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Journal of Physics Conference Series

Impurity effects on dx2−y2 -wave superconducting state in strongly correlated Hubbard model

Ryo Sato, Hisatoshi Yokoyama

Published Sep 1, 2019• 0 citations
Publisher

Abstract

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 $V={V}_{U}^{(\pm )}\sim \pm U$?> V = V U ( ± ) ∼ ± U . The phase realized for <?CDATA $V\lt {V}_{U}^{(-)}$?> V < V U ( − ) is robust d-SC and the charge carriers are holes, whereas for <?CDATA $V\gt {V}_{U}^{(+)}$?> 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.

DOI
10.1088/1742-6596/1293/1/012029

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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 $V={V}_{U}^{(\pm )}\sim \pm U$?> V = V U ( ± ) ∼ ± U . The phase realized for <?CDATA $V\lt {V}_{U}^{(-)}$?> V < V U ( − ) is robust d-SC and the charge carriers are holes, whereas for <?CDATA $V\gt {V}_{U}^{(+)}$?> 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.
Abstract In view of cuprate superconductors, effects of point-type impurity potential (V) on half-filled antiferromagnetic and paramagnetic states are studied for a strongly correlated square-lattice Hubbard model (U/t = 12) with a diagonal transfer (t′), using a variational Monte Carlo method. In the trial states, we introduce a Rice-Brinkman-type one-body projector for V, which enables us to treat the whole range of V (− ∞ < V/t < ∞) with small statistical errors. Filling-control-type Mott (insulator-to-metal) transitions are found to occur at <?CDATA V=VU(±)V=V_{U}^{\left( \pm \right)}V=VU(±)​?> V = V U ( ± ) (∼ ±U). In the metallic states <?CDATA (∣V∣>∣VU(±)∣)\left( \left| V \right|>\left| V_{U}^{\left( \pm \right)} \right| \right)(∣V∣>​VU(±)​​)?> ( | V | > | V U ( ± ) | ) , charge carriers are holes (electrons) in the case of attractive (repulsive) potential. The mechanism of the transitions is intuitively understood.
In view of cuprate superconductors, effects of point-type repulsive impurity potential ( V ) on partially filled antiferromagnetic (AF) states are studied for a strongly correlated square-lattice Hubbard model ( U/t = 12) with a diagonal transfer ( t ' = −0.3 t ), using a variational Monte Carlo method. To simplify interpretation, here we focus on the case of δ imp = δ, where δ imp and δ are densities of impurity sites and doped holes, respectively, with δ = 0.04 − 0.20. As a result, a filling-control-type Mott transition occurs at V = V M ( ∼ 2 t ) irrespective of δ ; a partially filled AF state becomes Mott insulating for V > V M . Such impurity-induced Mott transitions extensively appear beyond the above parameter settings.
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.
Abstract In connection with recent tera-Hertz photoexcitation experiments in which strongly correlated materials are changed from Mott-insulating to metallic, we statically study the properties of excited states beyond the Mott gap in the <?CDATA dx2−y2{d}_{{x}^{2}-{y}^{2}}dx2−y2​?> d x 2 − y 2 -wave superconducting (d-SC) branch at half filling, by applying a variational Monte Carlo method to a two-dimensional Hubbard model. It is found that the first-order Mott transition previously found at U = U c for the lowest-energy state vanishes for the excited states. As a result, an insulator-to-d-SC transition occurs as the strength of excitation (corresponding to light intensity) is increased for U/t (> U c /t) fixed. As a mechanism, this conduction is led by newly created free carriers (unbound doublons and holons) in the excited states.
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.
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.