Effects of order parameter self-consistency in as±−sjunction

Abstract

The properties of Josephson tunneling between a single band s-wave superconductor and a two band s± superconductor are studied, in relation to recent experiments involving iron-based superconductors. We study both a single junction and a loop consisting of two junctions. In both cases, the relative phase between the order parameters of the two superconductors is tuned and the energy of the system is calculated. In a single junction, we find four types of behaviors characterized by the location of minima in the energy/phase relations. These phases include a newly found double minimum junction which appears only when the order parameters are treated self-consistently. We analyze the loop geometry setup in light of our results for a single junction, where the phase difference in the junctions is controlled by a threaded flux. We find four types of energy/flux relations. These include states for which the energy is minimized when the threaded flux is an integer or half integer number of flux quanta, a time reversal broken state and a meta-stable state.

Proximity and Josephson effects in microstructures based on multiband superconductors (Review Article)

“…A similar behavior in a dc SQUID based on s and s 6wave superconductors has also been confirmed in the framework of a self-consistent microscopic description using the Bogolyubov-de Gennes equation. 68 In addition to the three regimes that were found earlier using the phenomenological Ginzburg-Landau approach, the paper has also revealed the existence of another state, when a single global minimum is realized at…”

“…A similar behavior in a dc SQUID based on s and s 6wave superconductors has also been confirmed in the framework of a self-consistent microscopic description using the Bogolyubov-de Gennes equation. 68 In addition to the three regimes that were found earlier using the phenomenological Ginzburg-Landau approach, the paper has also revealed the existence of another state, when a single global minimum is realized at U ¼ n þ 1 2 À Á U 0 . As in the case of the Josephson effect, a dc SQUID formed by s-wave single-band and three-band superconductors, gives rise to a number of fundamentally new features of macroscopic quantum interference that are not observed in other similar systems based on two-band and other superconducting compounds with an unusual type of symmetry of the order parameter .…”

“…Panels (b) and (d) show similar dependences obtained from non-selfconsistent calculations for the same parameters as in panels (a) and (c), respectively. 68 that l 0 > l c > 0, for which the energy minimum of the system is realized for the phase difference equal to p. For l 0 < l c , small changes in the chemical potential lead to transitions from the zero phase difference to p and vice versa. It was also found that increasing the gap in the single-band superconductor reduces the number of these transitions at fixed values of the tunnel amplitudes.…”

“…In Ref. 68, they were used to develop the selfconsistent theory of proximity effect in a heterostructure formed by an s 6 -wave two-band superconductor and its single-band analogue. Numerical solution of the Bogolyubovde Gennes equations allowed determine the energy of the system as a function of the phase difference between the order parameter of the single-band superconductor and the first order parameter of the s 6 -wave two-band superconductor E(/) ( Fig.…”

“…The region in which an additional minimum with zero phase difference can possible exists is marked in blue. 68 Here A is the junction, v n is the projection of the Fermi velocity v F on the normal direction to the interface plane, D ij denotes the tunneling probability of a quasiparticle from the band i of the left superconductor L to the band j of the right bank R. The total current I through the contact is obtained by summing up I ¼ P ij I ij . Almost immediately after the electron-phonon mechanism of two-band superconductivity in MgB 2 was established and the coupling constant matrices in this compound were determined, this equation was applied to the calculating of the Josephson tunneling in S 2 IS 2 and S 1 IS 2 contacts, where S 1 and S 2 are single-gap niobium and double-gap magnesium diboride, respectively.…”