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arXiv:cond-mat/9511096 · Physical review. B, Condensed matter

Spin-gap phase of strongly correlated fermions

Pascal Lederer, Elihu Abrahams

Published Apr 15, 1996• 3 citations
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Abstract

We discuss the possible existence of a ``spin-gap'' phase in the low-doping regime of strongly correlated two-dimensional (2D) electrons within the gauge field description of the t-J model. The spin-gap phase was recently shown by \"Ubbens and Lee to be destroyed by gauge field quantum fluctuations for a single-layer 2D system in the absence of disorder and for a full gap. We show that the same conclusion applies both in the dirty limit and for the case of a gapless spinon condensate. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.10680

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We discuss the possible existence of a ``spin-gap'' phase in the low-doping regime of strongly correlated two-dimensional (2D) electrons within the gauge field description of the t-J model. The spin-gap phase was recently shown by "Ubbens and Lee to be destroyed by gauge field quantum fluctuations for a single-layer 2D system in the absence of disorder and for a full gap. We show that the same conclusion applies both in the dirty limit and for the case of a gapless spinon condensate. \textcopyright{} 1996 The American Physical Society.
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.
A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z2_{2}2​ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z2_{2}2​, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
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The spherical limit of strongly commensurate dirty bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions and consequently that the ground state in the effective Anderson localization problem always remains localized. As a result there is only a gapped Mott insulator phase in the theory. Comparisons with other studies and the parallel with disordered fermions in 2D are discussed. We conjecture that while for the physical cases N = 2 (XY) and N = 1 (Ising) the theory should have the ordered phase, it may not for N = 3 (Heisenberg).
We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo N\'eel or spiral magnetic order below a density-dependent transition temperature T∗{T}^{*}T∗. Fluctuations of the spin orientation are described by a nonlinear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are designed for moderate, not for strong, Hubbard interactions. The stiffnesses are strongly doping dependent with discontinuities at half-filling and a pronounced electron-hole asymmetry. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order shares characteristic features with the pseudogap regime in high-Tc{T}_{c}Tc​ cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime exhibits electronic nematicity.