Tunable breakdown of the polaron picture for mobile impurities in a topological semimetal

TL;DR

This paper explores how the polaron picture for mobile impurities in a topological semimetal can either hold or break down depending on band asymmetry, revealing tunable impurity dynamics and diffusion behaviors.

Contribution

It demonstrates the tunable breakdown of the polaron model in a topological semimetal based on particle-hole asymmetry, using conformal field theory techniques.

Findings

Stable quasiparticle with $D(T) o ext{ln}^2 T$ when hole band has smaller effective mass.

Vanishing quasiparticle weight and orthogonality catastrophe when hole band has larger mass.

Diffusion coefficient exhibits different temperature dependencies in the two regimes.

Abstract

Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T) \propto \ln^2 T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain $D(T)\propto T^{\nu}$ with an interaction-dependent exponent $\nu$. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.