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

X-ray photoelectron spectroscopy study of Sr and Ba compounds

We report measurements of low-temperature specific heat on the 4 f 2 -based heavy-fermion superconductor PrOs 4 Sb 12 . In magnetic fields above 4.5 T in the normal state, distinct anomalies are found which demonstrate the existence of a field-induced ordered phase (FIOP). The Pr nuclear specific heat indicates an enhancement of the 4 f magnetic moment in the FIOP. Utilizing a Maxwell relation, we conclude that anomalous entropy, which is expected for a single-site quadrupole Kondo model, is not concealed below 0.16 K in zero field. We also discuss two possible interpretations of the Schottky-like anomaly at ∼3 K, i.e., a crystalline-field excitation or a hybridization gap formation.

Thermodynamical Study on the Heavy-Fermion Superconductor PrOs4Sb12: Evidence for Field-Induced Phase Transition

Hole concentration and T c in Bi 2 Sr 2 CaCu 2 O 8+δ

Novel Kondo-like behaviors realized in the Pr-based filled skutterudites are reviewed based on the electronic transport properties, specific heat and de Haas–van Alphen (dHvA) experiments, along wi...

Novel Kondo Behaviors Realized in the Filled Skutterudite Structure

The Madelung energy in the (Y, Ca)(Ba, La) 2 Cu 3 O 6+δ system has been calculated in order to find the distribution of hole carriers among sites. We regard the compoundas a superconductor, when the lowest-energy distribution is such that holes enter sites in CuO 2 sheets, whereas we regard it as a semiconductor, when no holes enter sites in the CuO 2 sheets. Based on this criterion, we find a phase diagram, where the superconducting region is separated from the semi-conducting region by a boundary. A good agreement with the experimental finding by Tokura et al . is obtained, when account is taken of the ordering of exygen vacancies in the basal plane of Fig. 1 in the text. It is found that for some compounds with small δ(∼0.25), holes are spontaneously produced in CuO 2 sheets, so that the compounds may be a superconductor although their nominal hole content is zero.

The Madelung Energy in Copper-Oxide-Based Ceramics

The effective magnetic field at nuclei in rare earth metals has been calculated. The contribution from the orbital angular momentum of 4f- electrons was found to amount to several thousand kilo-oersteds.

Internal Magnetic Field in Rare Earth Metals

The one-dimensional Schrodinger equation with the Kroning-Penny potential plus the electric-field potential eFx has been solved numerically. All the interband effects are included in the exact numerical calculation. Although an infinite crystal was considered, localized wave functions have been obtaind at energies which make a Stark ladder. One Stark ladder is associated with one band. When the probability of the Zener tunneling to the next band is appreciable for given values of parameters, the wave function necessarily penetrates into the region of the next band and is not localized.

Electrons in Infinite One-Dimensional Crystals in a Uniform Electric Field

The double-time Green's function method incorporated with Tyablikov's decoupling is applied to the nearly two-dimensional ferromagnets of layer-structure copper compounds. Besides the strong intralayer ferromagnetic exchange interaction we take account of weak perturbations, i.e., interlayer exchange interaction, intralayer exchange anisotropy, and dipolar interaction. We obtain the leading two in the inverse transition temperature T c -1 , i.e., terms logarithmically singular and constant with respect to the weak perturbation. Spin contraction at zero temperature is very small. Outside the very vicinity of zero temperature the equation for spontaneous magnetization σ as a function of k B T /2 J is reduced to a much simpler one containing only one parameter k B T c c a l c /2 J . Comparison of the calculated T c and temperature dependence of σ with experimental deta seems to show the soundness of applying the RPA theory to these systems. The contributions of dipolar interaction are examined.

Phase Transition of Nearly Two-Dimensional Heisenberg Ferromagnets with Weak Perturbations

Based on the s-d interaction model for dilute magnetic alloys, we have calculated the resistivity as a function of temperature in the presence of an external magnetic field to the second Born approximation. The logarithmic singularity of resistivity is suppressed by the external magnetic field. For 2µ H ≫ k B T the ln T term is replaced by ln 2µ H . Depending upon the values of parameters, the magnetoresistance is found to be either positive or negative, and the resistivity-versus-temperature curve may have either maximum or minimum, or both. The R - T curves are plotted for a wide variety of values of the exchange integrals, the spin-independent potentials and the external magnetic fields. It is also shown that the curves are classified into five patterns. The physical meaning of the obtained results is discussed. It is suggested that the negative and positive magnetoresistances observed in impurity conduction in semiconductors are explained from our model.

Jun Kondo

Papers

The Madelung Energy in Copper-Oxide-Based Ceramics

Internal Magnetic Field in Rare Earth Metals

Electrons in Infinite One-Dimensional Crystals in a Uniform Electric Field

Phase Transition of Nearly Two-Dimensional Heisenberg Ferromagnets with Weak Perturbations

Resistivity of Dilute Magnetic Alloys in the Presence of External Magnetic Fields