Enhancement of quantum dot peak-spacing fluctuations in the fractional quantum Hall regime

– The fluctuations in the spacing of the tunneling resonances through a quantum dot have been studied in the quantum Hall regime. Using the fact that the ground-state of the system is described very well by the Laughlin wavefunction, we were able to determine accurately, via classical Monte Carlo calculations, the amplitude and distribution of the peakspacing fluctuations. Our results clearly demonstrate a big enhancement of the fluctuations as the importance of the electronic correlations increases, namely as the density decreases and filling factor becomes smaller. We also find that the distribution of the fluctuations approaches a Gaussian with increasing density of random potentials. Several experimental studies[1, 2, 3] have recently demonstrated that the fluctuations in the ground-state energy of a quantum dot, which are manifested in the fluctuations in the resonant-tunneling-peak spacings, are much larger than what one expect from models that ignore electron correlations. Numerical studies[1, 4, 5, 6] have indeed revealed an enhancement of the ground-state energy fluctuations due to electron-electron interactions. In this work we present calculations for an interacting electron system in a regime that can be treated almost exactly the quantum Hall regime. The ground-state wavefunction in this regime is faithfully described by the Laughlin wavefunction [7]. Consequently, as long as the potential fluctuations do not mix in excited states (i.e. when the potential energy is smaller than the gap), the peak-spacing fluctuations (PSF) can be evaluated as expectation values in the Laughlin state. As such expectation values can be easily calculated using the plasma analogy [7], via, e.g., classical Monte Carlo simulations, we are able to obtain the magnitude of the PSF, their distribution and their dependence on the range of the potentials and the electron number. Indeed we find that the more important the electronic correlations (the lower the filling factor), the larger the magnitude of the PSF. In addition, we also find that the distribution of PSF is Gaussian, in agreement with experiments [1, 2, 3]. The experimentally measured quantity is the spacings between the resonant-tunneling peaks through the quantum dot. At low enough temperatures (smaller than the excitation energies of the dot), the peak spacing is determined by the addition spectrum, ∆ 2 ≡ ( E g − E g ) − ( E g − E g ) , (1) where E g is the ground-state energy of the N-particle system. In the constant-interaction model [8] E g = N(N − 1)U/2 + ∑N i ǫi, where U is the charging energy and ǫi is the Typeset using EURO-TEX