Fermion - chern - simons theory of half - filled landau level

Steven H. Simon, Ady Stern, Bertrand I. Halperin

1. Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level Authors: Chong Wang, Nigel R. Cooper, Bertrand I. Halperin, and Ady Stern Phys. Rev. X 7, 031029 (2017) 2. Particle-hole symmetry and electromagnetic response of a half- filled Landau level Authors: Michael Levin and Dam Thanh Son Phys. Rev. B 95, 125120 […]

M. O. Goerbig, Pascal Lederer, C. Morais Smith

Wolfgang Weller, J. Dietel, Thomas Koschny +1 more

We consider electrons in two dimensions in a strong magnetic field at half filling of the lowest Landau level using the Chern-Simons approach. Starting from a lattice Hamiltonian for the electrons, we derive a path integral (PI) formulation for the composite fermions (CF) which respects the order of the operators. We use a time lattice with intermediate times in order to have a PI expressed in density fluctuations. This formulation reveals that there is no infrared (IR) singularity in the grand-canonical potential in lowest order perturbation theory.

Edward H. Rezayi, Mike Gaston, F. D. M. Haldane +2 more

Ajit Coimbatore Balram, Jainendra K. Jain

Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the half filled Landau level, Dam T. Son has made an intriguing proposal [Phys. Rev. X {\bf 5}, 031027 (2015)] that composite fermions are Dirac particles. We ask what features of the Dirac-composite fermion theory and its various consequences may be reconciled with the well established microscopic theory of the fractional quantum Hall effect and the 1/2 state, which is based on {\em non-relativistic} composite fermions. Starting from the microscopic theory, we derive the assertion of Son that the particle-hole transformation of electrons at filling factor $\nu=1/2$ corresponds to an effective time reversal transformation (i.e. $\{\vec{k}_j\}$$\rightarrow$$\{-\vec{k}_j\}$) for composite fermions, and discuss how this connects to the absence of $2k_{\rm F}$ backscattering in the presence of a particle-hole symmetric disorder. By considering bare holes in various composite-fermion $\Lambda$ levels (analogs of electronic Landau levels) we determine the $\Lambda$ level spacing and find it to be very nearly independent of the $\Lambda$ level index, consistent with a parabolic dispersion for the underlying composite fermions. Finally, we address the compatibility of the Chern-Simons theory with the lowest Landau level constraint, and find that the wave functions of the mean-field Chern-Simons theory, as well as a class of topologically similar wave functions, are surprisingly accurate when projected into the lowest Landau level. These considerations lead us to introduce a normal form for the unprojected wave functions of the $n/(2pn-1)$ states that correctly capture the topological properties even without lowest Landau level projection.