Noise measurements and fractional charge in fractional quantum Hall liquids

Abstract

We present a calculation of noise in the tunneling current through junctions between two two-dimensional electron gases (2DEG) in inequivalent Laughlin fractional quantum Hall (FQH) states, as a function of voltage and temperature. We discuss the interpretation of measurements of suppressed shot noise levels of tunneling currents through a quantum point contact (QPC) in terms of tunneling of fractionally charged states. We show that although this interpretation is always possible, for junctions between different FQH states the fractionally charged states involved in the tunneling process are not the Laughlin quasiparticles of the isolated FQH states that make up the junction, and should be regarded instead as solitons of the coupled system. The charge of the soliton is, in units of the electron charge, the harmonic average of the filling fractions of the individual Laughlin states, which also coincides with the saturation value of the differential conductance of the QPC. For the especially interesting case of a QPC between states at filling fractions $\nu=1$ and $\nu={{1/3}}$, we calculate the noise in the tunneling current exactly for all voltages and temperatures and investigate the crossovers. These results can be tested by noise experiments on $(1,{{1/3}})$ QPCs. We present a generalization of these results for QPC's of arbitrary Laughlin fractions in their weak and strong coupling regimes. We also introduce generalized Wilson ratios for the noise in the shot and thermal limits. These ratios are universal scaling functions of $V/T$ that can be measured experimentally in a general QPC geometry.