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International Journal of Modern Physics B

STATIC PROPERTIES OF THE BOSON-FERMION MODEL: SCALE ENERGY ANALYSIS

Mario Cuoco, Canio Noce, J. Ranninger, A. ROMANO

Published Mar 10, 2003• 0 citations
Publisher

Abstract

The analysis of the pseudogap phase in high-T c superconductors is often performed in terms of scenarios where itinerant electrons are coupled to bosonic excitations. Within this context, we have investigated the static properties of the boson-fermion model on a ring of finite size length by means of the thermal Lanczos method. As a result, we have determined the temperature dependence of the specific heat and the static susceptibility for different values of the exchange coupling associated to processes in which bosons decey into pairs of itinerant electrons, and vice-versa. The nature and the scale of energies of the relevant excitations which control the temperature behaviour of these thermodynamic quantities are also discussed.

DOI
10.1142/s0217979203016212

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•Jun 1, 2013•5 citations
The analysis of the pseudogap phase in high-T c superconductors is often performed in terms of scenarios where itinerant electrons are coupled to bosonic excitations. Within this context, we have investigated the static properties of the boson-fermion model on a ring of finite size length by means of the thermal Lanczos method. As a result, we have determined the temperature dependence of the specific heat and the static susceptibility for different values of the exchange coupling associated to processes in which bosons decey into pairs of itinerant electrons, and vice-versa. The nature and the scale of energies of the relevant excitations which control the temperature behaviour of these thermodynamic quantities are also discussed.
We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.
The properties of a mixture of mutually interacting bound electron pairs and itinerant fermions (the boson-fermion model) on a lattice are further studied. We determine the superconducting critical temperature from a pseudogap phase by applying a self-consistent TTT-matrix approach, which includes the pairing fluctuations and the boson self-energy effects. The analysis is made for a three dimensional cubic lattice with tight-binding dispersion for electrons and for both standard bosons and the case of hard-core bosons. The results describe the BCS-Bose-Einstein condensation crossover with varying position of the bosonic (local pair) level and give a further insight into the nature of resonance superfluidity in the boson-fermion model.
The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are (i) a crossover from a poor metal to an insulator and finally a superconductor as the temperature decreases; (ii) the buildup of a finite amplitude of local electron pairing below a certain temperature T∗,{T}^{*},T∗, followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature ${T}_{\ensuremath{\varphi}};$ and (iii) the opening of a pseudogap in the density of states of the electrons below T∗,{T}^{*},T∗, rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been obtained so far on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single- to two-particle transport as the temperature decreases and the superconducting state is approached.
A theoretical analysis of the thermodynamic response functions of the 2D single{band Hubbard model is carried out by means of the composite operator method.It is shown that all the features of these quantities can be explained by looking at the dependence of the thermodynamic variables on their conjugate ones.In this way, the electronic speci c heat and the entropy per site are determined in the paramagnetic phase.Also, for the electronic speci c heat and internal energy we present two dierent schemes of calculation.It is found that the numerical data from quantum Monte Carlo techniques for the internal energy and electronic speci c heat are well reproduced by determining them through the rst and second temperature derivatives of the chemical potential.The anomalous normal state properties in hole{doped cuprate high Tc superconductors are also well described.Finally, we obtain several characteristic crossing points for the response functions when plotted versus some thermodynamic variables.These peculiar features indicate the existence of more than one energy scale competing with thermal excitations and indicate, as already noted by Vollhardt, a crossover from a non{interacting to a highly correlated behaviour.
We study the thermodynamic properties of short coherence length superconductors in the pseudogap phase. Our description is based on the attractive Hubbard model that reproduces well these features in the intermediate coupling regime (U=4t).(U=4t).(U=4t). Basing ourselves on the self-consistent T-matrix approximation, we perform an analytical calculation that yields an expression for the thermodynamic grand potential of the electronic system. It shows that the relevant degrees of freedom above the critical temperature are well-defined bosonic fluctuations describing virtual Cooper pairing. The latter are described by the low-energy expansion of the T matrix whose evaluation reveals that these pairing fluctuations behave quite similarly to free bosons undergoing a Bose-Einstein condensation (BEC). We then carefully analyze the conditions allowing for this interpretation and finally consider the case of underdoped high-temperature superconductors where typical BEC features have been observed experimentally.
We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point-dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities. Copyright (c) EPLA, 2013