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Physical review. B, Condensed matter

Flux-density wave and superconducting instability of the staggered-flux phase

Ziqiang Wang, Gabriel Kotliar, Xiaofang Wang

Published Nov 1, 1990• 42 citations
Publisher

Abstract

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${)}^{2}$, 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.

DOI
10.1103/physrevb.42.8690

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We study the stability of the Fermi-liquid and staggered flux phases in the t-J model for densities off half-filling using a large-N slave-boson approach. We examine the stability of the Fermi-liquid phase with respect to flux-density-wave (FDW) and bond-density-wave (BDW), or spin-Peierls, fluctuations at arbitrary wave vector as a function of doping \ensuremath{\delta} and the ratio \ensuremath{\delta}t/J. For densities near half-filling the Fermi liquid becomes unstable below a critical tc{\mathit{t}}_{\mathit{c}}tc​ towards an FDW state with an incommensurate wave vector k near (\ensuremath{\pi},\ensuremath{\pi}). The critical ratio \ensuremath{\delta}tc{\mathit{t}}_{\mathit{c}}tc​/J for the Fermi-liquid--FDW transition diverges rapidly as \ensuremath{\delta}\ensuremath{\rightarrow}0. For \ensuremath{\delta}>18%, the FDW instability of the Fermi liquid is preempted by a BDW instability at incommensurate k. We examine the stability of the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 staggered flux phase with respect to coupled FDW and BDW fluctuations and find that, upon lowering t/J at small \ensuremath{\delta}, the staggered flux phase remains stable for \ensuremath{\delta}t/J above a nonzero critical ratio and then develops an instability of primarily BDW character. At nonzero \ensuremath{\delta} and still lower \ensuremath{\delta}t/J, the staggered flux phase also develops an instability with respect to long-wavelength FDW fluctuations; tc{\mathit{t}}_{\mathit{c}}tc​/J for this instability is approximately independent of \ensuremath{\delta}. We study the response function for such fluctuations analytically, showing the nontrivial k dependence induced by the presence of a small density of holes in the staggered phase. It is conjectured that this long-wavelength FDW instability is associated with the existence off half-filling of a commensurate flux phase with lower energy than the staggered flux phase.
The authors have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP+d) of the extended t-J model at various hole densities ( delta ). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. They found that the SFP is stable against the projected Fermi liquid up to delta approximately=20%. For moderately large J, J/t>or=0.4, the SFP+d state may be favoured against the pure d-wave state but only at very low hole density ( delta approximately 20%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.
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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.