Skyrmion Flux Lattices in $p\,$-wave Superconductors

In $p\,$-wave superconductors, topological excitations known as skyrmions are allowed, in addition to the usual vortices. In strongly type-II materials in an external magnetic field, a skyrmion flux lattice is expected to be energetically favored compared to a vortex flux lattice [1]. We analytically calculate the energy, magnetization curves ($B(H)$), and elasticity of skyrmion flux lattices in $p\,$-wave superconductors near the lower critical field $H_{c1}$, and use these results with the Lindemann criterion to predict their melting curve [2]. In striking contrast to vortex flux lattices, which {\it always} melt at an external field $H > H_{c1}$, skyrmion flux lattices {\it never} melt near $H_{c1}$. This provides a simple and unambiguous test for the presence of skyrmions. In addition, the internal magnetic field distributions (which are measurable by muon spin rotation techniques [3]) of skyrmion and vortex lattices are very different. \medskip\par\noindent [1] A. Knigavko, B. Rosenstein, and Y.F. Chen, Phys. Rev. B {\bf 60}, 550 (1999). \par\noindent [2] Qi Li, John Toner, and D. Belitz, cond-mat/0607391 \par\noindent [3] J.E. Sonier, J. Phys. Cond. Matt. {\bf 16}, S4499 (2004)