Journal of Low Temperature Physics

, Volume 187, Issue 5–6, pp 545–552 | Cite as

Multiple Phase Transition in Unconventional Superconducting Films



When Andreev bound states are formed at the surfaces of a superconducting film, there may arise, as the ground state of the film, a superconducting state with broken time-reversal symmetry (\(\mathcal {T}\)). In this state, Cooper pairs with a finite center-of-mass momentum \(\mathbf {q}\) are formed without external fields. We focus on the \(\mathcal {T}\)-breaking state in a d-wave superconducting film and investigate the effect of the Fermi surface shape on its stability region in the T\(D^{-1}\) phase diagram (T: temperature, D: film thickness). The phase boundaries separating the normal state, the \(\mathcal {T}\)-breaking superconducting state, and the trivial (\(\mathbf {q} = 0\)) superconducting state are determined for various Fermi surface shapes ranging from cylindrical to square. It is found that the region of the \(\mathcal {T}\)-breaking phase is substantially enlarged when the Fermi surface is square-shaped. This is mainly because the critical thickness \(D_c\) between the normal and \(\mathcal {T}\)-breaking states is significantly reduced when the Fermi surface has a good nesting property.


Superconducting film Time-reversal symmetry Andreev bound states Odd-frequency Cooper pairs 



This work was supported in part by JSPS KAKENHI Grant Number 15K05172.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Graduate School of Integrated Arts and SciencesHiroshima UniversityHigashi-HiroshimaJapan

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