Unusual Sequence of the Critical Magnetic Fields $$H_{c1}$$, $$H_{c2}$$, and $$H_{c}$$ in Multicomponent Superconductors

Abstract

AbstractAll superconductors in a magnetic field are characterized by three critical magnetic fields: lower critical $$H_{c1}$$ H c 1 , upper critical $$H_{c2}$$ H c 2 and thermodynamic critical field $$H_{c}$$ H c . Only two sets of inequalities $$H_{c2}>H_c>H_{c1}$$ H c 2 > H c > H c 1 or $$H_{c1}>H_c>H_{c2}$$ H c 1 > H c > H c 2 are possible in a single-component superconductor. Here, we report our study of the critical fields in multicomponent superconductors with two superconducting components in the framework of the Ginzburg-Landau functional. We derive the relationship between the phases of the components of the superconducting complex order parameter from the charge conservation law in explicit form and insert it into the Ginzburg-Landau functional. Using the modified Ginzburg-Landau equation, we acquire the single vortex state including the analytical expression for asymptotics. Also, we obtain the analytical form for the state in the upper critical field. We find that in some cases an unusual sequence of critical fields $$H_{c1},H_{c2}>H_c$$ H c 1 , H c 2 > H c can be realized in multicomponent superconductors.