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arXiv:cond-mat/0103007 · Physical review. B, Condensed matter

Effective gauge-field theory of the t−J model in the charge-spin separated state and its transport properties

Ikuo Ichinose, Tetsuo Matsui, Masaru Onoda

Published Aug 23, 2001• 58 citations
arXivHTMLPDF

Abstract

We study the slave-boson $t\ensuremath{-}J$ model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, ${A}_{i}.$ The charge-spin separation occurs below a certain temperature, ${T}_{\mathrm{CSS}},$ as a deconfinement phenomenon of the dynamics of ${A}_{i}.$ Below a certain temperature ${T}_{\mathrm{SG}}(<{T}_{\mathrm{CSS}}),$ the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and ${A}_{i}$ acquires a mass ${m}_{A}.$ The effective field theory near ${T}_{\mathrm{SG}}$ takes the form of a Ginzburg-Landau theory of a complex scalar field $\ensuremath{\lambda}$ coupled with ${A}_{i},$ where $\ensuremath{\lambda}$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at ${T}_{\mathrm{SG}}.$ By using this field theory, we calculate the dc resistivity $\ensuremath{\rho}.$ At $T>{T}_{\mathrm{SG}},$ $\ensuremath{\rho}$ is proportional to T. At $T<{T}_{\mathrm{SG}},$ it deviates downward from the T-linear behavior as $\ensuremath{\rho}\ensuremath{\propto}T{1\ensuremath{-}{c(T}_{\mathrm{SG}}\ensuremath{-}{T)}^{d}}.$ When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\ensuremath{\lambda},$ the exponent d deviates from its mean-field value $1/2$ and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.

DOI
10.1103/physrevb.64.104516

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We propose an explanation of several experimental features related to the "pseudogap" in high Tc cuprates in terms of a spin-charge gauge theory. In this approach, based on a formal spin-charge separation applied to the t-J model, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap ms~J(δ| ln δ|)1/2, where δ is the doping concentration) and holons with "small" Fermi surface (∊F~tδ) interacting via a gauge field. The main effect of gauge fluctuations is to introduce a dissipation ~T/χ, where χ is the diamagnetic susceptibility. The competition between the two energy scales, ms and T/χ, is the root in our approach of many phenomena peculiar to in-plane transport properties of the "pseudogap phase". Furthermore the gauge interaction induces binding of spinon and holon into an "electron" resonance. This binding introduces another energy scale, the recombination rate, which dominates the out-of-plane resistivity, yielding an insulating behavior. A good agreement is found between the experimental data and theoretically derived doping and temperature dependence of resistivity, both in-plane and out-of-plane, and spin relaxation.
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