Vortex lattice solutions of the ZHK Chern–Simons equations. (26th August 2020)

• Record Type: Journal Article
• Authors: Rajaratnam, K; Sigal, I M
• Is Part Of: Nonlinearity. Volume 33:Number 10(2020)
• Page Start: 5246
• Page End: 5271
• Publication Date: 2020-08-26
• Subjects: Chern–Simons equation -- vortex lattice solution -- magnetic flux quantization -- fractional quantum Hall effect -- partial differential equations; 35Q40, 35J61, 81V74, 58J28; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab9248
• Languages: English
• ISSNs: 0951-7715

Abstract

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.