A simple model of a degenerate two-dimensional Bose liquid interacting with a fluctuating gauge field is investigated as a possible candidate to describe the charge degree of freedom in the normal state of the cuprate superconductors. We show that the fluctuating gauge field efficiently destroys superfluidity even in the Bose degenerate regime. We discuss the nature of the resulting normal state in terms of the geometric properties of the imaginary-time paths of the bosons. We will also present numerical results on the transport properties and the density correlations in the system. We find a transport scattering rate of \ensuremath{\hbar}/${\mathrm{\ensuremath{\tau}}}_{\mathrm{}\mathrm{tr}}$\ensuremath{\sim}${2\mathrm{k}}_{\mathrm{B}}$T, consistent with the experiments on the cuprates in the normal state. We also find that the density correlations of our model resemble the charge correlations of the t-J model.
A simple model of a degenerate two-dimensional Bose liquid interacting with a fluctuating gauge field is investigated as a possible candidate to describe the charge degree of freedom in the normal state of the cuprate superconductors. We show that the fluctuating gauge field efficiently destroys superfluidity even in the Bose degenerate regime. We discuss the nature of the resulting normal state in terms of the geometric properties of the imaginary-time paths of the bosons. We will also present numerical results on the transport properties and the density correlations in the system. We find a transport scattering rate of \ensuremath{\hbar}/\ensuremathτtr\ensuremath{\sim}2kBT, consistent with the experiments on the cuprates in the normal state. We also find that the density correlations of our model resemble the charge correlations of the t-J model.
We study the effect of a strongly fluctuating gauge field on a degenerate Bose liquid, relevant to the charge degrees of freedom in doped Mott insulators. We find that the superfluidity is destroyed. The resulting metallic phase is studied using quantum Monte Carlo methods. Gauge fluctuations cause the boson world lines to retrace themselves. We examine how this world-line geometry affects the physical properties of the system. In particular, we find a transport relaxation rate of the order of 2kBT, consistent with the normal state of the cuprate superconductors. We also find that the density excitations of this model resemble those of the full t- J model.
Two unrelated problems can be reduced to a model of a Bose gas interacting with a gauge field: (i) the effect of thermal fluctuations on a system of vortices in bulk superconductors in fields Hc1\ensuremath{\ll}H\ensuremath{\ll}Hc2, and (ii) charged, spinless excitations in two-dimensional (2D) strongly correlated electron systems. Both problems are important for the theory of high-temperature superconductors. We study this model in three regimes: at finite temperatures, assuming that the gauge field is purely transverse; at T=0, for the purely static (2D Coulomb) interaction; and at T=0, for a weak Coulomb interaction and a strong transverse one. Transverse interactions suppress the temperature of the superfluid transition significantly. A sufficiently strong transvese interaction is shown to produce a phase separation as the temperature decreases (in the absence of Coulomb repulsion). If there is Coulomb repulsion, the ground state does not have off-diagonal long-range order but the superfluid density is not zero unless the Coulomb constant exceeds a critical value. Sufficiently strong coupling to the transverse field destroys superfluidity as well. In the normal state formed at large couplings, the translational invariance is intact. We propose a bosonic ground state that is not superfluid at T=0. We discuss the implications of these results both for vortex liquids and strongly correlated electron systems.
In this thesis, we study various issues arising from the QED theory of underdoped, high temperature superconductors in 2+1 dimensions. The theory breaks up roughly into two sectors: fermionic and bosonic. With regard to the fermionic sector, we consider confinement of the emergent gauge field which we take to be compact. In the absence of fermions, the interaction between monopoles is Coulombic and the well known result is that the pure gauge theory is permanently confining. With the addition of fermions, the interaction becomes logarithmic, and an analogy with the usual Kosterlitz-Thouless transition suggests a deconfinement transition for the fermions. We show, however, that, when screening is taken into account, the deconfined phase is destabilized and fermions remain permanently confined. The bosonic sector models Cooper pair phase fluctuations, whose effect on the depletion of the superfluid density we examine in two separate studies. In the first of these, we study the quantum XY model, and show that the quasi-two dimensionality, low critical temperatures and large d-wave gap characteristic of underdoped cuprates severely constrain the form of the superfluid density. Under these assumptions, we find that phase fluctuations alone are insufficient to account for recent observations of deviations from Uemura scaling, and that the quasiparticle contribution is a necessity. We use our results to satisfactorily fit the recent data. In the second study, we model the cuprates by a layered system of interacting bosons and examine the collective excitations in this system. Depending on the anisotropy and the interaction strength, we find find four different regimes of temperature dependence of the superfluid density. We argue that interactions in the underdoped cuprates are effectively short-ranged and weak. Finally, we study the related issue of disordered, interacting bosons in the large-N limit and 2 strong commensuration. Perturbatively at weak disorder and numerically at strong, we show that th screening of the random potential due to interactions is insufficient to delocalize the single-particl states so that no superfluid transition occurs from the Mott insulator.
