Onset of pseudogap and density wave in a system with a closed Fermi surface

We study the influence of anisotropy, treated as a dimensional crossover between 1D and 3D system, on the topological instability induced by a (self-consistent) uniaxial periodic potential. The mechanism on which the instability is based involves the topological reconstruction of the Fermi surface, from initially closed pockets to the surface with open Fermi sheets, creating two peculiar points in the band dispersion - the saddle point and elliptical point, between which the pseudogap in electron density of states develops. The self-consistent periodic potential appears as a result of interactions, either electron-phonon, or electron electron, which, linked with the topological instability of the system, results in formation of a new ground state of the system - the density wave provided that the relevant coupling constant is larger than critical. Our analysis shows that the phase transition takes place along the whole continuous interval of a dimensional crossover between 1D and 3D, but that the critical coupling strength significantly increases with the dimensionality of the system. It is our intention to give an initial framework for understanding the nature of charge density waves experimentally observed in a number of materials, like high$-T_c$ cuprates or graphite intercalates, both being materials with a closed, rather isotropic Fermi surface far from the nesting regime.Comment: 11 pages, 6 figure

DC and optical signatures of the topological reconstruction of the Fermi surface for electrons with parabolic band dispersion

We study the main intra-band and inter-band transport properties at zero temperature of free electron-like system undergoing a topological reconstruction of the Fermi surface for the two-dimensional and three-dimensional case. The calculated intra-band properties include the single-particle density of states, the total and the effective concentrations of electrons and the thermopower. As for the inter-band case, the real part of the conductivity has been calculated within the vanishing inter-band relaxation approximation as a function of the incident photon energy. Within this approach, it is shown that the optical conductivity has a nonvanishing component parallel to the reconstruction wave vector and the shape which depends on the value of the Fermi energy. Each dimensionality has its particular features in the transport quantities presented in the paper, which are discussed and compared with those in the free electron scenario. Finally, we identify the signature of the topological reconstruction of the Fermi surface in the intra-band and inter-band transport functions

The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons

Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons - particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high permeability ($\mu_r$) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect (IQHE), is sandwiched between two blocks of the high-$\mu_r$ material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-$\mu_r$ materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.Comment: are welcom

Chaotic dynamics and orbit stability in the parabolic oval billiard

Chaotic properties of the one-parameter family of oval billiards with parabolic boundaries are investigated. Classical dynamics of such billiard is mixed and depends sensitively on the value of the shape parameter. Deviation matrices of some low period orbits are analyzed. Special attention is paid to the stability of orbits bouncing at the singular joining points of the parabolic arcs, where the boundary curvature is discontinuous. The existence of such orbits is connected with the segmentation of the phase space into two or more chaotic components. The obtained results are illustrated by numerical calculations of the Poincaré sections and compared with the properties of the elliptical stadium billiards

Classical and quantum chaos in the generalized parabolic lemon-shaped billiard

Two-dimensional billiards of a generalized parabolic lemonlike shape are investigated classically and quantum mechanically depending on the shape parameter δ. Quantal spectra are analyzed by means of the nearest-neighbor spacing distribution method. Calculated results are well accounted for by the proposed new two-parameter distribution function P(s), which is a generalization of Brody and Berry-Robnik distributions. Classically, Poincaré diagrams are shown and interpreted in terms of the lowest periodic orbits. For δ=2, the billiard has some unique characteristics resulting from the focusing property of the parabolic mirror. Comparison of the classical and quantal results shows an accordance with the Bohigas, Giannoni, and Schmit conjecture and confirms the relevance of the new distribution for the analysis of realistic spectral data

Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs

Chaotic properties of a new family, ellipse hyperbola billiards (EHB), of lemon-shaped two-dimensional billiards, interpolating between the square and the circle, whose boundaries consist of hyperbolic, parabolic, or elliptical segments, depending on the shape parameter δ, are investigated classically and quantally. Classical chaotic fraction is calculated and compared with the quantal level density fluctuation measures obtained by fitting the calculated level spacing sequences with the Brody, Berry-Robnik, and Berry-Robnik-Brody distributions. Stability of selected classical orbits is investigated, and for some special hyperbolic points in the Poincaré sections, the “blinking island” phenomenon is observed. Results for the EHB billiards are compared with the properties of the family of generalized power-law lemon-shaped billiards

Magnetic oscillations and field-induced spin-density waves in (TMTSF)_2ClO_4

We investigated the effects of magnetic field on a quasi-one-dimensional band of interacting electrons with a transverse dimerizing potential. One-particle problem in bond-antibond representation is solved exactly as well as the problem of magnetic breakdown through the dimerization gap. The resulting propagator is used to calculate the spin-density-wave (SDW) response of the interacting system within the matrix RPA for the SDW susceptibility. We find that the value of the anion potential fitting experiments in relaxed (TMTSF)_2ClO_4 is large, of the order of inter-chain hopping. In particular we predict the magnetic field induced transition of the first order between interband SDW0 and intraband SDW+/- phases. We reproduce the rapid oscillations with a period of 260 Tesla and the overall profile of the (TMTSF)_2ClO_4 phase diagram

Nanomechanical manipulation of superconducting charge-qubit quantum networks

We suggest a nanoelectromechanical setup and corresponding time-protocol for controlling parameters in order to demonstrate nanomechanical manipulation of superconducting charge-qubit quantum network. We illustrate it on an example reflecting important task for quantum information processing - transmission of quantum information between two charge-qubits facilitated by nanomechanics. The setup is based on terminals utilizing the AC Josephson effect between bias voltage-controlled bulk superconductors and mechanically vibrating mesoscopic superconducting grain in the regime of the Cooper pair box, controlled by the gate voltage. The described manipulation of quantum network is achieved by transduction of quantum information between charge-qubits and intentionally built nanomechanical coherent states, which facilitate its transmission between qubits. This performance is achieved using quantum entanglement between electrical and mechanical states.Comment: 8 pages, 4 figure