My interest lies in basic problems and phenomena in statistical mechanics, superconductivity and superfluidity. Below are some of the recent achievements.

Superconductivity | Superfluidity | Nonequilibrium statistical mechanics

  • Non-empirical calculation of the upper critical field Hc2 in type-II superconductors
    [ T. Kita and M. Arai: Phys. Rev. B 70 (2004) 224522;
    M. Arai and T. Kita: J. Phys. Soc. Jpn. 73 (2004) 2924]

    Superconductivity, discovered by Kamerlingh Onnes in 1911, is a phenomenon where electrical resistivity of certain metals and compounds drops to zero below some critical temperature Tc. Electrons are fermions where the Pauli exclusion principle prohibits any condensation into a single one-particle state. Thus, it is not surprising that the phenomenon had rejected many attempts of outstanding theorists before 1957, when Bardeen, Cooper, and Schrieffer (BCS) finally presented a theory that explains major experimental results.

    An essence of the BCS theory is that, in the presence of some attractive force between them, fermions at low temperatures fall into a single two-particle bound state with a coherent phase. The absence of the resistivity can be realized as a coherent motion of the collective bound state. A major difference from the Bose-Einstein condensation of Bose systems lies in the fact that the formation of bound pairs and superconductivity (superfluidity) occur simultaneously.

    Superconductors can be classified into two groups according to their response to the static magnetic field H. Type-I superconductors expel the field completely due to the Meissner effect. Type-II superconductors, on the other hand, can sustain finite magnetic field in the bulk region in the form of the quantized flux-line lattice for Hc1 < H < Hc2. The two characteristic fields Hc1 and Hc2, called the lower and upper critical fields, respectively, are among the most basic quantities of type-II superconductors.

    Despite its importance, however, Hc2 was difficult to describe quantitatively. As first noticed by Hohenberg and Werthamer [Phys. Rev. 153 493 (1967)], detailed Fermi-surface structures play an essential role for Hc2. However, most of theoretical investigations on Hc2 had been carried out by adopting some model Fermi surfaces such as the sphere, and agreements with experiments had been poor.

    With these observations, we obtained a new Hc2 equation which can be solved efficiently by using Fermi surfaces from modern electronic structure calculations based on the density functional theory. Using it, we then carried out detailed calculations of Hc2 for clean Nb, NbSe2, and MgB2. The results excellently reproduce both the directional and temperature dependences observed experimentally, including the marked upward curvature of NbSe2 near Tc. This work was performed in collaboration with Masao ARAI at National Institute for Materials Science (NIMS).

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