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Beyond Migdal's theorem, the theoretical study on the strong coupling superconductivity under the quantizing magnetic field in the system of isotropic 3-dimensional electron gas is reported. The vertex correction is taken into account to the formulation, previously developed by the present authors in the expression of Dyson-Eliashberg theory, which appears in J. Phys. Soc. Jpn. 63 (1994) 1465. Under the condition that Ward-Takahashi identity is exactly satisfied, the set of equations including the vertex correction up to infinite order is proposed in the context of the theoretical investigation by Nambu in Phys. Rev. 117 (1960) 648. Numerical results for demanded strength of the field H for the given concentration of the electron density N are presented in relation with the investigation of the problem of how the Nambu-Goldstone mode appears. The possibility of new superconducting phase under the ultra-high field is also discussed.

To investigate a field-induced level crossing of the ground-state doublet in PrTr2Zn20 (Tr = Rh, Ir), we performed ultrasonic measurements in pulsed magnetic fields applied along the [110] and [001] directions and analyzed the results in the framework of the strain-susceptibility approach. Above 40 T for H || [110], we observed an elastic softening of the transverse modulus (C11 − C12)/2 corresponding to the ground-state doublet. In both compounds the softening is followed by a minimum at about 47 T at low temperatures. We predict the presence of a new field-induced phase boundary in PrTr2Zn20 at this field with two possible cases. The magnetic field of the minimum cannot be explained by only the quadrupole interaction.

The effects of uniaxial strain and hydrostatic pressure on Y0.98Ca0.02Ba2Cu4O8 [called Y0.98(Ca0.02)-124] are investigated via AC magnetic measurements under stress corresponding to a pressure of (at most) 20 GPa. Hydrostatic contraction results in the largest enhancement of the superconducting transition temperature (Tc), whose maximum is 99 K, which is slightly lower than the maximum Tc achieved in YBa2Cu4O8 (called Y-124). The Meissner signal disappears at a hydrostatic pressure of approximately 15 GPa. This pressure region representing the Meissner signal is reduced by the out-of-plane contraction (along the c-axis), whereas it is increased by the in-plane contraction (along the c-plane). In the case of Y-124, both uniaxial contractions result in the disappearance of the Meissner signal at approximately 10 GPa prior to reaching the overdoped region. However, by doping Ca into the Y-site, we could investigate uniaxial strain effects characteristic of the so-called 124 structure without causing the stre...

The formulation of strong coupling theory for superconductivity in the ultra-high magnetic field is made in the expression of Dyson's equation for the case where electrons are confined only in a few Landau levels. The set of self-consistent equations is proposed in the procedure of Eliashberg theory. Further, results of numerical calculation for the 2-dimensional system performed by the use of Frolich-type potential are discussed. In the dependence of the critical temperature T c on the field, the convex-structures appear whose peaks correspond to the half-filling in Landau levels. For the ultra-high field where electrons occupy only the ground Landau level, T c increases with increasing the field. However, it has the tendency to be suppressed by the effect of the retardation for the interaction. On the contrary, the renormalization coefficient increases more abruptly. These behaviors are characteristic features shown clearly in the present calculation.

YbPtGe with the orthorhombic e-TiNiSi-type structure is reported as a heavy-fermion ferromagnet with the magnetic transition temperature TC = 5.4 K. Recent research suggested that its magnetic anisotropy can be ascribed to the crystal electric field (CEF) effect. In order to clarify the CEF effect and to investigate the magnetic phase transition in this compound, ultrasonic measurements of YbPtGe and related theoretical calculation have been performed. The transverse elastic moduli C44, C55, and C66 exhibit a softening characteristic with a peak around 150 K while the longitudinal moduli C11, C22, and C33 show a continuous hardening in the temperature (T) range above TC. Theoretical strain-susceptibility fitting indicates that the softening results from a quadrupole interaction between the ground and excited Kramers doublets of CEF. For the elastic moduli below TC, abrupt elastic hardening is observed in C22, C33, and C55 while C11, C44, and C66 exhibit a step-like softening. The difference between the so...

To investigate the crystal electric field effect and antiferromagnetic transitions at 2.4 and 1.4 K, we carried out ultrasonic measurements on the Yb-based heavy-fermion antiferromagnet YbIrGe. We found characteristic softening of the elastic moduli originating from a quadrupole interaction. By theoretical analyses of the transverse elastic moduli, the magnetic susceptibility, and the Schottky specific heat between 10 and 300 K, we determined the crystal electric field: the ground doublet and an excited doublet separated by 138 K. The moduli exhibit elastic hardening below both 2.4 and 1.4 K, suggesting a strong coupling between a strain and magnetic order parameters. We estimated the strain dependence of the transition temperature at 2.4 K along the a- and c-axes from the Ehrenfest relation for the first time.