Abstract
We examine vortices in Abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symmetry to be accompanied by a constant background charge density/magnetic field. Focussing attention on power law scalar potentials ∼ |Φ|2s which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for large winding number |n| ≫ 1. The solutions depending on a single dimensionless parameter α, behave as uniform incompressible droplets with radius \( \sim \sqrt{\alpha \left|n\right|} \), and energy scaling linearly with |n|, independent of coupling constant. In all cases, the vortices transition from type I to type II at a critical value of the dimensionless parameter, \( {\alpha}_c=\frac{s}{s-1} \), which we confirm with analytical arguments and numerical methods.
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Kumar, S.P., Stratiev, S. Abelian Chern-Simons vortices at finite chemical potential. J. High Energ. Phys. 2020, 41 (2020). https://doi.org/10.1007/JHEP04(2020)041
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DOI: https://doi.org/10.1007/JHEP04(2020)041