Vortex lattice solutions of the ZHK Chern-Simons equations
Krishan Rajaratnam, Israel Michael Sigal
TL;DR
This paper proves the existence of vortex lattice solutions in the non-relativistic Chern-Simons equations related to the fractional Hall effect, showing they form a hexagonal lattice with minimal energy.
Contribution
It establishes the existence of vortex lattice solutions with lattice symmetry and topological degree one, extending Abrikosov lattice concepts to Chern-Simons equations.
Findings
Vortex lattice solutions exist with lattice symmetry.
Hexagonal lattice minimizes the energy per unit area.
Solutions resemble Abrikosov lattice solutions in superconductivity.
Abstract
We consider the non-relativistic Chern-Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice symmetry and with topological degree one per lattice cell) similar to the Abrikosov solutions of superconductivity. We derive an asymptotic expression for the energy per unit area and show that it attains minimum at the hexagonal lattice.
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