Coulomb energy of quasiparticle excitations in Chern–Simons composite fermion states

The attachment of flux tubes to electrons by a Chern–Simons (CS) singular gauge transformation of the wavefunction opened up the field theoretical description of the fractional quantum Hall effect (FQHE). Nevertheless, in Jainʹs composite fermion (CF) theory, quasiparticles are believed to be vortices carrying a fractional charge in addition to the winding phase of the CS flux tubes. The different structure of the wavefunction in these two cases directly affects the excitation energy gaps. By using a simple ansatz we were able to evaluate analytically the Coulomb excitation energies for the mean-field level CS wavefunction, thus allowing a direct comparison with corresponding numerical results obtained from Jainʹs CF picture. The considerable difference between the excitation energies found in these two cases demonstrates in quantitative terms the very different impact that the internal structure of the wavefunction has in these two approaches, often used interchangeably to describe the FQHE.