RKKY in half-filled bipartite lattices: graphene as an example

Abstract

We first present a simple proof that for any bipartite lattice at half filling the RKKY interaction is antiferromagnetic between impurities on opposite (i.e., A and B) sublattices and is ferromagnetic between impurities on the same sublattices. This result is valid on all length scales. We then focus on the honeycomb lattice and examine the theorem in the long distance limit by performing the low energy calculation using Dirac electrons. To find the universal (cutoff free) result we perform the calculation in smooth cutoff schemes, as we show that the calculation based on a sharp cutoff leads to wrong results. We also find the long distance behavior of the RKKY interaction between "plaquette" impurities in both coherent and incoherent regimes.

v3. The published version. 6 pages, 1 figure

References in corpus (5)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• "Deconfined" quantum critical points
• Local defects and ferromagnetism in graphene layers
• Exchange interaction of magnetic impurities in graphene
• Quantum critical point in the Kondo-Heisenberg model on the honeycomb lattice

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