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arXiv:cond-mat/0110356 · Physical Review B

t−J model for a bilayer: Coexisting superconductivity and planar-flux phases

Hongbo Zhao, Jan R. Engelbrecht

Published Feb 15, 2005• 13 citations
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Abstract

We study the bilayer generalization of the $t\text{\ensuremath{-}}J$ model with both hopping and exchange coupling between the two layers. Within the enlarged mean-field parameter space, we find dimerized, $s+id$, flux ladder and planar flux phases. Of particular interest is the planar flux phase that persists farther away from half-filling, and coexists with, and even stabilizes, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-superconductivity. The orbital currents in the phase generate staggered moments that are rotated away from the $c$-axis.

DOI
10.1103/physrevb.71.054508

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We study the bilayer generalization of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model with both hopping and exchange coupling between the two layers. Within the enlarged mean-field parameter space, we find dimerized, s+ids+ids+id, flux ladder and planar flux phases. Of particular interest is the planar flux phase that persists farther away from half-filling, and coexists with, and even stabilizes, dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-superconductivity. The orbital currents in the phase generate staggered moments that are rotated away from the ccc-axis.
We study the stability of the staggered-flux phase in the t-J model away from half-filling using a systematic large-N slave-boson approach. Found below a critical doping concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$=a(J/t)2{)}^{2})2, is a flux-density-wave instability with an incommensurability wave number \ensuremath{\sim}${\mathrm{\ensuremath{\delta}}}^{3/4}$. The instability towards a modulated-flux state is due to low-lying phase fluctuations of the valence bonds. When the doping parameter exceeds ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$, we find a fully gapped d-wave superconducting state due to residual quasiparticle interactions.
We study by the Gutzwiller approximation the melting of the valence-bond crystal phase of a bilayer Hubbard model at sufficiently large interlayer hopping. We find that a superconducting domain, with order parameter ${d}_{{z}^{2}\ensuremath{-}{r}^{2}}$, zzz being the interlayer direction and rrr the intralayer one, is stabilized variationally close to the half-filled nonmagnetic Mott insulator. Superconductivity exists at half filling just at the border of the Mott transition and extends away from half filling into a whole region till a critical doping, beyond which it gives way to a normal-metal phase. This result suggests that superconductivity should be unavoidably met by liquefying a valence-bond crystal, at least when each layer is an infinite-coordination lattice and the Gutzwiller approximation becomes exact. Remarkably, this same behavior is well established in the other extreme of two-leg Hubbard ladders, showing it might be of quite general validity.
Coupling two strongly correlated layers opens a distinct route to repulsion-driven superconductivity. Yet the same interlayer coupling makes the optimization of superconductivity highly nontrivial. Using the dynamical vertex approximation, we determine the superconducting landscape in the enlarged parameter space spanned by filling and interlayer hopping. We identify an optimal regime at intermediate interlayer hopping and moderate doping away from half filling, where the system exhibits high superconducting transition temperatures (TcT_{\rm c}Tc​) with an interband s±s_{\pm}s±​-wave gap structure. Toward half filling, however, strong self-energy effects can suppress the superconducting tendency by reducing the low-energy spectral weight. We further show that a Fermi-surface distortion induced by longer-range hoppings can weaken this suppression and enhance TcT_{\rm c}Tc​. Our results establish how filling, interlayer hopping, and Fermi-surface geometry jointly optimize the superconducting regime in the strongly correlated bilayer Hubbard model.
In order to study the time-reversal symmetry (T{\cal T}T) breaking near a (110) surface of a high-TCT_CTC​ cuprate YBCO, we consider the flux phase in a bilayer t−Jt-Jt−J model. Although the stable solution in the bulk is the dx2−y−2d_{x^2-y-2}dx2−y−2​-wave superconducting (SC) state, free energy of the flux phase is close to it, and thus the flux phase may occur when the SC order is disturbed by inhomogeneity, e.g., surface or impurity. It is found that, depending on the doping rate, the flux phase in which spontaneous magnetic fields in two layers have opposite signs may be stabilized. This may lead to a surface state with local T{\cal T}T violation but without local magnetic field.
We study the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model of a doped Mott insulator in connection to high-Tc{T}_{c}Tc​ superconductors. The nearest neighbor Coulomb interaction (V)(V)(V) is treated quantum mechanically on equal footing as the antiferromagnetic exchange interaction (J)(J)(J). Motivated by the SU(2)SU(2)SU(2) symmetry at half-filling, we construct a large-NNN theory which allows a systematic study of the interplay between staggered flux order and superconductivity upon doping. We solve the model in the large-NNN limit and obtain the ground state properties and the phase diagram as a function of doping. We discuss the competition and the coexistence of the staggered flux and the ddd-wave superconductivity in the underdoped regime and the disappearance of superconductivity in the overdoped regime.