[Paper Review] Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

K. T. Law, D. E. Feldman+1 more|arXiv (Cornell University)|Jun 14, 2005

Quantum and electron transport phenomena3 citations

TL;DR

This paper proposes using an electronic Mach-Zehnder interferometer to probe fractional statistics of quasiparticles in the fractional quantum Hall effect. By measuring the flux-dependent component of the tunneling current, the method reveals that the current's dependence on magnetic flux follows a power law whose exponent directly encodes the quasiparticle statistics, enabling direct experimental detection of fractional statistics without requiring noise measurements or controlled quasiparticle trapping.

ABSTRACT

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.

Motivation & Objective

• To develop a direct experimental method for probing the fractional statistics of identical quasiparticles in the fractional quantum Hall effect.
• To overcome limitations of prior methods that require measuring current noise or current-current correlations.
• To eliminate the need for precise control over the number of trapped quasiparticles, a major challenge in previous approaches.
• To demonstrate that the flux-dependent current component scales as a power law with the flux-independent component, where the exponent encodes quasiparticle statistics.
• To enable observation of fractional statistics in larger interferometer geometries than previously feasible.

Proposed method

• Model the interferometer as two quantum Hall edges connected by two quantum point contacts (QPC1 and QPC2), with tunneling between edges.
• Use a perturbative approach in tunneling amplitudes Γ₁ and Γ₂ to calculate the current as a function of voltage bias, temperature, and magnetic flux.
• Derive the current as the sum of flux-independent (I₀) and flux-dependent (IΦ) components, with IΦ oscillating with period Φ₀ = hc/e.
• Apply bosonization techniques to handle quasiparticle statistics, particularly incorporating Klein factors to account for fractional statistics in the fractional QHE regime.
• Use an effective single-impurity model with periodic boundary conditions to derive the current in the limit of weak tunneling.
• Employ contour integration and detailed balance arguments to relate current responses under voltage reversal, validating the consistency of the theoretical framework.

Experimental results

Research questions

• RQ1 Can the electronic Mach-Zehnder interferometer detect fractional statistics of quasiparticles without requiring noise measurements?
• RQ2 How does the flux-dependent component of the tunneling current scale with the flux-independent component, and what determines the scaling exponent?
• RQ3 What is the role of quasiparticle statistics in modifying the current-voltage characteristics in the interferometer?
• RQ4 How does temperature influence the scaling behavior of the current components in the interferometer?
• RQ5 Can the method distinguish between electron tunneling (b = 1/2) and fractional quasiparticle tunneling (b > 1/2) in the fractional quantum Hall regime?

Key findings

• The flux-dependent current component IΦ scales as [I₀(Γ₁, Γ₂) - I₀(Γ₁, 0)]^b, where the exponent b depends on the quasiparticle statistics.
• For electron tunneling, the exponent b is exactly 1/2, consistent with fermionic statistics.
• For fractional quasiparticles in the ν = 1/(2m+1) fractional quantum Hall state, the exponent b exceeds 1/2 and increases with decreasing filling factor.
• The temperature dependence of the linear conductance G at low temperatures scales as T^(1/ν₁ + 1/ν₂ - 2), with the leading term determined by the filling factors ν₁ and ν₂.
• The current response under voltage reversal satisfies detailed balance relations, confirming consistency with thermodynamic equilibrium and the validity of the perturbative approach.
• The method allows for observation of interference patterns at larger interferometer sizes than in standard setups, enhancing experimental feasibility.