Zero-mode anomaly in the RKKY interaction on bipartite lattices

TL;DR

This paper investigates the influence of zero modes on the RKKY interaction in bipartite lattices like graphene, revealing that zero modes significantly alter the expected magnetic interactions and challenge existing sign rules.

Contribution

The study introduces SUSY quantum mechanics to analyze zero modes in bipartite lattices, showing their critical role in determining the sign of RKKY interactions.

Findings

RKKY interaction between different sublattices is always antiferromagnetic.

Same sublattice RKKY interaction is not always ferromagnetic.

Zero modes are crucial in understanding magnetic interactions on bipartite lattices.

Abstract

Carrier-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction plays an important role in itinerant magnetism. There have been intense interest on its general trend on bipartite lattice with particle-hole symmetry. In particular, recently fabricated graphene is well described by the honeycomb lattice within tight-binding approximation. We use SUSY quantum mechanics to study the RKKY interaction on bipartite lattices. The SUSY structure naturally differentiate the zero modes and those paired states at finite energies. The significant role of zero modes is largely ignored in previous literature because their measure is often zero in the thermodynamic limit. Employing both real-time and imaginary-time formalism, we arrive at the same conclusion: The RKKY interaction for impurity spins on different sublattices is always antiferromagnetic. However, for impurity spins on the same sublattice, the carrier-mediated RKKY interaction is not always ferromagnetic. Only in the absence of zero modes, the sign rule on the bipartite lattice holds true. Our finding highlight the importance of the zero modes in bipartite lattices. Their significance needs further investigation and may lead to important advances in carrier-mediated magnetism.