Symmetry of superconducting pairing state in a staggered field

Abstract

In order to investigate the symmetry of a superconducting (SC) pairing state in a staggered field, we solve the linearizedÉliashberg's equation based on the random phase approximation and the fluctuation exchange approximation in the Hubbard model under a staggered field. We show that an odd-frequency spin-triplet (equal-spin) s-wave pairing state can be realized in the system. It is caused by the fact that the staggered field suppresses the in-plane spin susceptibility and enhances the charge susceptibility. The latter is due to a spin-dependent modulation in the electron density. The result suggests that the antiferromagnetic (AF) background gives a contribution inherently different from the AF spin fluctuation to SC pairing state.

Signatures of odd-frequency pairing in the Josephson junction current noise

“…( 6), whose mean value is given in terms of the Keldysh Green functions as (26) Integrating the expression, and noticing that the contribution outside the gap vanishes, we obtain the expression in Eq. (7) Expression for current noise in the imaginary-time formalism…”

“…It has been demonstrated that electron-electron interactions mediated by phonons cannot stabilize an odd-ω gap by itself [5]. In contrast, other mechanisms, such as spin, charge, or current fluctuations, may be favorable [6][7][8]. Disordered systems [9,10], heavy fermion compounds [11][12][13][14][15], topological materials [16][17][18], and multiband superconductors [19][20][21][22] have been suggested to host odd-ω pairs in the equilibrium situation.…”

“…Instead, dynamic measurements, depending on non-local correlation functions in time, represent natural probes to detect the presence of these pairs. In the past, the effects of odd-ω pairs have been analyzed in the density of states [18,29,38,[41][42][43] and spectral density [17,21,34,46], Josephson current [31,35,44,47], Meissner effect [22,33,48], optical conductivity [49], spin and charge susceptibilities [7,44,50] and the current noise through normal leads [51]. Also, spin measurements have been used as an indirect evidence of the presence of odd-ω pairs [52,53].…”

Microscopic theory of the superconducting gap in the quasi-one-dimensional organic conductor (TMTSF)2ClO4 : Model derivation and two-particle self-consistent analysis

“…6. The reason for this involves the stabilization of odd-frequency pairing near the magnetic transition [113,116]. Although we do not exclude the possibility of oddfrequency pairing in this material, odd-frequency pairings are difficult to obtain at least in the Hubbard model with the parameter set used herein, since the tendency towards SDW ordering saturates at low temperatures.…”

“…The SC states we considered in this study are both the singlet and triplet channels in spin space, in addition to the even-and odd-frequency pairings [108][109][110][111][112][113][114][115][116]. Adopting the notation of the pairing states from previous studies [72,117,118], we label the pairing states by frequency, spin, parity of the gap function, and gap symmetry in wavenumber space, such as even-frequency, spin-singlet, even-parity (ESE), then the gap symmetry is added from the calculation result.…”