Exact Polaron-Polaron interactions in a Quantum Hall Fluid

TL;DR

This paper provides an exact analytical solution for polaron-polaron interactions in a quantum Hall system, revealing conditions under which these interactions vanish or diverge, with implications for cold-atom experiments and semiconductor physics.

Contribution

It derives an exact solution for polaron-polaron interactions mediated by light fermions in a quantum Hall regime, including analytical and numerical results for different Landau level manifolds.

Findings

Polaron interactions are zero when fermions outnumber impurities in the lowest Landau level.

The mediated interaction potential diverges as -1/R at short distances.

Interactions vanish beyond the magnetic length, indicating a finite range.

Abstract

We present an exact solution for effective polaron-polaron interactions between heavy impurities, mediated by a sea of non-interacting light fermions in the quantum Hall regime with highly degenerate Landau levels. For weak attraction between impurities and fermions, where only the manifold of lowest Landau levels is relevant, we obtain an analytical expression of mediated polaron-polaorn interactions. Remarkably, polaron interactions are exactly zero when fermions in lowest Landau levels outnumber heavy impurities. For strong attraction, different manifolds of higher Landau levels come into play and we derive a set of equations that can be used to numerically solve the mediated polaron interaction potential. We find that the potential vanishes when the distance R between impurities is larger than the magnetic length, but strongly diverges at short range following a Coulomb form -1/R. Our exact results of polaron-polaron interactions might be examined in cold-atom setups, where a system of Fermi polarons in the quantum Hall regime is realized with synthetic gauge field or under fast rotation. Our predictions could also be useful to understand the effective interaction between exciton-polarons in electron-doped semiconductors under strong magnetic field.