On the Sign of Fermion-Mediated Interactions

TL;DR

This paper introduces a unified framework based on Green's function symmetry classification to determine the sign of fermion-mediated interactions, with a focus on systems exhibiting chiral symmetry.

Contribution

It establishes a theorem for the sign of fermion-mediated interactions in chiral symmetric systems and demonstrates its validity through multiple material examples.

Findings

Theorem for sign determination in chiral symmetric systems

Application to electron-mediated interactions in materials

Framework unifies understanding of interaction signs

Abstract

We develop a unified framework for understanding the sign of fermion-mediated interactions by exploiting the symmetry classification of Green's functions. In particular, we establish a theorem regarding the sign of fermion-mediated interactions in systems with chiral symmetry. The strength of the theorem is demonstrated within multiple examples with an emphasis on electron-mediated interactions in materials.