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

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 dx2-y2-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