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arXiv:cond-mat/9702218 · Physical Review Letters

Massless Dirac Fermions, Gauge Fields, and Underdoped Cuprates

Don H. Kim, Patrick A. Lee, Xiao-Gang Wen

Published Sep 15, 1997• 59 citations
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Abstract

We study $2+1$ dimensional massless Dirac fermions and bosons coupled to a U(1) gauge field as a model for underdoped cuprates. We find that the uniform susceptibility and the specific heat coefficient are logarithmically enhanced (compared to linear-in- $T$ behavior) due to the fluctuation of a transverse gauge field which is the only massless mode at finite boson density. We analyze existing data, and find good agreement in the spin gap phase. Within our picture, the drop of the susceptibility below the superconducting ${T}_{c}$ arises from the suppression of gauge fluctuations.

DOI
10.1103/physrevlett.79.2109

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We study 2+12+12+1 dimensional massless Dirac fermions and bosons coupled to a U(1) gauge field as a model for underdoped cuprates. We find that the uniform susceptibility and the specific heat coefficient are logarithmically enhanced (compared to linear-in- TTT behavior) due to the fluctuation of a transverse gauge field which is the only massless mode at finite boson density. We analyze existing data, and find good agreement in the spin gap phase. Within our picture, the drop of the susceptibility below the superconducting Tc{T}_{c}Tc​ arises from the suppression of gauge fluctuations.
We propose that the recently observed violation of the Wiedemann-Franz law in the normal state of underdoped cuprates is caused by spin-charge separation and dynamical chiral symmetry breaking in a (2+1)(2+1)(2+1)-dimensional system consisting of massless Dirac fermions, charged bosons, and a gauge field. While the d-wave spinon gap vanishes at the Fermi points, the nodal fermions acquire a finite mass due to strong gauge fluctuations. This mass provides a gap below which no free fermions can be excited. This implies that there is not a residual linear term for the thermal conductivity, in good agreement with experiments. Other physical implications of the chiral symmetry breaking are also discussed.
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The U(1)×SU(2) Chern–Simons gauge theory is applied to study the 2D t–J model describing the normal state of underdoped cuprate superconductors. The U(1) field produces a flux phase for holons converting them into Dirac-like fermions, while the SU(2) field, due to the coupling to holons gives rise to a gap for spinons. An effective low-energy action involving holons, spinons and a self-generated U(1) gauge field is derived. The Fermi surface and electron spectral function obtained are consistent with photoemission experiments. The theory predicts a minimal gap proportional to doping concentration. It also explains anomalous transport properties.
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.
We analyze the phase diagram of single and bi-layer cuprates using the gauge-field description of the t-J model. For T>TBET>T_{\text{BE}}T>TBE​ the in-plane fermion-pairing order parameter Δ∥Δ_{\scriptscriptstyle\parallel}Δ∥​ is eliminated by gauge field fluctuations, leading us to predict the absence of a spin-gap phase in single-layer cuprates. For bi-layer cuprates the inter-layer order parameter Δ⊥Δ_\perpΔ⊥​ is enhanced by spin correlations, and is less affected by gauge fluctuations. We believe that the spin gap in bi-layer materials is due to inter-layer fermion pairing, and that for these underdoped samples the superconducting gap may be nodeless.
We outline the basic ideas involved in a recently proposed [17] derivation of a gauge theory for underdoped cuprates in the “spin gap phase”, performed essentially step by step starting from the t — J model, considered as a model Hamiltonian for the CuO2 layers. The basic tool is the U(1) x SU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a “spingap” not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (±π/2, ±π/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.