Functional renormalization group for a large moiré unit cell

Physical review. B./Physical review. B, vol. 102

Abstract

Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states. For the exploration of these, renormalization group methods are an appropriate, flexible tool that takes into account the mutual influence of competing tendencies. Here we show that, within reasonable, nontrivial approximations, the functional renormalization group known from simpler two-dimensional systems can be employed for the large-unit cell moir\'e superlattices with more than 10 000 bands, remedying the need to employ ad hoc restrictions to effective low-energy theories of a few bands and/or effective continuum theories. This provides a description on the atomic scale, allowing one to absorb available ab initio information on the model parameters and therefore lending the analysis a more concrete quantitative character. For the case of twisted bilayer graphene models, we explore the leading ordering tendencies, depending on the band filling and the range of interactions. The results indicate a delicate balance between distinct magnetically ordered ground states, as well as the occurrence of a charge modulation within the moir\'e unit cell for sufficiently nonlocal repulsive interaction.

Authors 3

1. Lennart Klebl Aachen Institute for Theory of Statistical Physics

   RWTH Aachen University · Jülich Aachen Research Alliance

   Affiliation as printed

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

2. Dante Marvin Kennes 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

3. Carsten Honerkamp Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany