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arXiv:cond-mat/9812187 · Physical review. B, Condensed matter

Competition between stripes and pairing in a t−t′−J model

Steven R. White, Douglas J. Scalapino

Published Jul 1, 1999• 184 citations
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Abstract

As the number of legs $n$ of an $n$-leg, $t\ensuremath{-}J$ ladder increases, density-matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model in which a diagonal, single-particle, next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ is introduced. We find that this can suppress the formation of stripes and, for ${t}^{\ensuremath{'}}$ positive, enhance the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like pairing correlations. The effect of ${t}^{\ensuremath{'}}>0$ is to cause the stripes to evaporate into pairs and for ${t}^{\ensuremath{'}}<0$ to evaporate into quasiparticles. Results for $n=4$ and 6 $n$-leg ladders are discussed.

DOI
10.1103/physrevb.60.r753

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As the number of legs nnn of an nnn-leg, t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J ladder increases, density-matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a t\ensuremath−t\ensuremath′\ensuremath−J{t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}Jt\ensuremath−t\ensuremath′\ensuremath−J model in which a diagonal, single-particle, next-nearest-neighbor hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ is introduced. We find that this can suppress the formation of stripes and, for t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ positive, enhance the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-like pairing correlations. The effect of t\ensuremath′>0{t}^{\ensuremath{'}}>0t\ensuremath′>0 is to cause the stripes to evaporate into pairs and for t\ensuremath′<0{t}^{\ensuremath{'}}<0t\ensuremath′<0 to evaporate into quasiparticles. Results for n=4n=4n=4 and 6 nnn-leg ladders are discussed.
Using density-matrix renormalization-group techniques, we have studied the ground states of the four-leg t-J ladder doped near half-filling. Depending upon J/t and the hole doping x, three characteristic types of ground states are found: (1) a state containing ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ pairs, (2) a striped charge-density wave (CDW) domain-wall state, and (3) a phase-separated regime. The CDW domain walls consist of fluctuating hole pairs and this state has significant ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ pair field correlations.
Results for a doped three-leg ttt-JJJ ladder obtained using the density-matrix renormalization group are reported. At low hole doping, the holes form a dilute gas with a uniform density. The momentum occupation of the odd band shows a sharp decrease at a large value of kF{k}_{F}kF​ similar to the behavior of a lightly doped ttt-JJJ chain, while the even modes appear gapped. The spin-spin correlations decay as a power law consistent with the absence of a spin gap, but the pair-field correlations are negligible. At larger doping we find evidence for a spin gap and as xxx increases further we find three-hole diagonal domain walls. In this regime there are significant pair-field correlations and the internal pair orbital has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like symmetry.
Inspired by the observation of a robust ddd-wave superconducting phase driven by tuning the next-nearest-neighbor (NNN) electron hopping in recent density matrix renormalization group (DMRG) studies of six- and eight-leg $t\text{\ensuremath{-}}J$ model, we systematically study the phase diagram of the two-leg $t\text{\ensuremath{-}}J$ ladder with the NNN couplings (including NNN hopping and spin interaction) in a large region of doping level, by means of the DMRG calculations. Upon doping from half filling, we identify the Luther-Emery liquid (LEL) phase, which can be distinguished as the pairing-dominant and charge density-dominant regime by comparing the Luttinger parameter ${K}_{\ensuremath{\rho}}$. With the growing NNN couplings, pairing correlations are enhanced and correspondingly ${K}_{\ensuremath{\rho}}$ increases, driving the system from the density-dominant to the pairing-dominant regime. In the Tomonaga-Luttinger liquid (TLL) phase in the larger doping region, we identify two TLL regimes with different features of charge density correlation. At the quarter filling (1/21/21/2 doping level), we find that the strong dimer orders of bond energy in the open system actually decay algebraically and thus do not indicate a spontaneous translational symmetry breaking. Our results show that in the LEL phase of the two-leg ladder, the NNN couplings seem to play the similar role as that on the wider $t\text{\ensuremath{-}}J$ cylinder, and studies on this more accessible system can be helpful toward understanding the emergence of the remarkable ddd-wave superconducting phase on the wider system.
The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength U/t,U/t,U/t, and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.
') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.