Scanning tunneling microscopy of fractional quantum Hall states: Spectroscopy of composite-fermion bound states

Abstract

From the vantage point of an incompressible fractional quantum Hall (FQH) state, an electron injected into it is a complex bound state of an odd number of composite fermions (CFs) dressed by a cloud of particle-hole pairs of CFs, where each CF itself is the bound state of an electron and an even number of quantized vortices. Recent scanning tunneling microscopy experiments provide a spectroscopic probe of the internal energy levels of this bound state, yielding unique information on the short-distance correlations in the FQH liquids. We present detailed calculations showing that the internal energy levels of this bound state, as manifested in the energy-resolved local density of states, depend sensitively on the filling factor and on whether an electron is added or removed. In general, multiple, approximately equally spaced peaks are predicted, with their separation providing a measure of a renormalized CF cyclotron energy. We discuss what aspects of experiments are explained by our model and which ones remain to be explained.