Vortex nucleation barriers and stable fractional vortices near\n boundaries in multicomponent superconductors

The magnetization process of a superconductor is determined by the potential\nbarrier for vortex nucleation and escape. In multicomponent superconductors,\nfractional vortices with a winding in the phase of only one of the components\ncan be stable topological solitons that carry a fraction of the flux quantum.\nWhile the formation of such objects in the bulk costs logarithmically or\nlinearly divergent energy, these objects were shown to be stable near samples'\nboundaries in the two-component London model. Therefore, the conventional\nBean-Livingston picture of magnetic flux entry does not apply to these\nsuperconductors, since the entry process can involve fractionalization of a\nvortex. In this paper, we address the nonlinear problem of determining the\npotential barrier for fluxoid penetration in a multicomponent superconductor,\nincluding the effects of various intercomponent couplings, by using the\nrecently developed gauged string method. The method allows numerically exact\n(i.e., convergent) calculation of a sphaleron configuration in a gauge theory\nand thus the height of the nucleation barrier. We show how the fractionalized\nnucleation processes result in multiple sphalerons and intermediate states due\nto the complex shape of the energy landscape of multicomponent superconductors.\n