# Braiding of anyon quasiparticles in fractional edge-state Mach-Zehnder interferometer

• Thursday 01 June 2017, 13:45-15:00
• Theory Library.

We consider tunneling between two edges of abelian Quantum Hall liquids (QHL) , in general, of different filling factors, $\nu_{0,1}=1/(2 m_{0,1}+1)$ with $m_0 \geq m_1\geq 0$, through two separate point contacts in the geometry of a Mach-Zehnder interferometer. Complete theoretical description of MZI valid for arbitrary tunneling strength in its contacts is developed based on the standard model of electron tunneling in the weak-tunneling limit. In this model the scaling up of the electron tunneling amplitudes with voltage or temperature to the strong-tunneling limit generates a nontrivial model of quasiparticle tunneling in MZI as a dual to weak electron tunneling. The quasi-particle formulation of the interferometer is derived through the instanton duality transformation in the limit of strong electron tunneling amplitudes, which is reached at large voltage or temperature. For $1+m_{0}+m_{1}=m>1$, the tunneling of quasiparticles of fractional charge $e/m$ leads to non-trivial $m$-state dynamics of effective flux through the interferometer. This dynamics demonstrates anyon braiding of the tunneling quasiparticles. For symmetric MZI with equal propagation times along the two edges between the contacts an exact solution is also constructed from the known Bethe ansatz solution of the single contact tuneling. We use this solution to find a full counting statistics of the charge transfer in MZI as a function of voltage $V$ at zero temperature. Its low-$V$ behavior can be interpreted in terms of the regular Poisson process of electron tunneling, while its large-$V$ asymptotics reflects the $m$-state dynamics of quasiparticles with fractional (for $m>1$) charge and anyon braiding statistics.

This talk is part of the Theoretical Physics Seminars series.