Two point-contact interferometer for quantum Hall systems

TL;DR

This work introduces a two point-contact interferometer in a quantum Hall bar to probe interference in strongly correlated edge states. By analyzing Aharonov-Bohm oscillations, fractional-charge-induced periods, and voltage-driven Fabry-Perot patterns within edge-state theory, it shows how to extract fractional charge $e^*=e/m$ and fractional statistics, while also distinguishing Fermi-liquid from Luttinger-liquid edge behavior. The authors provide a perturbative framework for tunneling between edges, exact results for the $g=1$ case, and finite-temperature generalizations, along with realistic numerical estimates for experimental feasibility. The device offers a robust, topology-based method to explore fundamental anyonic properties and non-Fermi liquid edge dynamics with potential practical impact for quantum Hall physics experiments.

Abstract

We propose a device, consisting of a Hall bar with two weak barriers, that can be used to study quantum interference effects in a strongly correlated system. We show how the device provides a way of measuring the fractional charge and fractional statistics of quasiparticles in the quantum Hall effect through an anomalous Aharanov-Bohm period. We discuss how this disentangling of the charge and statistics can be accomplished by measurements at fixed filling factor and at fixed density. We also discuss a another type of interference effect that occurs in the nonlinear regime as the source-drain voltage is varied. The period of these oscillations can also be used to measure the fractional charge, and details of the oscillations patterns, in particular the position of the nodes, can be used to distinguish between Fermi-liquid and Luttinger-liquid behavior. We illustrate these ideas by computing the conductance of the device in the framework of edge state theory and use it to estimate parameters for the experimental realization of this device.

Figures (5)

• Figure 1: Two point-contact interferometer. Two gates are placed a distance $a$ apart. The gate voltages are adjusted so as to bring the edges of a FQH state with filling fraction $\nu$ close together, but not pinch the constriction. In this way, quasiparticles carrying fractional charge and statistics can tunnel from one edge to the other. A magnetic flux $\Phi$ can be inserted in the region between the point-contacts that is bounded by the edge states. A central gate allows the charge in the region to be selectively depleted. The transmitted current (the Hall current $I_H=\nu e^2/h$ minus the tunneling current $I^1_t+I_t^2$) oscillates as a function of the inserted flux, the voltage difference between the edges and the voltage of the central gate. An overall back gate on the device allows magnetic field sweeps at constant filling factor.
• Figure 2: Modulation $H_g(x)$ for $g=1,1/3,1/5$. Notice that the decay rate of the modulation is $x^{-g}$. Also, the position of the zeros of $H_g(x)$ (those of $J_{g-1/2}(x)$) are approximately given by $x_n\approx\pi(n+\xi_g)$, $n$ integer, where $\xi_g=\frac{1+g}{2}$ is a $g$ dependent shift
• Figure 3: Temperature decay of the modulation $H_g$ for $g=1,1/3,1/5$. The quantity plotted is $H_g(\omega_J=0,a,T)$ vs. $T$, with $T$ measured in units of $\omega_{\rm osc}=2\pi \frac{v}{a}$ (the energy scale associated with the point-contact separation $a$). Notice that the modulation decays exponentially with $T$ for large temperatures, and that the decay rate is faster for larger $g$.
• Figure 4: Dependence of the modulation $H_g(\omega_J,a,T)$ on $\omega_J$ for different $T$. The quantity plotted is the rescaled $H_g$ ($H_g(\omega_J,a,T)/H_g(0,a,T)$) so as to show how the shape of the modulation curve changes with $T$ for different $g$. Notice that all curves collapse for $g=1$, i.e., all frequencies get suppressed uniformly as temperature is increased. For $g=1/3$ and $g=1/5$, however, notice that the curves do not collapse together anymore, and that higher $\omega_J$ are supressed more strongly than lower $\omega_J$ as $T$ is increased.
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