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arXiv:cond-mat/9811146

Preformed Pairs, SU(2) Slave-boson Theory, and High T_c Superconductors

C. L. Wu, Chung‐Yu Mou, Xiao-Gang Wen, Darwin Chang

Published Nov 11, 1998• 0 citations
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Abstract

A preformed-pair model was considered. The quantum disordered phase of the d-wave superconducting state was obtained by turning on an on-site repulsion. The low energy effective theory of the quantum disordered phase was derived, which was found to be qualitatively equivalent to the low energy effective theory of the SU(2) slave-boson theory in the staggered-flux phase. Many physical properties of the disordered phase at low energies were obtained, such as the Mott insulator property at zero doping, spin gap and low superfluid density at low doping.

DOI
10.48550/arxiv.cond-mat/9811146

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A preformed-pair model was considered. The quantum disordered phase of the d-wave superconducting state was obtained by turning on an on-site repulsion. The low energy effective theory of the quantum disordered phase was derived, which was found to be qualitatively equivalent to the low energy effective theory of the SU(2) slave-boson theory in the staggered-flux phase. Many physical properties of the disordered phase at low energies were obtained, such as the Mott insulator property at zero doping, spin gap and low superfluid density at low doping.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
I study the effect of Coulomb interaction on superconducting order in a ddd-wave lattice superconductor at T=0T=0T=0 by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion UUU. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at T=0T=0T=0 has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large UUU. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
We study the stability of the spin gap phase in the U (1) slave-boson theory of the t - J model in connection with the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those in the strange-metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum-critical (QC) and quantum-disordered (QD) regime of the boson system. We also show that the regime of QD bosons with the paired fermions can be regarded as a strong-coupling version of the recently proposed nodal liquid theory.
The U(1) slave-boson mean-field theory of the t - J model has been used by many authors as a starting point for the theoretical analysis of high - Tc cuprate superconductors. With suitable refinements, the theory can explain a lot of qualitative features of cuprates. However, the theory does not produce a correct description of the low-energy quasi-particle properties in the under-doped regime. There exist several possible schemes to resolve this difficulty, among them, one generalizes the U(1) theory to SU(2) formulation and the other introduces confinement between spinons and holons. In this thesis, we generalize the Landau transport equations of the U(1) slave-boson mean-field theory of the t - J model to the SU(2) formulation. We first generalize the SU(2) slave-boson mean-field theory to the time-dependent regime. After eliminating the boson and constraint fields exactly in the linear-response regime at zero-temperature, we obtain a set of transport equations for quasi-particles, which has a similar structure as the Landau transport equations for Fermi-liquid superconductors, with all the Landau parameters explicitly given except that besides the usual effective interaction in the particle-hole channel in Fermi-liquid theory, we find an effective interaction in the particle-particle channel, which reflects the SU(2) symmetry between particles and holes. The transport equation is SU(2) invariant at half-filling. Around q⃗ = 0, the electron density couples only to the transverse part of the external field and the quasi-particle charge is still of order x. Besides the SU(2) formulation approach, we also investigate spinon-holon confinement in the U(1) slave-boson theory. The optical and thermal conduc-tivities of U (1) slave-boson theory with confinement are calculated. For optical conductivity, we consider only the contributions from static impurities. The qualitative behavior of our results agrees with experimental results. However, to explain the experiments quantitatively, we need to study further the con-tributions from phonons. We found a phenomenological effective Hamiltonian for the quasi-particle Green's functions in the U(1) slave-boson theory with spinon-hoion confinement. Starting from this effective Hamiltonian, we exam-ine the thermal conductivity within the theory. In particular, we compare the thermal conductivity for four different situations: (i) the ordinary d-wave su-perconducting state with four Dirac Fermi points; (ii) the normal metal state with a half-pocket Fermi surface; (iii) the spinon-holon confinement supercon-ducting state with a half-pocket Fermi surface; (iv) BCS superconducting state with a half-pocket Fermi surface.
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.