Phase transition from straight into twisted vortex lines in dipolar Bose-Einstein condensates

The non-local nonlinearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates. In particular, it may distort significantly the stability of straight vortex lines due to the rotonization of the Kelvin-wave spectrum. In the present paper, we analyze this instability, showing that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.