Bound states in two-dimensional Fermi systems with quadratic band touching

TL;DR

This paper explores how bound states form between impurities and fermions in a 2D system with quadratic band touching, revealing control over bound state degeneracy via anisotropic interactions.

Contribution

It introduces the effect of anisotropic dipolar exchange interactions on bound states in 2D quadratic band touching systems, using renormalization group and ladder approximation methods.

Findings

Number of bound states can be tuned by exchange interaction anisotropy

Degeneracy and momentum dependence of binding energies reflect quadratic band touching properties

Distinctive bound state features due to symmetry-breaking interactions

Abstract

The formation of bound states between mobile impurity particles and fermionic atoms has been demonstrated in spin-polarized Fermi gases with attractive interspecies interaction. We investigate bound states of mobile impurities immersed in a two-dimensional system with a symmetry-protected quadratic band touching. In addition to the standard s-wave interaction, we consider an anisotropic dipolar exchange interaction that locally breaks point group symmetries. Using a weak-coupling renormalization group approach and a ladder approximation for the impurity-fermion propagator, we establish that the number of bound states can be controlled by varying the anisotropy of the exchange interaction. Our results show that the degeneracy and momentum dependence of the binding energies reflect some distinctive properties of the quadratic band touching.