Effect of inter-edge Coulomb interactions on transport through a point contact in nu=5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G(H) = 1/2e(2)/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G(H) = 5/2e(2)/h) and the fully disconnected case (G(H) = 0).

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

Exact energy eigenvalues for an attractive Coulomb potential with zero-radius hard core

Following a peratization procedure, the exact energy eigenvalues for an attractive Coulomb potential, with a zero-radius hard core, are obtained as roots of a certain combination of di-gamma functions. The physical significance of this entirely new energy spectrum is discussed.

Calculation of Coulomb interaction strengths for 3d transition metals and actinides

Coulomb interaction strengths (Udd and Uff) have been calculated from Hartree-Fock-Slater atomic calculations for 3d transition and 5f actinide elements, respectively. By decomposing the different contributions to the response (screening) to the 3d charge fluctuation, we show that a substantial reduction in Udd arises due to the relaxation of the 3d charge distribution itself. This, combined with the screening due to the response of the 4s charge density, is shown to provide a very compact screening charge comparable to the metallic case, explaining the success of the atomic calculations for estimating U even in the metals. A pronounced dependence of Udd (or Uff) on the number of electrons nd (nf) or the electronic configuration is also shown here.

Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Fermi-Edge Transmission Resonance in Graphene Driven by a Single Coulomb Impurity

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude approximate to e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.