Quantum Elliptic Vortex in a Nematic-Spin Bose-Einstein Condensate

We find a novel topological defect in spin-nematic superfluid theoretically. A quantized vortex spontaneously breaks its axisymmetry, leading to an elliptic nematic-spin Bose-Einstein condensates with small positive quadratic Zeeman effect. The new is considered the Joukowski transform of conventional vortex. Its oblateness grows when length exceeds spin healing length. This structure sustained by balancing hydrodynamic potential and elasticity soliton connecting two spots, which are observable situ magnetization imaging. theoretical analysis clearly defines difference between half quantum vortices polar antiferromagnetic phases spin-1 condensates.