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arXiv:1208.1102 · Journal of the Physical Society of Japan

Crossover between BCS Superconductor and Doped Mott Insulator of d -Wave Pairing State in Two-Dimensional Hubbard Model

Hisatoshi Yokoyama, Masao Ogata, Yukio Tanaka, Kenji Kobayashi, Hiroki Tsuchiura

Published Jan 15, 2013• 100 citations
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Abstract

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 $U$ 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.

DOI
10.7566/jpsj.82.014707

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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.
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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.
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We examine the competition and relationship between an antiferromagnetic (AF) Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting (SC) state in two dimensions using semianalytical, i.e., diagrammatic calculations of the t-U-W model. The AF Mott insulator is described by the ground state of the half filled Hubbard model on a square lattice with on-site Coulomb repulsion U and nearest-neighbor single-particle hopping t. To this model, an extra term W is added, which depends upon the square of the single-particle nearest-neighbor hopping. Staying at half band filling and a constant value of U, it was previously shown with quantum Monte Carlo (QMC) simulations that one can generate a quantum transition as a function of the coupling strength W between an AF Mott insulating state and a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\mathrm{SC}$ state. Here we complement these earlier QMC simulations with physically more transparent diagrammatic calculations. We start with a standard Hartree-Fock (HF) calculation to capture the ``high-energy'' physics of the t-U-W model. Then, we derive and solve the Bethe-Salpeter equation, i.e., we account for fluctuation effects within the time-dependent HF or generalized random-phase approximation scheme. Spin and charge susceptibility as well as the effective interaction vertex are calculated and systematically compared with QMC data. Finally, the corresponding BCS gap equation obtained for this effective interaction is solved.