Electron tunneling into Fractional Quantum Hall Effect*

The low energy excitation spectrum of the Fractional Quantum Hall Effect (FQHE) is described in terms of composite fermions, which are fundamentally distinct from electrons. When an electron is added into an FQHE state, it disintegrates into many fractionally charged composite fermions. Because of the absence of electron-like quasiparticles, the a priori expectation is that the electron tunneling spectrum will contain no sharp peaks. Surprisingly, theoretical work [1] predicted at least one sharp peak in the tunneling spectrum of FQH liquids. Recent STM experiments [2] have indeed observed one or more peaks. In this work, we show that the addition of a hole to (i.e., removal of an electron from) an FQH liquid at ν = n/(2np+1) can be exactly described in terms of a finite number of composite fermion basis functions, allowing us to predict the qualitative and quantitative features of electron tunneling spectral function.  The addition of an electron cannot be readily described in terms of composite fermions, leading to a qualitatively different behavior for the spectral function. We also study the effect of the tip potential and predict features that can arise from the insertion of a spin-reversed electron. 

  

1. J. K. Jain and M. R. Peterson, Reconstructing the Electron in a Fractionalized Quantum Fluid, Phys. Rev. Lett. 94, 186808 (2005). 

2. Y. Hu et al., High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States, http://arxiv.org/abs/2308.05789.