RKKY interaction in one-dimensional flat-band lattices

Physical review. B./Physical review. B, vol. 108

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band in the energy spectrum. Importantly, these features are not captured by the conventional RKKY approximation based on nondegenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a nonperturbative approach becomes necessary in the absence of a gap.

Authors 7

1. Katharina Laubscher

   University of Basel

   Affiliation as printed

   Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

2. Clara S. Weber Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · University of Pennsylvania · RWTH Aachen University

   Affiliation as printed

   Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA - Fundamentals of Future Information Technology, D-52056 Aachen, Germany

3. Maximilian Hünenberger

   University of Basel

   Affiliation as printed

   Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

4. Herbert Schoeller Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA - Fundamentals of Future Information Technology, D-52056 Aachen, Germany

5. Dante Marvin Kennes Aachen Institut für Theorie der Statistischen Physik

   Jülich Aachen Research Alliance · Center for Free-Electron Laser Science · Max Planck Institute for the Structure and Dynamics of Matter · RWTH Aachen University

   Affiliation as printed

   Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA - Fundamentals of Future Information Technology, D-52056 Aachen, Germany

   Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany

6. Daniel Loss

   University of Basel

   Affiliation as printed

   Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

7. Jelena Klinovaja

   University of Basel

   Affiliation as printed

   Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland