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Register a new userWhy a noninteracting model works for shot noise in fractional charge experiments
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A fractional quasiparticle charge is a manifestation of strong interactions in the fractional quantum Hall effect. Nevertheless, shot noise of quasiparticles is well described by a formula, derived for noninteracting charges. We explain the success of that formula by proving that in the limits of strong and weak backscattering it holds irrespectively of microscopic details in weakly and strongly interacting systems alike. The derivation relies only on principles of statistical mechanics. We also derive an approximate model-independent formula for shot noise in the regime of intermediate backscattering. The equation is numerically close to the standard `noninteracting fitting formula but suggests a different physical interpretation of the experimental results. We verify our theoretical predictions with a shot noise experiment at the filling factor $3/5$.
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Consider two Fermi gases with the same {it average} currents: a transport gas, as in solid-state experiments where the chemical potentials of terminal 1 is $mu+eV$ and of terminal 2 and 3 is $mu$, and a beam, i.e., electrons entering only from terminal 1 having energies between $mu$ and $mu+eV$. By expressing the current noise as a sum over single-particle transitions we show that the temporal current fluctuations are very different: The beam is noisier due to allowed single-particle transitions into empty states below $mu$. Surprisingly, the correlations between terminals 2 and 3 are the same.
We have experimentally identified fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact (QPC) in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 ? T1) over a wide range of T1, where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process will enable us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.
We study the photoassisted shot noise generated by a periodic voltage in the fractional quantum Hall regime. Fluctuations of the current are due to the presence of a quantum point contact operating in the weak backscattering regime. We show how to reconstruct the photoassisted absorption and emission probabilities by varying independently the dc and ac contributions to the voltage drive. This is made possible by the peculiar power-law behavior of the tunneling rates in the chiral Luttinger liquid theory, which allow to approximate the typical infinite sums of the photoassisted transport formalism in a simple and particularly convenient way.
The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a ``bunching effect, while for higher states in the Jain sequences they should exhibit an ``anti-bunching effect.
We study the transport properties of an Anderson-Holstein model with orbital degeneracies and a tunneling phase that allows for the formation of dark states. The resulting destructive interference yields a characteristic pattern of positive and negative differential conductance features with enhanced shot noise, without further asymmetry requirements in the coupling to the leads. The transport characteristics are strongly influenced by the Lamb-shift renormalization of the system Hamiltonian. Thus, the electron-vibron coupling cannot be extracted by a simple fit of the current steps to a Poisson distribution. For strong vibronic relaxation, a simpler effective model with analytical solution allows for a better understanding and moreover demonstrates the robustness of the described effects.
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