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Journal of Physics Conference Series

Insulator-to-superconductor transition by exciting half-filled d-wave pairing state beyond Mott gap

Hisatoshi Yokoyama, Kenji Kobayashi, Tsutomu Watanabe, Masao Ogata

Published Jul 1, 2020• 1 citation
Publisher

Abstract

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 ${d}_{{x}^{2}-{y}^{2}}$?> 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.

DOI
10.1088/1742-6596/1590/1/012016

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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 ${d}_{{x}^{2}-{y}^{2}}$?> 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.
In connection with recent experiments on excitation in which Mott insulators change to conductors, we study the properties of excited states beyond the Mott gap as quasi-stationary states for a two-dimensional Hubbard (t-t'-U) model at half filling. A variational Monte Carlo method is used with trial wave functions for paramagnetic or normal (PM), superconducting with dx2-y2-wave (d-SC), isotropic s-wave, and extended s-wave symmetries, and antiferromagnetic (AF) states. The excited states are generated by imposing a minimum number of doubly occupied sites (doublons) D_L on the lowest-energy states. For U>W (W: band width), d_L=D_L/Ns (Ns: number of sites) corresponds to the excitation intensity. It is found that the AF state is the most stable among the states we treated for d_L<0.14 and insulating. The PM and d-SC states become conductive over a threshold d_Lc, and the conduction is caused by unbound doublons and holons (empty sites). The PM state arises for d_L>0.14, but the d-SC state is always hidden by the AF state. The s-wave-type superconducting states are not stabilized for any parameter set.
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.
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.
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.
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.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion UUU from a Gossamer superconductor at small UUU. At the critical value U=UcU={U}_{c}U=Uc​, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at U>UcU>{U}_{c}U>Uc​ to a Gossamer SC state at U<UcU<{U}_{c}U<Uc​ at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.