Ambiguity in the statistics of single-component winding vortex in a two-band superconductor

There are four topologically different paths to interchange two single-component winding vortices in a two-band superconductor having a weak inter-band interaction, where each band has its own superconducting component and its own phase, theta(v), other than the ordinary quantum phase, Theta (v is the index of the band and Theta is defined at the region of theta(1) = theta(2).). The acquired phase for the interchange of two single-winding vortices depends on the path, and three values Theta(soliton),-Theta(soliton) and 0, are observed. Theta(soliton) is the phase-slip accompanying the inter-band phase difference soliton (i-soliton). The interchange requires the creation and annihilation of the i-soliton and gives rise to an ambiguity in the statistics. (C) 2008 Elsevier B.V. All rights reserved.