Magnetic ordering in moiré graphene multilayers from a continuum Hartree+ U approach

Nanotechnology, vol. 37, pp. 035001

Abstract

Abstract Recently, symmetry-broken ground states, such as correlated insulating states, magnetic order and superconductivity, have been discovered in twisted bilayer graphene (tBLG) and twisted trilayer graphene (tTLG) near the so-called magic angles. Understanding the magnetic order in these systems is challenging, however, as atomistic methods become extremely expensive near the magic angle and continuum approaches fail to capture important atomistic details. In this work, we develop an approach to incorporate short-ranged Hubbard interactions self-consistently in a continuum model. In addition, we include long-ranged Coulomb interactions which are known to be important when doping the flat bands of tBLG and tTLG. Therefore, for the first time, magnetic order in moiré graphene multilayers is self-consistently explored in a continuum model with atomistic detail. With this approach, we perform a systematic analysis of the magnetic phase diagram of tBLG as a function of doping level and twist angle, near the magic angle. Our results are consistent with previous perturbative atomistic Hartree+ U calculations. Furthermore, we investigated magnetic order of tTLG, which were found to be similar to those in tBLG. In the future, the developed continuum model can be utilized to investigate magnetic ordering tendencies from short-range exchange interactions in other moiré graphene multilayers as a function of doping, twist angle, screening environment, among other variables.

Authors 7

1. Christopher T. S. Cheung corresponding

   Imperial College London · Thomas Young Centre

   Affiliation as printed

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

   Materials, Imperial College London, Department of Materials, Imperial College London, London, SW7 2AZ, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND

2. Valerio Vitale corresponding

   Scuola Internazionale Superiore di Studi Avanzati · Imperial College London · University of Trieste · National Research Council · Thomas Young Centre · Istituto Officina dei Materiali

   Affiliation as printed

   CNR-IOM-Istituto Officina dei Materiali, National Research Council of Italy, c/o SISSA Via Bonomea 265, Trieste IT-34136, Italy

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

   Dipartimento di Fisica, Università degli Studi di Trieste, strada costiera 11, 34151 Trieste, Italy

   National Research Council of Italy, CNR-IOM-Istituto Officina dei Materiali, c/o SISSA Via Bonomea 265, Trieste , IT-34136, ITALY

3. Lennart Klebl corresponding

   University of Würzburg · Complexity, Topology and Dynamics in Quantum Matter

   Affiliation as printed

   Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany

   Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Würzburg, 97070, GERMANY

4. Ammon Fischer corresponding Aachen Institute for Theory of Statistical Physics

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

   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, Otto-Blumenthal-Straße 26, Aachen, Nordrhein-Westfalen, 52056, GERMANY

5. Dante Marvin Kennes corresponding Aachen Institute for Theory of Statistical Physics

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

   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

   RWTH Aachen University and JARA –, Institute for Theory of Statistical Physics, Aachen, 52056, GERMANY

6. Arash A. Mostofi corresponding

   Imperial College London · Thomas Young Centre

   Affiliation as printed

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

   Department of Materials, Imperial College London, South Kensington Campus, London, SW7 2AZ, London, SW7 2AZ, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND

7. Zachary A. H. Goodwin corresponding

   Imperial College London · University of Oxford · Harvard University · Thomas Young Centre

   Affiliation as printed

   Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom

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

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

   Materials, Oxford University, Parks Road, Oxford, OX1 2JD, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND