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 take into account the mutual influence of competing tendencies. Here we show that, within reasonable, non-trivial 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 non-local repulsive interaction.
Highlights
In recent years, the field of two-dimensional materials has made major experimental and theoretical leaps, which led to many fascinating discoveries and have broadened our spectrum on available phases of matter in these highly controllable structures
We show that the treatment of twisted graphene bilayers close to the so-called magic angle using these approximations, resolving all individual carbon sites in the large moiré unit cell, yields similar results to what we know from our previous study using the random-phase approximation (RPA) of the crossed particle-hole channel [41]
The three main types of ordering found as runaway flows in this paper are shown in terms of their leading eigenvectors in Fig. 5: (a) ferromagnetic order throughout the unit cell with some residual antiferromagnetism on the carbon-carbon-bond scale in the AB regions, (b) nodal antiferromagnetic order with a sign change of the antiferromagnetic order parameter on the atomic scale around the AA regions, and (c) chargemodulated states that form a honeycomb lattice of the AB and BA regions
Summary
The field of two-dimensional materials has made major experimental and theoretical leaps, which led to many fascinating discoveries and have broadened our spectrum on available phases of matter in these highly controllable structures. Examples of these findings include superconducting [1,2] or magnetic [3] phases realized down to the monolayer limit and, related to that, the discovery of quantum anomalous Hall behavior in thin films [4,5,6,7,8,9,10,11], with potentially far-reaching technological applications in the realm of spintronics and quantum computing.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
