論文

We theoretically investigate strong-coupling properties of an odd-frequency Fermi superfluid. This pairing state has the unique property that Cooper pairs are formed between fermions, not at the same time, but at different times. To see whether or not such unequal-time pairs still exhibit bosonic behavior, we examine the space-time structure of the odd-frequency Cooper-pair wave function at T=0, by employing the combined path-integral formalism with the BCS-Eagles-Leggett-type superfluid theory. In the strong-coupling regime, the odd-frequency pair wave function still has different space-time structure from that in the ordinary even-frequency s-wave superfluid state; their magnitudes are found to become close to each other, except for the equal-time pairing component. In this regime, we also evaluate the superfluid phase transition temperature Tc within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink. The calculated Tc in the strong-coupling regime of the odd-frequency system is found to be well described by the Bose-Einstein condensation of tightly bound Bose molecules. Our results indicate that, in spite of vanishing equal-time pairing, odd-frequency Cooper pairs still behave like bosons in the strong-coupling regime, as in the even-frequency s-wave superfluid case.

We theoretically investigate a voltage-biased normal metal-superconductor-normal metal (NSN) junction. Using the nonequilibrium Green's function technique, we derive a quantum kinetic equation to determine the superconducting order parameter self-consistently. The derived equation is an integral-differential equation with memory effects. We solve this equation by converting it into a system of ordinary differential equations with the use of a pole expansion of the Fermi-Dirac function. When the applied voltage exceeds the critical value, the superconductor switches to the normal state. We find that when the voltage is decreased from the normal phase, the system relaxes to a Larkin-Ovchinnikov-type (LO) inhomogeneous superconducting state, even in the absence of a magnetic Zeeman field. We point out that the emergence of the LO-type state can be attributed to the nonequilibrium energy distribution of electrons due to the bias voltage. We also point out that the system exhibits bistability, which leads to hysteresis in the voltage-current characteristic of the NSN junction.

We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to the spontaneous surface current is also examined in detail. Our result excludes the possibility of the recently proposed d-wave superconductivity having the surface flow and finite total current.

Effects of nonmagnetic impurities with unitarity scattering in two-dimensional d-wave superconductors are investigated by the numerical diagonalization of finite-size systems of up to 35×35 sites. It is shown that a localized state with almost zero excitation energy is formed around an impurity site if it is isolated. However, its localized state is extended in real space along the direction of the node of the d-wave gap, so that the localized states of adjacent impurities easily interfere with each other forming a kind of impurity band, i.e., resonance states around the zero energy. It is also pointed out that there exists a strong association between the resonance density of states due to impurity scattering in the unitarity limit and the so-called zero-bias anomaly of tunneling conductance.

A novel proximity effect, that the d-wave superconductivity induces a different symmetric order parameter in the normal metal side, is investigated for the normal metal (N)-d-wave superconductor (S) junction in the clean limit. The induced superconductivity is obtained self-consistently on the basis of the quasi-classical theory and the condition of this effect to occur is clarified. Our result shows that the deformation of the pair amplitude and the direction of the NS boundary with respect to the phase of the d-wave superconductivity are crucial in this phenomenon. A characteristic structure appearing in the local density of states due to this proximity effect is also examined comparing with the conventional case.

Condition for the mid gap state to exist in inhomogeneous superconductor is investigated. On the basis of the Andreev equations, a general expression of the wavefunction of this bound state is derived. Then, the mid gap state is shown to exist only if signs of the pair potential is different, which an quasiparticle feels in the initial and final states in the scattering process described by the Andreev equations. It is also studied why some inhomogeneous systems have no mid gap state. Our results present a unified picture that the absence of the mid gap states results from their hybridization due to the spatial variation of the order parameter and the presence of the normal reflection.

The tunneling probability for a positive muon in high-purity tantalum is significantly enhanced by the onset of superconductivity. This establishes the predominant influence of low energy infrared couplings to the conduction electrons in the quantum tunneling motion of a charged interstitial atom in metals. © 1997 The American Physical Society.

