution function of a self-interacting polymer in dimensions $d>4$.

cond-mat.dis-nn↗

arXiv1998

Field Theory of Mesoscopic Fluctuations in Superconductor/Normal-Metal Systems

Thermodynamic and transport properties of mesoscopic conductors are strongly influenced by the proximity of a superconductor: An interplay between the large scale quantum coherent wave functions in the normal mesoscopic and the superconducting region, respectively, leads to unusual mechanisms of quantum interference. These manifest themselves in both the mean and the mesoscopic fluctuation behaviour of superconductor/normal-metal (SN) hybrid systems being strikingly different from those of conventional mesoscopic systems. After reviewing some established theories of SN-quantum interference phenomena, we introduce a new approach to the analysis of SN-mesoscopic physics. Essentially, our formalism represents a unification of the quasi-classical formalism for describing {\it mean} properties of SN-systems on the one hand, with more recent field theories of mesoscopic {\it fluctuations} on the other hand. Thus, by its very construction, the new approach is capable of exploring both averaged and fluctuation properties of SN-systems on the same microscopic footing. As an example, the method is applied to the study of various characteristics of the single particle spectrum of SNS-structures.

cond-mat.mes-hall↗

arXiv1998

Delocalization in coupled one-dimensional chains

A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $ε=0$, and it is shown that a delocalization transition at this energy takes place if and only if $N$ is odd. This even-odd effect is explained by level repulsion of the transmission eigenvalues.

cond-mat.dis-nn↗

arXiv1998

Random Dirac Fermions and Non-Hermitian Quantum Mechanics

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.

cond-mat.dis-nn↗