Eur. Phys. J. B 65, 155-178 (2008)
https://doi.org/10.1140/epjb/e2008-00343-2

Topological objects in two-gap superconductor

¹ Center for Theoretical Physics and School of Physics, College of Natural Sciences, Seoul National University, Seoul 151-742, Korea
² Institute of Modern Physics, Chinese Academy of Sciences, P.O. Box 31, Lanzhou 730000, P. R. China

Corresponding author: ^a ymcho@yongmin.snu.ac.kr

Received: 13 November 2007
Revised: 13 June 2008
Published online: 10 September 2008

Abstract

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology and , in addition to the well-known Abelian topology . Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB₂, Sr₂RuO₄, ³He, and liquid metallic hydrogen.