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Journal of the Physical Society of Japan

Pairing of Fermious Coupled with Spin-1/2 Heisenberg System –Exact Diagonalization Study for Mechanism of High-Tc Superconductivity–

Yasuhiro Hatsugai, Masatoshi Imada, Naoto Nagaosa

Published Apr 1, 1989• 33 citations
Publisher

Abstract

A coupled spin-fermion system is investigated as a model of high- T c superconductivity. By the exact diagonalization technique, the binding energy of two fermions and several correlation functions in the ground state are calculated to study possible pairings of holes in orbitals of p π , p σ , d 3 z 2 - r 2 etc. The bound states of fermions are suggested in two regions in the parameter space. In the small transfer region, it is caused by local defects induced in the antiferromagnet at the fermion sites. The larger transfer region is characterized by the relatively extended disturbance of the antiferomagnetic correlation of the substrate spins, where the fermion forms singlet-like cloud around it. The latter is a characteristic feature of the antiferromagnetic fermion-spin coupling. The relevance of the latter region to high- T c superconductivity is discussed. The possibilities of bound states of fermions in Kondo lattices are also investigated.

DOI
10.1143/jpsj.58.1347

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Physical review. B, Condensed matter•Jan 1, 1988•53 citations
A coupled spin-fermion system is investigated as a model of high- T c superconductivity. By the exact diagonalization technique, the binding energy of two fermions and several correlation functions in the ground state are calculated to study possible pairings of holes in orbitals of p π , p σ , d 3 z 2 - r 2 etc. The bound states of fermions are suggested in two regions in the parameter space. In the small transfer region, it is caused by local defects induced in the antiferromagnet at the fermion sites. The larger transfer region is characterized by the relatively extended disturbance of the antiferomagnetic correlation of the substrate spins, where the fermion forms singlet-like cloud around it. The latter is a characteristic feature of the antiferromagnetic fermion-spin coupling. The relevance of the latter region to high- T c superconductivity is discussed. The possibilities of bound states of fermions in Kondo lattices are also investigated.
A coupled spin-fermion model is investigated by the exact diagonalization of finite lattices to discuss magnetic mechanism of superconductivity. An extended cloud of singlet liquid (extended Kondo singlet) is found around the fermion in a strong coupling region characterized by strong Kondo coupling and large transfer. The existence of the bound state of two fermions is found. The relevance of its Cooper pairing to high-Tc superconductivity is discussed. The relation to the weak coupling region and also to the small transfer region in this model is discussed.
The formation of bound states of holes in an antiferromagnetic spin-1/2 background is studied using numerical techniques applied to the t-J Hamiltonian on clusters with up to 26 sites. An analysis of the binding energy as a function of cluster size suggests that a two-hole bound state is formed for couplings larger than a ``critical'' value J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ The symmetry of the bound state is dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2. We also observed that its ``quasiparticle'' weight Z2h{\mathit{Z}}_{2\mathit{h}}Z2h​ (defined in the text), is finite for coupling J/t\ensuremath{\ge}J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$. Thus, in the region J/t\ensuremath{\ge}J/t${\mathrm{\ensuremath{\Vert}}}_{\mathit{c}}$ the bound state of two holes behaves like a quasiparticle with charge Q=2e, spin S=0, and dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in theories of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates is briefly discussed.
The effect of a magnetic (S=1/2) impurity coupled to a two-dimensional system of correlated electrons (described by the t-J model) is studied by exact diagonalizations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding \ensuremath{\sim}0.3J. Several peaks appear in the single-hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s-, and p-wave bound states.
By means of the exact-diagonalization method we have studied the finite-size two-band model with the interband pair-transfer interaction by calculating the superconducting (SC) correlation function P s etc. in the ground state. Occurrence of SC was clearly indicated by the increase of P s . The diagram of the observed SC region was constructed in the plane of the relative position of the second band versus on-site Coulomb energy U . In the low-density limit it proved close to the region where a negative- U situation is realized by the pair-transfer interaction. On the high-density side, the SC region was found to be more extended than the latter in accord with the previous interband-ladder-diagram results. Inclusion of the exchange interaction was found to reduce the SC region in a restricted region where two bands substantially share electrons. The two-band situations in cuprates are argued to be relevant to the high T c through the present mechanism.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio tU\frac{t}{U}Ut​ and the doping fraction xxx. We find three different phases in the (x,tUx,\frac{t}{U}x,Ut​) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.