Dynamical properties of a two-dimensional electron gas in a magnetic field within the composite fermion model

摘要

We investigate the response of a two-dimensional electron gas, in thefractional quantum Hall regime, to the sudden appearance of a localised chargedprobe using the Chern-Simons theory of composite fermions. The dynamicstructure factor of the electron gas is found to have a major influence on thespectral function of the probe. In particular, there is an orthogonalitycatastrophe when the filling factor is an even-denominator filling fraction dueto the compressibility of the state, but there is no catastrophe atodd-denominator filling factors because these states have a gap to excitations.The catastrophe is found to be more severe for composite fermions in zeroeffective magnetic field than it is for electrons in zero real magnetic field.Oscillations in the spectral function, arising when the composite fermions areat integer filling, have a period equal to the composite fermion cyclotronenergy. We propose a tunneling experiment which directly measures the spectralfunction from which one could determine the composite fermion effective mass.