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arXiv:cond-mat/0602479

Fermi liquid behavior and spin-charge separation in underdoped cuprates

Ching-Kit Chan, Tai Kai Ng

Published Feb 21, 2006• 0 citations
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Abstract

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 $F_1>-1$ in the superconducting phase to $F_1=-1$ in the pseudo-gap phase. Consequences of this proposal are discussed.

DOI
10.48550/arxiv.cond-mat/0602479

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The Gaussian fluctuations in slave-boson mean-field theory of t−Jt-Jt−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>−1F_1>-1F1​>−1 in the superconducting phase to F1=−1F_1=-1F1​=−1 in the pseudo-gap phase. Consequences of this proposal are discussed.
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.
This thesis studies two modern mean field theories of the t-J model for high Tc superconductors, namely the Slave-Boson Mean Field Theory and the Spinon-Dopon Mixing Mean Field Theory, from the view point of the traditional Fermi Liquid language. This study mainly focuses on whether the two mean field theories are consistent with Fermi Liquid behaviour in the underdoped regime of the superconducting and pseudogap phases of the t-J model. Historically, experimental results indicate that the superconducting phase can be well described by the conventional Fermi liquid-like quasiparticle picture; while the pseudogap phase exhibits non-trivial non-Fermi Liquid properties. This work aims at interpreting the pseudogap phase in a generalized Fermi Liquid framework and explaining why the simple quasiparticle picture works so well in the superconducting phase even in this strongly correlated superconducting system. Within the Gaussian approximation, we formally derived the Landau interaction in Fermi liquid theory, which serves as the key to classify the behaviour of the quasiparticles in different phases. It is found that the Slave-Boson Mean Field Theory describes the superconducting to the pseudogap phase transition as a transition with an interesting Landau parameter F1s changing from 1+F1s~x to 1+F1s=0, reflecting the occurrence of a quasiparticle instability. A new phase is proposed and its experimental consequences are discussed. On the other hand, we also find that the Spinon-Dopon Mixing Mean Field Theory can be understood in a conventional Fermi Liquid framework; even though quasiparticles in the theory carry larger charges. The issue of superfluid density is also clarified.
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 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.
In this paper we generalize slave-boson mean-field theory for $t\ensuremath{-}J$ model to the time-dependent regime, and derive transport equations for $t\ensuremath{-}J$ model, both in the normal and superconducting states. By eliminating the boson and constraint fields exactly at zero temperature in the linear-response regime we obtain a set of transport equations for physical electrons which have the same form as Landau transport equations for normal Fermi liquid and Fermi-liquid superconductor, respectively, with all Landau parameters explicitly given. Our theory can be viewed as a refined version of U(1) Gauge theory where all lattice effects are retained and strong correlation effects are reflected as strong Fermi-liquid interactions in the transport equation. Some experimental consequences are discussed.
Theoretical attempts to explain the origin of high temperature superconductivity are challenged by the complexity of the normal state, which exhibits three regimes with increasing hole doping: a pseudo-gap regime when underdoped, strange power laws near optimal doping and more conventional metallic behavior when heavily overdoped. We suggest that the origin of this behavior is linked to a zero temperature quantum phase transition separating the overdoped Fermi liquid from a spin-charge separated underdoped phase. Central to our analysis is a new Z2Z_2Z2​ gauge theory formulation, which supports topological vortex excitations - dubbed visons. The visons are gapped in the underdoped phase, splitting the electron's charge and Fermi statistics into two separate excitations. Superconductivity occurs when the resulting charge eee boson condenses. The visons are condensed in the overdoped phase, thereby confining the charge and statistics of the electron leading to a Fermi liquid phase. Right at the quantum confinement transition the visons are in a critical state, leading to power law behavior for both charge and spin.