多バンド超伝導体






Two years after the BCS theory was proposed, an extension to two overlapping bands was considered by
Moskalenko [1] and Suhl, Matthias and Walker [2]. After these works, Peretti [3], Kondo [4] and Geilikman [5]
reconsidered superconductors with multiple bands. The motivation of Kondo's work is to understand the small isotope
effect observed for some transition metal superconductors.
Kondo investigated the exchangelike integral between different bands, which is a nonphonon effective attractive interaction,
and proposed a possibility of small, being less than 0.5, or vanishing of the isotope effect of the critical temperature T_{c}
using the twoband model.
It was found by early works that the critical temperature is enhanced higher than both of critical temperatures of uncoupled superconductors
due to the interband coupling.
The GinzburgLandau model was extended to include two conduction bands [69].
Kondo, at the same time, introduced different phases assigned to two different gaps with phase difference π.
This indicates that we can take the phase difference φ to be 0 or π for the twoband model.
A simple generalization to a threeband model was investigated much later than Kondo's work. It was shown independently
that the phase difference other than 0 or π is possible [1012].
It was indicated that the intermediate value of the phase difference φ leads to time reversal symmetry breaking, which is a new state in
threeband superconductors [1322].
There have been many works for a pairing state with time reversal symmetry breaking with relation to ironbased
superconductors, and also from the viewpoint of holographic superconductors.
Leggett considered small fluctuation of phase difference, which yields fluctuation in the density of Cooper pairs.
This indicates a possibility of a collective excitation of phase difference mode.
Leggett examined the Josephson term Jcos(φ) perturbatively using cos(φ)=1(1/2)φ^{2}+⋅⋅.
In the presence of large fluctuation of φ we are not allowed to use this approximation.
In this situation we must employ a sineGordon model.
This model has a kink solution with fluctuation from φ = 0 to 2π, which results in a new collective mode.
An intensive study of multigap superconductivity started since the discovery of MgB_{2}, and especially ironbased superconductors.
A new kind of superconductivity, called the type 1.5, was proposed for MgB_{2} where it seems that there is an attractive
intervortex interaction preventing the formation of Abrikosov vortex lattice.
A theoretical prediction was given based on the model with vanishing Josephson coupling.
There is a controversy on this subject.
We expect that the Higgs mode plays a role in this issue because Higgs mode will produce an attractive force between vortices.
A threeband model is now considered as a model for ironbased superconductors and the time reversal symmetry breaking is
investigated intensively.
References:
[1] V. A. Moskalenko: Fiz. Metal and Metallored 8, 2518 (1959).
[2] H.Suhl, B. T. Mattis, L. W. Walker: Phys. Rev. Lett. 3, 552 (1959).
[3] J. Peretti: Phys. Lett. 2, 275 (1962).
[4] J. Kondo: Prog. Theor. Phys. 29, 1 (1963).
[5] B. T. Geilikman, R. O. Zaitsev, V. Z. Kresin: Sov. Phys. Solid State 9, 642 (1967).
[6] T. Yanagisawa, Y. Tanaka, I. Hase, K. Yamaji: J. Phys. Soc. Jpn. 81, 024712 (2012).
[7] D. R. Tilley: Proc. Phys. Soc. 84, 573 (1964).
[8] I. P. Ivanov: Phys.Rev. E79, 021116 (2009).
[9] N. V. Orlova et al.: Phys. Rev. B87, 134510 (2013).
[10] V. Stanev, Z. Tesanovic: Phys. Rev. B81, 134522 (2010).
[11] Y. Tanaka, T. Yanagisawa: J. Phys. Soc. Jpn. 79, 114706 (2010).
[12] Y. Tanaka, T. Yanagisawa: Solid State Commnun. 150, 1980 (2010).
 
