Dephasing by electron-electron interactions in a ballistic Mach-Zehnder interferometer

TL;DR

This paper investigates how electron-electron interactions cause dephasing in a ballistic Mach-Zehnder interferometer, revealing universal power-law coherence decay at high energies using bosonization and semiclassical methods.

Contribution

It provides an exact and semiclassical analysis of dephasing due to finite-range interactions, highlighting the universal high-energy decay behavior independent of interaction strength.

Findings

Universal power-law decay of coherence at high energies

Semiclassical approach matches exact solutions at high energies

Keldysh perturbation theory effective for weak interactions and short distances

Abstract

We consider a ballistic Mach-Zehnder interferometer for electrons propagating chirally in one dimension (such as in an integer Quantum Hall effect edge channel). In such a system, dephasing occurs when the finite range of the interaction potential is taken into account. Using the tools of bosonization, we discuss the decay of coherence as a function of propagation distance and energy. We supplement the exact solution by a semiclassical approach that is physically transparent and is exact at high energies. In particular, we study in more detail the recently predicted universal power-law decay of the coherence at high energies, where the exponent does not depend on the interaction strength. In addition, we compare against Keldysh perturbation theory, which works well for small interaction strength at short propagation distances.