Collective excitations in two-band superconductors

Abstract

We investigate eigen oscillations of internal degrees of freedom (Higgs mode and Goldstone mode) of two-band superconductors using generalization of the extended time-dependent Ginzburg-Landau theory, formulated in a work Grigorishin (2021) [1], for the case of two coupled order parameters by both the internal proximity effect and the drag effect. It is demonstrated, that Goldstone mode splits into two branches: common mode oscillations with acoustic spectrum, which is absorbed by gauge field, and anti-phase oscillations with energy gap (mass) in spectrum determined by interband coupling, which can be associated with Leggett mode. Analogously, Higgs oscillations splits into two branches also: massive one, whose energy gap vanishes at critical temperature Tc, another massive one, whose energy gap does not vanish at Tc. It is demonstrated, that the second branch of Higgs mode is nonphysical, and it with Leggett mode together can be removed by special choice of coefficient at the "drag" term in Lagrangian. In the same time, such choice leaves only one coherence length, thereby prohibiting so-called type-1.5 superconductors. We analyze experimental data about Josephson effect between two-band superconductors. In particular, it is demonstrated, that the resonant enhancement of the DC current through a Josephson junction at a resonant bias voltage Vres, when the Josephson frequency or its harmonics match the frequency of some internal oscillation mode or its harmonics in two-band superconductors (banks), can be explained with the coupling between AC Josephson current and Higgs oscillations. Thus, explanation of the effect does not need Leggett mode.

Collective excitations in three-band superconductors

“…two massive modes. These modes are analogous to Laggett mode in two-band superconductors [7]. Let us consider a symmetrical threeband system…”

“…The case < 0 corresponds to attractive interband interaction (for example, in MgB 2 ), the case > 0 corresponds to repulsive interband interaction (for example, in iron-based superconductors). It should be noted, that effect of interband coupling = 0, even if the coupling is weak, is nonperturbative for the smaller OP (for example Ψ 1 ) [7]: applying of the interband coupling washes out the smaller parameter up to new critical temperature T c T c1 . In the same time, the effect on the larger parameter Ψ 2 is not so significant -applying of the interband coupling slightly increases the critical temperature T c T c2 only.…”

“…In a work [7] it has been investigated eigen oscillations of internal degrees of freedom (Higgs mode and Goldstone mode) of two-band superconductors using generalization of the extended time-dependent Ginzburg-Landau (ETDGL) theory [1], for the case of two coupled OP by both the internal proximity effect and the drag effect. It is demonstrated, that, due to the internal proximity effect, Goldstone mode splits into two branches: common mode oscillations with acoustic spectrum, which is absorbed by gauge field, and anti-phase oscillations with energy gap (mass) in spectrum determined with the interband coupling , which can be associated with Leggett mode.…”

“…Proceeding from aforesaid, we are aimed to obtain eigen oscillations of internal degrees of freedom (Higgs modes and Goldstone modes) of three-band superconductors using method developed in a work [7] for the case of three coupled order parameters by both the internal proximity effect and the drag effect. We should find out the role of the drag effect in dynamics of three-band superconductors.…”

“…Non-perturbativness of the internal proximity effect is demonstrated. We investigate eigen oscillations of internal degrees of freedom (Higgs modes and Goldstone modes) of three-band superconductors using method developed in a work Grigorishin (2021) [7] for the case of coupled order parameters by both the internal proximity effect and the drag effect. It is demonstrated, that Goldstone mode splits into three branches: common mode oscillations with acoustic spectrum, which is absorbed by gauge field, and two modes of anti-phase oscillations with energy gap (mass) in spectrum determined by interband coupling, which are analogous to Leggett mode in two-band superconductors.…”