A theoretical review is given on high temperature superconductivity in copper oxides (cuprates) by focusing on the hole doping cases based on the view that it is realized in carrier doped Mott insulators, as noted by Anderson in the initial stage. From the detailed knowledge of electronic states deduced from experiments that showed the undoped parent case is Mott insulators (charge transfer type insulators, to be precise) and that the hole doping is mainly on oxygen sites, the t?J model, as derived by Zhang and Rice, is shown to be a canonical model for hole doped cuprates and values of various parameters of the model have been assessed. Results of many different numerical methods so far obtained for this t?J model, especially the variational Monte Carlo method, have clearly indicated the stability of the -wave superconductivity at absolute zero for the parameter region of actual experimental interest and the particular doping dependences of the condensation energy of superconductivity reflecting particular features of doped Mott insulators. For finite temperatures, on the other hand, the field theoretical slave-boson approximation based on the spin (spinons) and charge (holons) separations and the gauge fields as a glue combining them predicts qualitatively particular features of the existence of characteristic crossover temperatures of the spin singlet of the resonating valence bond (RVB) state, TRVB and the onset of Bose condensation of holons, TB, triggering coherent motion of electrons as convoluted particles of spinons and holons. The considerations based on the gauge field indicate that the onset temperature of superconductivity, Tc, is the lower one of these two, i.e. either TB (overdoped cases) or TRVB (underdoped cases), respectively. These characteristic features of the 'phase diagram' at finite temperatures are in overall agreement with various experimental observations, especially with the existence of spin-gap or pseudo-gap phases. In more detailed examinations of the underdoped region, the antiferromagnetic long-range order and superconductivity show a very intricate relationship at low temperatures depending on the system; they coexist as clarified in the inner layer of Hg-1245 but spin glass states intervene between them in La2?xSrxCuO4 (LSCO). It is argued that these differences can be attributed to the different degrees of disorder. Actually, theories based on the t?J model have also predicted the coexistence of antiferromagnetism and superconductivity in the ground state of clean systems. On the other hand, interesting experimental findings of large Nernst effect and 'Fermi arc' in LSCO and impurity effects in YBCO have prompted the necessity of theoretical investigations of electronic states of lightly doped Mott insulators in the presence of strong disorder.

https://iopscience.iop.org/article/10.1088/0034-4885/71/3/036501/pdf

The t–J model for the oxide high-Tc superconductors

Two-dimensional t - J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J / t - n plane. Near the half filling where the high temperature superconductivity is expected, the d x 2 - y 2 -wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s -type wave becomes a quantitatively good state for large J / t although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case ( J / t =2).

Phase Diagram and Pairing Symmetry of the Two-Dimensional t-J Model by a Variation Theory.

An outline is given of the model for some high-temperature superconductors which assumes that the carriers are holes in the (hybridized) oxygen 2p band and form ‘spin polarons’ with the moments on the copper atoms. A comparison is made with observations of spin polarons in Gd3-x v x S4 and with the properties of La1-x Sr x VO3 in relation to those of La2-x Sr x CuO4. It is assumed, following several authors, that in the superconductors the polarons form bipolarons, which are bosons, and a comparison is made with some other treatments of this hypothesis. It is proposed that in many such superconductors the boson, essentially a pair of these holes, moves in an impurity band, and that normally all the polarons (fermions) form bipolarons; the fermions repel each other on the same site (positive Hubbard U) but attract when on adjacent sites; the critical temperature T c is then that at which the Bose gas becomes non-degenerate. In such materials a non-degenerate gas of bosons would carry the current a...

The spin-polaron theory of high-Tc superconductivity

Aspects of electron correlations in the cuprate superconductors

We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates, which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in the picosecond range, can be explained even quantitatively with the multimagnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the $s$-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor, which can be traced back to strong correlations and consequently large exciton-magnon coupling.

Ultrafast charge recombination in a photoexcited Mott-Hubbard insulator.

Several effective models, as derived from a general two-band Hubbard model for CuO2 layers in oxide superconductors are studied. In particular we compare the Hubbard model with the hole-spin models (unsymmetrized and symmetrized) and a generalized effectice single-band (t-J) model.1 Our exact diagonalization results for a finite CuO2 chain of 4 cells show that spectral properties of a single mobile quasiparticle in a general Hubbard model can be well reproduced by reduced effective models. This remains valid even in the mixed valence regime, where the straightforward derivation of the hole-spin model is not possible due to the breakdown of the perturbation expression using hopping parameter in the Hubbard model as a small parameter.

Comparison of effective models for CuO2 layers in oxide superconductors.

The motion of a single fermion coupled to the planar antiferromagnetic spin background is examined within the Kondo-lattice model, including the local spin-fermion coupling and the spin-dependent hopping. The perturbation theory using lowest-order magnon processes and the self-consistent calculation of the quasiparticle spectra, yields several features obtained by an analogous treatment of the t-J model by Kane et al. Qualitative differences are, however, found in low excited states with the self-energy showing a nonanalytical behavior \ensuremath{\Sigma}''(\ensuremath{\omega}g0)\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{\alpha}}}$, \ensuremath{\alpha}\ensuremath{\le}1, due to the local Kondo-like coupling. Within the perturbation theory we get \ensuremath{\alpha}=1, while the self-consistent treatment yields \ensuremath{\alpha}=1/2. The modified self-consistent equations lead also to better results for the quasiparticle mass.

Dynamics of a fermion in the Kondo-lattice model for strongly correlated systems.

In a t-J model on a chain, an additional next-nearest-neighbor hopping term destroys the complete spin-charge separation at J/t\ensuremath{\ll}1 and induces the formation of stable spin-polarized Sg0 states. The properties of a single ferromagnetic polaron are investigated by the exact diagonalization of small systems and by the approximative treatment of an effective model, describing a spinless fermion coupled to the spin background. Both methods give consistent results on the critical ${\mathit{J}}_{\mathit{c}}$ for the polaron formation on the increase of the spin S and the polaron size with decreasing J. A very large enhancement of the polaron mass with increasing S is observed. Systems with a finite concentration of holes are also studied within the same framework. Analytical considerations indicate on the bound many-hole states and consequently on phase-separated regions in the phase diagram.

A. Ramak

Papers

Comparison of effective models for CuO2 layers in oxide superconductors.

Dynamics of a fermion in the Kondo-lattice model for strongly correlated systems.

Ferromagnetic polarons in a one-dimensional t-J model with next-nearest-neighbor hopping