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arXiv:cond-mat/9810141 · Physical review. B, Condensed matter

Superconductivity and the spin-triplet collective mode in the t−J model close to antiferromagnetic instability

Damian G. Marinaro, Oleg P. Sushkov

Published Dec 1, 1998• 1 citation
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Abstract

To investigate relations between long-range antiferromagnetic (AF) order, superconductivity and two-particle triplet collective excitations we consider a modified two dimensional $t\ensuremath{-}J$ model at doping close to half filling. The model includes additional hopping ${J}^{\ensuremath{''}}$ and nearest sites Coulomb repulsion V. The additional parameters allow us to control closeness of the system to the AF instability. We demonstrate the possibility of coexistence of long-range AF order and $d\ensuremath{-}g$-wave superconductivity. In the phase with long-range AF order we find, analytically, superconducting gaps and spin-wave renormalization. We demonstrate that at approaching the point of the AF instability the spin-triplet collective excitation arises with energy below the superconducting gap.

DOI
10.1103/physrevb.58.14934

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To investigate relations between long-range antiferromagnetic (AF) order, superconductivity and two-particle triplet collective excitations we consider a modified two dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model at doping close to half filling. The model includes additional hopping J\ensuremath′′{J}^{\ensuremath{''}}J\ensuremath′′ and nearest sites Coulomb repulsion V. The additional parameters allow us to control closeness of the system to the AF instability. We demonstrate the possibility of coexistence of long-range AF order and d\ensuremath−gd\ensuremath{-}gd\ensuremath−g-wave superconductivity. In the phase with long-range AF order we find, analytically, superconducting gaps and spin-wave renormalization. We demonstrate that at approaching the point of the AF instability the spin-triplet collective excitation arises with energy below the superconducting gap.
To investigate the non-Fermi liquid behavior we consider the extended two-dimensional t-J model which includes additional hopping t''. In the regime t,J << t'' we were able to solve the model analytically. It has a very rich phase diagram including antiferromagnetic (AF) insulator and AF strange metal with different kinds of pseudospin-singlet superconducting pairings (p,d,g-waves). We also demonstrate a collective triplet excitation with energy below the superconducting gap
The coexistence or exclusivity of dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ (≲ \lesssim ≲ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t (≳ \gtrsim ≳ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.
In this paper we study the ground-state phase diagram of a one-dimensional $t\ensuremath{-}U\ensuremath{-}J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-12\frac{1}{2}21​ XY\mathrm{XY}XY model takes place. In the case of weakly anisotropic antiferromagnetic exchange the system shows a long-range dimerized (Peierls) ordering in the ground state. The complete weak-coupling phase diagram of the model, including effects of the on-site Hubbard interaction, is obtained.
The possibility of coexistence of superconductivity (SC) and antiferromagnetic long-range order (AFLRO) of the two-dimensional extended $t\text{\ensuremath{-}}J$ model in the very underdoped region is studied by the variational Monte Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and ddd-wave SC for the physical parameters, J∕t=0.3J∕t=0.3J∕t=0.3, ${t}^{\ensuremath{'}}∕t=\ensuremath{-}0.3$ and ${t}^{\ensuremath{''}}∕t=0.2$, is located near hole density ${\ensuremath{\delta}}_{c}\ensuremath{\cong}0.06$, and there is no coexistence. The phase transition is first order between these two homogeneous phases at ${\ensuremath{\delta}}_{c}$.
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.
Interplay between antiferromagnetism (AF) and d-wave superconductivity (dSC)(d\mathrm{SC})(dSC) is investigated in the slave-boson scheme of the two-dimensional $t\ensuremath{-}J$ model on the square lattice. So far, it seems that their coexistence is believed to be a general feature. It is, however, reported in this paper that the coexistence is suppressed significantly by ${t}^{\ensuremath{''}},$ the third neighbor hopping. This effect will lead to noticeable material dependence of the possible bulk coexistence of AF and dSC.d\mathrm{SC}.dSC.