Short Versus Long Range Exchange Interactions in Twisted Bilayer Graphene

Advanced Physics Research, vol. 2

Abstract

Abstract This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle band structure of TBG with Hubbard interactions for three magnetic orderings: modulated anti‐ferromagnetic (MAFM), (NAFM) and hexagonal anti‐ferromagnetic (HAFM). Then, it develops an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, it observes a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, the HF potential plays a major role in the band structure, with HAFM and MAFM being secondary effects, but NAFM appears to still significantly distort the electronic structure at the magic angle. These findings suggest that the spin‐valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favor magnetic order, since the atomistic Hubbard interaction will break this symmetry in favor of spin polarization.

Authors 9

1. Alejandro Jimeno‐Pozo corresponding

   IMDEA Nanoscience

   Affiliation as printed

   Imdea Nanoscience Faraday 9 28049 Madrid Spain

   Imdea Nanoscience, Faraday 9, 28049 Madrid, Spain

2. Zachary A. H. Goodwin

   Harvard University · Thomas Young Centre · Imperial College London

   Affiliation as printed

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials Imperial College London South Kensington Campus London SW7 2AZ UK

   John A. Paulson School of Engineering and Applied Sciences Harvard University Cambridge MA 02138 USA

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ UK

   John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138 USA

3. Pierre A. Pantaleón

   IMDEA Nanoscience

   Affiliation as printed

   Imdea Nanoscience Faraday 9 28049 Madrid Spain

   Imdea Nanoscience, Faraday 9, 28049 Madrid, Spain

4. Valerio Vitale

   University of Trieste · Thomas Young Centre · Imperial College London

   Affiliation as printed

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials Imperial College London South Kensington Campus London SW7 2AZ UK

   Dipartimento di Fisica Università di Trieste Strada Costiera 11 34151 Trieste Italy

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ UK

5. Lennart Klebl

   Universität Hamburg

   Affiliation as printed

   I. Institute of Theoretical Physics University of Hamburg Notkestrasse 9 22607 Hamburg Germany

   I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany

6. Dante Marvin Kennes Aachen Institute for Theory of Statistical Physics

   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

   Institute for Theory of Statistical Physics RWTH Aachen University, and JARA Fundamentals of Future Information Technology 52062 Aachen Germany

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

   Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany

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

7. Arash A. Mostofi

   Thomas Young Centre · Imperial College London

   Affiliation as printed

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials Imperial College London South Kensington Campus London SW7 2AZ UK

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ UK

8. Johannes Lischner

   Thomas Young Centre · Imperial College London

   Affiliation as printed

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials Imperial College London South Kensington Campus London SW7 2AZ UK

   Departments of Physics and Materials and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ UK

9. Francisco Javier Esteban Guinea

   IMDEA Nanoscience · Donostia International Physics Center

   Affiliation as printed

   Donostia International Physics Center Paseo Manuel de Lardizabal 4 20018 San Sebastian Spain

   Imdea Nanoscience Faraday 9 28049 Madrid Spain

   Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastian, Spain

   Imdea Nanoscience, Faraday 9, 28049 Madrid, Spain