Multiband Superconductivity

       
 
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 exchange-like integral between different bands, which is a non-phonon effective attractive interaction, and proposed a possibility of small, being less than 0.5, or vanishing of the isotope effect of the critical temperature Tc using the two-band 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 Ginzburg-Landau model was extended to include two conduction bands [6-9]. 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 two-band model. A simple generalization to a three-band model was investigated much later than Kondo's work. It was shown independently that the phase difference other than 0 or π is possible [10-12]. It was indicated that the intermediate value of the phase difference φ leads to time reversal symmetry breaking, which is a new state in three-band superconductors [13-22]. There have been many works for a pairing state with time reversal symmetry breaking with relation to iron-based 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)φ2+⋅⋅. In the presence of large fluctuation of φ we are not allowed to use this approximation. In this situation we must employ a sine-Gordon 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 multi-gap superconductivity started since the discovery of MgB2, and especially iron-based superconductors. A new kind of superconductivity, called the type 1.5, was proposed for MgB2 where it seems that there is an attractive inter-vortex 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 three-band model is now considered as a model for iron-based 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).

 
 
 
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