Instability of the Abrikosov Lattice due to Nonanalytic Core Reconstruction of Vortices in Bosonic Superfluids

We study the impact of the nonanalytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that, in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may also be observable in clean superconducting films.

Figure 1

Deformation of a finite AL due to core reconstruction [14]. The panels show the configuration of the AL obtained by numerical minimization of the energy $u$ for a system with (left panel) 121 and (right panel) 127 vortices, taking into account their emergent dipole moments $d_i$. The lines in the figures represent the directors’ configuration. The length of each line is $10\sqrt{|D_i|}$, and each line has an angle corresponding to $(\arg D_i)/2$, in accordance with the convention for liquid crystals. The lattice constant is $a=3$.

Figure 2

An illustration of the supervortex structure which is a minimum of the energy $u$, ignoring surface contributions [Eqs. (20)–(22)]. (a) The shifts, ${\mathrm{\Delta }}_i$, of the vortices from their equilibrium position due to core reconstruction. (b) The configuration of $D_i$ (see Fig. 1 for the convention used in drawing the directors).