Fractional Quantum Hall Effect in Arbitrary Potentials

A Kohn-Sham density functional theory (DFT) of composite fermions (CFs) takes into account the flux attached to CFs in a self-consistent fashion [1,2]. We develop numerical methods that allow the treatment of fractional quantum Hall effect (FQHE) systems in arbitrary potentials without rotational symmetry. This will enable realistic modeling of the experimental set-ups of FQHE in mesoscopic devices by taking into account the effect of irregular geometries, disorder, anisotropy, etc. As an application, we study the evolution of the ground state density in FQHE with respect to the strength of the exchange-correlation potential of CFs and find the appearance of charge density waves as the exchange-correlation potential increases in magnitude.

[1] Yayun Hu and J. K. Jain, Phys. Rev. Lett. 123, 176802(2019)
[2] Yayun Hu, G. Murthy, S. Rao, J. K. Jain, arXiv:2010.09872