Dia- and paramagnetic Meissner effect from odd-frequency pairing in multi-orbital superconductors

Abstract

The Meissner effect is one of the defining properties of superconductivity, with a conventional superconductor completely repelling an external magnetic field. In contrast to this diamagnetic behavior, odd-frequency superconducting pairing has often been seen to produce a paramagnetic Meissner effect, which instead makes the superconductor unstable due to the attraction of magnetic field. In this work we study how both even-and odd-frequency superconducting pairing contributes to the Meissner effect in a generic two-orbital superconductor with a tunable odd-frequency pairing component. By dividing the contributions to the Meissner effect into intra-and inter-band processes, we find that the odd-frequency pairing actually generates both dia-and paramagnetic Meissner responses, determined by the normal-state band structure. More specifically, for materials with two electron-like (hole-like) low-energy bands we find that the odd-frequency inter-band contribution is paramagnetic but nearly canceled by a diamagnetic odd-frequency intra-band contribution. Combined with a diamagnetic even-frequency contribution, such superconductors thus always display a large diamagnetic Meissner response to an external magnetic field, even in the presence of large odd-frequency pairing. For materials with an inverted, or topological, band structure, we find the odd-frequency inter-band contribution to instead be diamagnetic and even the dominating contribution to the Meissner effect in the near-metallic regime. Taken together, our results show that odd-frequency pairing in multi-orbital superconductors does not generate a destabilizing paramagnetic Meissner effect and can even generate a diamagnetic response in topological materials.

Direct detection of odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy

“…Two-band superconductor.-Below, we demonstrate how our proposal works within a model of a two-band superconductor developed by Parhizgar and Black-Schaffer [21]. The Hamiltonian of a two-band superconductor in the basis…”

“…The anomalous Green's function F in frequency space consisting of even-and odd-frequency contributions have been derived in Ref. [21]. For our purposes, we need to transfer them to time representation by contour integration with the choice of the poles as ∓ε + ± iη and ∓ε − ± iη with η → +0 [19].…”

“…In this section, we present the way we perform the Fourier transformation of the anomalous Green functions, even and odd, for a model of a two-band superconductor described in Ref. 21.…”

Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces

“…Odd (even)-ω superconductivity refers to when the Cooper pair amplitude is odd (even) under the exchange of the time coordinates, or equivalently frequency, of the two constituent electrons, as introduced by Balatsky and Abrahams [2] following the first prediction of odd-frequency order by Berezinskii in 3 He [3]. Finite oddω pair amplitudes have been predicted to exist mostly in superconducting hybrid structures [1,[4][5][6][7], but also in a variety of other systems, such as multiband superconductors [8][9][10], topological materials [11][12][13][14][15][16][17], heavy-fermion compounds [18][19][20], and driven systems [21,22]. In several of these systems, experimental consequences of oddω pairs have also been explored, including its connection to zero-energy density of states (DOS) peaks [23][24][25][26][27][28].…”