Optical spectroscopy of composite fermion edge states in the fractional quantum Hall effect

Abstract

We show that edge states in fractional quantum Hall effect samples can be selectively probed and excited with sub-terahertz optical spectroscopy. Using the composite fermion (CF) mean-field framework, which maps the strongly correlated fractional quantum Hall problem onto an effective integer quantum Hall problem, we calculate the absorbance spectrum for the Jain sequence of filling fractions including both bulk and edge states. The CF edge-state absorption peaks appear in the millimeter-wave to sub-terahertz range, e.g., 60-500 GHz at B = 10 T in GaAs, i.e. they are blueshifted with respect to the bulk CF cyclotron frequency but are well below the integer quantum Hall cyclotron frequency scale at the same magnetic fields. The number of resolved peaks in each series of the absorption spectrum counts the filled Lambda-levels and fingerprints the fraction. Inversion symmetry breaking near the edge activates optical transitions forbidden in the bulk and enables second-order nonlinear processes in electric-dipole approximation. The absolute frequency scale of the spectrum is set by the CF effective mass, which is generated entirely by electron-electron interactions, so the absorption spectrum provides a direct optical probe of this interaction-induced mass.