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Physics Procedia

Superconductivity and Phase Separation in Extended Hubbard Model

Kenji Kobayashi, H. Yokoyama

Published Jan 1, 2014• 6 citations
Publisher

Abstract

Having cuprate superconductors in mind, we study the effect of intersite repulsion on antiferromagnetism (AF) and superconductivity (SC) in an extended Hubbard model on a square lattice with a diagonal transfer t′, using a variational Monte Carlo method. In the trial wave function, essential factors for Mott physics and band renormalization are included. It is found by introducing small intersite repulsion that the SC dome shrinks but AF is almost unchanged for U/t=10 (likely for cuprates). Meanwhile, instable range of doping rate (δ) toward phase separation becomes narrower. This instable range of δ almost coincides with the range of a finite AF gap, especially in good coincidence for t′/t=0.

DOI
10.1016/j.phpro.2014.09.006

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Having cuprate superconductors in mind, we study the effect of intersite repulsion on antiferromagnetism (AF) and superconductivity (SC) in an extended Hubbard model on a square lattice with a diagonal transfer t′, using a variational Monte Carlo method. In the trial wave function, essential factors for Mott physics and band renormalization are included. It is found by introducing small intersite repulsion that the SC dome shrinks but AF is almost unchanged for U/t=10 (likely for cuprates). Meanwhile, instable range of doping rate (δ) toward phase separation becomes narrower. This instable range of δ almost coincides with the range of a finite AF gap, especially in good coincidence for t′/t=0.
Withcuprate superconductors in mind, we study the effects of intersite repulsion V and diagonal transfer on antiferromagnetism (AF) and superconductivity (SC) inthe Hubbard model on a squarelattice, using a variational Monte Carlo method. In the trial wave function, essential factors for Mott physics and band renormalization are included. It is foundthat the effect of small V generally suppresses SC, but makesthe range of doping rate unstable toward phase separation narrower.The effect of also extends thearea stable against charge inhomogeneity, and, in particular,removesthe area of a coexistent state of SC and AF.
In view of cuprate superconductors, interplay between antiferromagnetism (AF) and superconductivity (SC) is studied for the square-lattice Hubbard model with a diagonal transfer t , using a variational Monte Carlo method.In the trial wave function, essential factors of Mott physics and band renormalization are introduced.It is found that whether AF and SC become coexistent or competitive is sensitive to the values of model parameters, U/t, t /t, and δ (doping rate).Furthermore, in case AF gap is finite, namely, in pure AF or coexisting cases, the state is unstable against phase separation.
Having cuprate superconductors in mind, we study a band-renormalization effect on a coexisting state of antiferromagnetism (AF) and superconductivity (SC) in a t-J model on a square lattice with a diagonal transfer t ′ and three-site hopping terms, using a variational Monte Carlo method. It is found that this t-J model with t ′/ t = –0.3 exhibits coexistence of AF and SC orders in lightly doped regime and robust SC for a wide range of doping rate δ . This result contrasts with the previous results of a large- U/t Hubbard model, in which the two orders are mutually exclusive and a coexisting state does not appear; the SC state appears only in heavily doped regime (δ≳ 0.2), after the pure AF state vanishes at δ ∼ 0.2.
To study the relationship between antiferromagnetism (AF) and superconductivity (SC) in cuprate superconductors, we have performed a variational Monte Carlo calculation on the two-dimensional Hubbard model with a diagonal transfer t' [1,2]. The following improvements are introduced into the variational function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect owing to the electron correlation up to the fourth-neighbor hoppings, and (3) refined doublon-holon correlation factors. It is found that the AF and SC orders become coexistent or competitive according to the values of model parameters, U/t, t'/t, and δ (doping rate), and the effective band is strongly renormalized for large U/t and low doping rates, so as to recover the nesting condition favorable to AF.
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.
Using a variational Monte Carlo method, the interplay between antiferromagnetism and superconductivity is studied for the two- dimensional Hubbard model with a diagonal transfer t’. It is found with a refined function that the optimized state is sensitive to the values of model parameters, U/t, t’/t, and δ (doping rate), and becomes a coexisting state or a pure superconducting (SC) state. SC properties in the coexisting state also undergo considerable changes around the crossover point Uco(~10t) from a fragile BCS type for U < Uco co to an unconventional one for U>Uco, in which pairs are formed through local exchange or doublon-holon processes, but supercurrent flows separately with the doped holes.