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

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.