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 H_{c2}
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 T_{c}.
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
H_{c1} < H < H_{c2}.
The two characteristic fields H_{c1} and H_{c2},
called the lower and upper critical fields, respectively,
are among the most basic quantities of type-II superconductors.
Despite its importance, however, H_{c2} 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 H_{c2}.
However, most of theoretical investigations on H_{c2} 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 H_{c2} 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
H_{c2} for clean Nb, NbSe_{2}, and MgB_{2}.
The results excellently reproduce both the directional and temperature dependences
observed experimentally,
including the marked upward curvature of
NbSe_{2} near T_{c}.
This work was performed in collaboration with Masao ARAI
at National Institute for Materials Science (NIMS).
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