Two-dimensional scattering and bound states of polar molecules in bilayers

TL;DR

This paper investigates how specific interaction potentials affect weakly-bound states and scattering in two-dimensional systems, with a focus on polar molecules in bilayer configurations, revealing anomalously weak bound states that alter scattering behavior.

Contribution

It introduces the concept of potentials with zero-momentum Born approximation leading to anomalously weak bound states in 2D, relevant for polar molecules in bilayers.

Findings

Weakly-bound states significantly influence 2D scattering properties.

Potentials with zero-momentum Born approximation cause anomalously weak bound states.

Implications for polar molecule bilayer experiments.

Abstract

Low-energy two-dimensional scattering is particularly sensitive to the existence and properties of weakly-bound states. We show that interaction potentials $V(r)$ with vanishing zero-momentum Born approximation $\int d^2r V(r)=0$ lead to an anomalously weak bound state which crucially modifies the two-dimensional scattering properties. This anomalous case is especially relevant in the context of polar molecules in bilayer arrangements.