Vortices with scalar condensates in two-component Ginzburg–Landau systems

Abstract

In a class of two-component Ginzburg–Landau models (TCGL) with a U(1)×U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov–Nielsen–Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices become unstable against core-condensation, while condensate-core (CC) vortices are stable. For LMH the ratio of the masses of the two types of condensates, M=m2/m1 is large, and then as a consequence the energy per flux quantum of the vortices, En/n becomes a non-monotonous function of the number of flux quanta, n. This leads to yet another manifestation of neither type 1 nor type 2, (type 1.5) superconductivity: superconducting and normal domains coexist while various “giant” vortices form. We note that LMH provides a particularly clean example of type 1.5 state as the interband coupling between electronic and protonic Cooper-pairs is forbidden.