Thermodynamical stability of odd-frequency superconducting state

Abstract

Odd-frequency pairing mechanism of superconductivity has been investigated for several decades. Nevertheless, its properties, including the thermodynamic stability, have remained unclear. In particular, it has been argued that the odd-frequency state is thermodynamically unstable, has an unphysical (anti-) Meissner effect, and thus can not exist as a homogeneous equilibrium phase. We argue that this conclusion is incorrect because it implicitly relies on the inappropriate assumption that the odd-frequency superconductor can be described by an effective Hamiltonian that breaks the particle conservation symmetry. We demonstrate that the odd-frequency state can be properly described within the functional integral approach using non-local-in-time effective action. Within the saddle point approximation, we find that this phase is thermodynamically stable, exhibits ordinary Meissner effect, and therefore can be realized as an equilibrium homogenous state of matter.

Low-Field Superconducting Phase of(TMTSF)2ClO4

“…Finally, we note that the thermodynamic stability of oddfrequency bulk SCs was initially questioned, but recent theoretical work now concludes that these states should actually be stable [47,48]. The example identified here would suggest that such an odd-frequency state can indeed exist in a bulk material.…”

Possible Odd-Frequency Superconductivity in Strong-Coupling Electron–Phonon Systems

“…Recently, it is pointed out that these difficulties can be settled by the appropriate treatment of the gap function with retardation in the path-integral framework. 37,38) As a result, the property of the OF state is ready to be examined without any theoretical ambiguity.…”

“…In this case, the ordinary Cooper instability is expected to occur in the isotropic s-wave pairing. Following the recent theoretical development for the OF superconductivity, 37,38) the gap equations for the s-wave EF singlet pairing ∆ αβ (k) = ∆ + (iω n )(iσ y ) αβ and the s-wave OF unitary triplet pairing 54) …”

Pair symmetry conversion in driven multiband superconductors

“…While some research has been dedicated to the thermodynamic stability of intrinsically odd-ω phases [3][4][5][6] , a great deal of previous research has been devoted to the identification of heterostructures in which odd-ω pairing could be induced including: ferromagnetic -superconductor heterostructures [7][8][9][10][11][12][13] , topological insulator -superconductor systems [14][15][16][17] , normal metal -superconductor junctions due to broken translation symmetry [18][19][20][21][22] , two-dimensional bilayers coupled to conventional s-wave superconductors 23 , and in generic two-dimensional electron gases coupled to superconductor thin films 24 . In addition to theoretical studies, there are experimental indications of the realization of odd-ω pairing at the interface of Nb thin films and epitaxial Ho 25 .…”