Compressibility in the Integer Quantum Hall Effect within Hartree-Fock Approximation

Abstract

Electron-electron interactions seem to play a surprisingly small role in the description of the integer quantum Hall effect, considering that for just slightly different filling factors the interactions are of utmost importance causing the interaction-mediated fractional quantum Hall effect. However, recent imaging experiments by Cobden et al. and Ilani et al. constitute strong evidence for the importance of electron-electron interactions even in the integer effect. The experiments report on measurements of the conductance and electronic compressibility of mesoscopic MOSFET devices that show disagreement with predictions from the single particle model. By diagonalising a random distribution of Gaussian scatterers and treating the interactions in Hartree-Fock approximation we investigate the role of electron-electron interactions for the integer quantum Hall effect and find good agreement with the experimental results.