Collective Excitations in Two-Band Superconductors

We investigate the eigen oscillations of internal degrees freedom (Higgs mode and Goldstone mode) two-band superconductors using extended time-dependent Ginzburg-Landau theory, formulated in a work Grigorishin (2021) \cite{grig2}, for case two coupled order parameters by both proximity effect drag effect. It is demonstrated, that splits into branches: common with acoustic spectrum, which absorbed gauge field, anti-phase energy gap (mass) spectrum determined interband coupling, can be associated Leggett mode. The Higgs branches also: massive one, whose vanishes at critical temperature $T_{c}$, another does not vanish $T_{c}$. second branch nonphysical, it, together mode, removed special choice coefficient "drag" term Lagrangian. In same time, such leaves only one coherence length, thereby prohibiting so-called type-1.5 superconductors. analyze experimental data about Josephson between particular, it resonant enhancement DC current through junction bias voltage $V_{\mathrm{res}}$, when frequency matches some oscillation (banks), explained coupling AC oscillations. Thus, explanation this need