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Physics Procedia

Strongly correlated nature of d-wave superconductivity in cuprates

H. Yokoyama, Shun Tamura, T. Miyagawa, Kenji Kobayashi, Masao Ogata

Published Jan 1, 2012• 1 citation
Publisher

Abstract

With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.

DOI
10.1016/j.phpro.2012.03.410

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With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.
With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of UUU for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.
Mechanisms of Mott transitions and d x 2 Ày 2 -wave superconductivity (SC) are studied in the half-filledband Hubbard model on square lattices with a diagonal hopping term (t 0 ), using an optimization (or correlated) variational Monte Carlo method.In the trial wave functions, a doublon-holon binding effect is introduced in addition to the onsite Gutzwiller projection.We mainly treat a d-wave singlet state and a projected Fermi sea.In both wave functions, first-order Mott transitions without direct relevance to magnetic orders occur at U ¼ U c , which is approximately the bandwidth, for arbitrary t 0 =t.These transitions originate in the binding or unbinding of a doublon to a holon.d-wave SC appears in a narrow range immediately below U c .The robust d-wave superconducting correlation is necessarily accompanied by enhanced antiferromagnetic correlation; the strength of SC decreases, as t 0 =t increases.
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.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
Abstract With cuprate superconductors in mind, we study the effects of point-type impurity potential (V) on a d x 2−y 2 -wave superconducting (d-SC) state in a strongly correlated squarelattice Hubbard model (U/t = 12) with a diagonal transfer (t′), using a variational Monte Carlo method. At half filling, insulator-to-conductor (filling-control-type Mott) transitions occur at <?CDATA V=VU(±)∼±UV={V}_{U}^{(\pm )}\sim \pm UV=VU(±)​∼±U?> V = V U ( ± ) ∼ ± U . The phase realized for <?CDATA V<VU(−)V\lt {V}_{U}^{(-)}V<VU(−)​?> V < V U ( − ) is robust d-SC and the charge carriers are holes, whereas for <?CDATA V>VU(+)V\gt {V}_{U}^{(+)}V>VU(+)​?> V > V U ( + ) a metallic (or weak d-SC) state appears with charge carriers of electrons. For a partially-filled case where the impurity density is equal to the doping rate, a d-SC-to-insulator transition arises at V ≡ V M ∼ 4t. In the weak-|V| phases, the impurity effects in the electron distribution are smeared out by the screening effect, whereas in the strong-|V| phases, the electron distribution directly depend on the impurity configurations.
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.