The Gaussian fluctuations in slave-boson mean-field theory of the $t\text{\ensuremath{-}}J$ model are analyzed in this paper in the low-doping regime where the superconducting to normal (pseudogap phase) transition is driven by vanishing of bose-condensation amplitude. By eliminating the boson and constraint fields exactly in the linear-response regime, we show that the Gaussian theory describes an unconventional Fermi liquid superconductor where the superconducting to normal transition is a new type of phase transition characterized by a change of Landau parameter from ${F}_{1}>\ensuremath{-}1$ in the superconducting phase to ${F}_{1}=\ensuremath{-}1$ in the pseudo-gap phase, corresponding to a state with spin-charge separation. The consequences of this proposal are discussed.
The Gaussian fluctuations in slave-boson mean-field theory of t−J model is analyzed in this paper in the low-doping regime where the superconducting to normal (pseudo-gap phase) transition is driven by vanishing of bose-condensation amplitude. By eliminating the boson and constraint fields exactly in the linear response regime we show that the Gaussian theory describes a Fermi liquid superconductor where the superconducting to normal transition is actually a spin-charge separation transition characterized by a change of Landau parameter from F1>−1 in the superconducting phase to F1=−1 in the pseudo-gap phase. Consequences of this proposal are discussed.
This Thesis analyzes the role of a mean-field theory and of the fluctuations in two different fermionic systems: the BCS-BEC crossover and high-Tc superconducting cuprates. In the first part of the Thesis we introduce the mean-field theory and the Gaussian-level fluctuations for the BCS-BEC crossover, i.e. the continuous evolution observed in ultracold neutral fermionic systems, from a weakly-coupled regime where fermions form Cooper pairs, to a strongly-coupled regime where the fermions at first form bosonic molecular dimers, subsequently undergoing Bose-Einstein condensation for low enough temperatures. We then analyze some problems related to the crossover: the condensate fraction for a spin-unbalanced Fermi gas, the Beliaev decay for collective excitations and the case of a two-dimensional Fermi gas, for which we calculate the first sound velocity and the Berezinskii-Kosterlitz-Thouless critical temperature, in very good agreement with recent experimental data. Finally we analyze a regularization procedure for the equation of state in the deep-BEC limit, allowing one to analytically derive the correct ratio between the fermionic and bosonic scattering lengths. In the second part of the Thesis we introduce a gauge approach to superconductivity in cuprates in which the hole is decomposed as the product of a spinful neutral particle, the spinon, and a spinless charged particle, the holon. The statistics of each particle is modified by binding it to a gauge field providing a statistical flux, this approach being analogous to Chern-Simons bosonization. We thus obtain a model characterized by three characteristic temperatures corresponding, respectively, to the appearance of a finite density of incoherent holon pairs, of a finite density of incoherent spinon pairs and, finally, to the phase coherence leading to superconductivity. Specifically in the present Thesis within this model we study the superfluid density, demonstrating that the spinon and holon contributions sum according to a Ioffe-Larking-like rule, analogous to that they found for resistivity, showing excellent agreement with experimental data in the moderate underdoping up to optimal doping region. We also demonstrated that the formalism reproduces the quasi-universality observed in experimental data at different dopings and allows for an analytical derivation of a relation that approximates the Uemura relation for moderate dopings.