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Physical review. B./Physical review. B

Emergence of dxy -wave superconductivity in a doped two-leg diagonal ladder

Jie Hou, Ting-Kuo Lee, Jie Lou, Yan Chen

Published Mar 12, 2019• 6 citations
Publisher

Abstract

We propose a doped two-leg spin-$1/2$ diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet ${d}_{xy}$-wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a ${d}_{xy}$-wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration $\ensuremath{\delta}$. Our work provides a physical understanding of the origin of ${d}_{xy}$ pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.

DOI
10.1103/physrevb.99.094510

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We propose a doped two-leg spin-1/21/21/2 diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet dxy{d}_{xy}dxy​-wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a dxy{d}_{xy}dxy​-wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration \ensuremathδ\ensuremath{\delta}\ensuremathδ. Our work provides a physical understanding of the origin of dxy{d}_{xy}dxy​ pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.
Abstract We construct a four-leg spin-1/2 t–J type model to simulate a doped two-leg spin-1 antiferromagnetic Heisenberg ladder. Employing renormalized mean-field theory with simple Gutzwiller factors, we obtain three degenerate superconducting states with different pairing symmetry. Through improving the Gutzwiller factors, we find that the state C with inter-layer modified d y 2 − z 2 -wave pairing has the lowest energy in a large doping range. Besides, we use the density matrix renormalization group method to solve the model. The negative binding energy reveals the pairing tendency, and the pair–pair correlation functions exhibit a slowly decaying behavior on certain types of bonds. From the pair correlations, we confirm the inter-layer modified d y 2 − z 2 -wave superconducting state as the ground state of the model.
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.
Abstract Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg ( t – J – K ) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K}\lesssim 0.65Kt​≲0.65 t K ≲ 0.65 , consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase.
We report the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung-singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t\text{\ensuremath{-}}J$ model, and are further coupled to a spin-1/21/21/2 Heisenberg model through the Kondo coupling JK{J}_{K}JK​. When the density of electrons xxx is one, the Mott insulator is in a Haldane phase or in a rung-singlet phase depending on whether JK{J}_{K}JK​ is negative or positive. Upon doping, a pair-density-wave with $\mathbf{Q}=\ensuremath{\pi}$ can emerge for both signs of JK{J}_{K}JK​. In the ${J}_{K}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ limit, the model reduces to the recently proposed type II $t\ensuremath{-}J$ model. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1S=1S=1 chains formed by Ni2+{\mathrm{Ni}}^{2+}Ni2+ in a solid-state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg. Long-range order of the PDW can be achieved in quasi-one-dimensional system with finite interwire coupling.
We investigate the hole-doped Kitaev-Heisenberg (ttt-JJJ-KKK) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength ttt and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K} \lesssim 0.65Kt​≲0.65, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t=1t=1t=1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.
We investigate electronic properties of the doped two-leg Hubbard ladder with both the onsite and the nearest-neighbor Coulomb repulsions, by using the the weak-coupling renormalization-group method. It is shown that, for strong nearest-neighbor repulsions, the charge-density-wave state coexisting with the p-density-wave state becomes dominant fluctuation where spins form intrachain singlets. By increasing doping rate, we have also shown that the effects of the nearest-neighbor repulsions are reduced and the system exhibits a quantum phase transition into the d-wave-like (or rung-singlet) superconducting state. We derive the effective fermion theory which describes the critical properties of the transition point with the gapless excitation of magnon. The phase diagram of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.