The plasma mode in the superconducting state is studied within the random phase approximation. It is proved that the plasma oscillation in the limit of zero momentum (g) is not affected by the superconductivity. This statement itself has been obtained so far under some special conditions where energies of the plasma frequency and the superconducting order parameter are much different. In this paper, we clarify that it holds true at all temperatures irrespective of (1) the magnitude of the plasma frequency, (2) the symmetry of the order parameter, and (3) details of the system, e.g., dimensionality and the layered structure. We also show that the plasma sum-rule is satisfied even in the superconducting state, which states that the spectrum of the density-density correlation function in the limit q → 0 is dominated by the plasma mode only Although the phase fluctuation of the order parameter couples with the charge one, the collective phase oscillation, so-called the Carlson-Goldman mode, does not contribute to the spectrum of the density-density correlation function in this limit.

Nuclear magnetic ordering is investigated in scandium crystal by the Monte Carlo simulation. We determine the phase diagram in the ground state with respect to interactions between the nuclear spins. In this phase diagram, we find a ferrimagnetic state with the total magnetization being smaller than the complete ferromagnetism by 1/3: This state changes into the ferromagnetism at a finite external magnetic field, which leads to a threefold jump in the magnetization as was observed by the experiment. Thus, this state is a strong candidate for the nuclear magnetic ordering in scandium below T ≲ 2[μK].

A spontaneous surface current state is investigated in unconventional superconductivity with broken time-reversal-symmetry. It is shown that a BCS supercurrent lowers the energy of the system in this state. The lowest state has zero total current; it satisfies the Bloch theorem which states absence of the total current in any stable state with no external field. We also show that the magnitude and the direction of the spontaneous current are strongly affected by the detail of the Fermi surface. We explain this effect in connection with a low-energy bound state near the surface originating from the anisotropy of the order parameter.

Effects of superconducting fluctuations on the Fulde-Ferrell (FF) state are discussed in a spatially isotropic three-dimensional superconductor under a magnetic field. For this system, Shimahara recently showed that within the phenomenological Ginzburg-Landau theory, the long-range order of the FF state is suppressed by the phase fluctuation of the superconducting order parameter [H. Shimahara: J. Phys. Soc. Jpn. 67 (1998) 1872; Physica B 259-261 (1999) 492]. In this letter, we investigate this instability of the FF state against superconducting fluctuations from the microscopic viewpoint, employing the theory developed by Nozières and Schmitt-Rink in the BCS-BEC crossover field. Besides the absence of the second-order phase transition associated with the FF state, we show that even if the pairing interaction is weak, the shift of the chemical potential from the Fermi energy due to the fluctuations is crucial near the critical magnetic field of the FF state obtained within the mean-field theory.

We investigate nonmagnetic impurity effects in two-band superconductors, focusing on the effects of interband impurity scatterings. Within the Born approximation, it is known that interband scatterings mix order parameters in the two bands. In particular, only one averaged energy gap appears in the excitation spectrum in the dirty limit [G. Gusman: J. Phys. Chem. Solids 28 (1967) 2327]. In this paper, we take into account the interband scattering within the t-matrix approximation beyond the Born approximation in the previous work. We show that, although the interband scattering is responsible for the mixing effect, this effect becomes weak when the interband scattering becomes very strong. In the strong interband scattering limit, a two-gap structure corresponding to two order parameters recovers in the superconducting density of states. We also show that a bound state appears around a nonmagnetic impurity depending on the phase of interband scattering potential.

We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing. © 2002 The American Physical Society.

We discuss the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance is shown to naturally lead to the BCS-BEC crossover, where the character of superfluidity continuously changes from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) type to the Bose-Einstein condensation (BEC) of tightly bound molecules, as one decreases the threshold energy 2ν of the Feshbach resonance. We also discuss effects of a trap, as well as the p-wave BCS-BEC crossover adjusted by a p-wave Feshbach resonance. © World Scientific Publishing Company.