Electronic, quantum transport and magnetic properties in twisted bilayer graphene

  The Moiré pattern of the magic-angle twisted bilayers graphene and twisted bilayer MoS₂ leads to localization of the low energy electrons in the AA-stacking regions, reflected by very flat bands at low energy.^[1],[2] This reduction of the kinetic energy enhances the relative importance of interactions and thus renders the bilayer systems much more susceptible to correlation effects, as show experimentally by the discovery of correlated insulators and superconductivity.^[3] Despite numerous theoretical and experimental studies, the understanding of this new electronic localization is still incomplete. The rotation angle is of course a key parameter, but we have also shown that a small expansion or contraction of one layer with respect to the other (“heterostrain”) can strongly modify the electronic structure of flat bands.^[4]

  Here we present theoretical study of the electronic structure and quantum scattering properties of charge carriers with electronic flat bands, taking into account as well as possible the structural parameters that condition them (rotation angle, bias voltage,^[5] heterostrain and/or local defects^[6]). We also investigate the magnetic instabilities using a combination of real-space Hartree-Fock and dynamical mean-field theories, starting from a tight-binding description of the non-interacting bilayer systems to which we add a local Hubbard interaction U in order to model the Coulomb repulsion between electron.^[7] We find that localized magnetic states emerge for values of the Coulomb interaction U that is significantly smaller than what would be required to render an isolated layer antiferromagnetic. We also show how heterostrain strongly modifies the magnetization and the local magnetic order for realistic values of U.

*Ref
 ^[1] R. Bistritzer, A.H. MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011).
 ^[2] G. Trambly de Laissardière, D. Mayou, L. Magaud, Nano Lett. 10, 804 (2010). S. Venkateswarlu, A. Honecker, G. Trambly de Laissardière, Phys. Rev. B 102, 081103(R) (2020).
 ^[3] Y. Cao et al., Nature 556, 43 (2018); Nature 556, 80 (2018).
 ^[4] L. Huder et al., Phys. Rev. Lett. 120, 156405 (2018).
      F. Mesple et al., Phys. Rev. Lett. 127, 126405 (2021).
 ^[5] G. Trambly de Laissardière et al., Phys. Rev. B 93, 235135 (2016).
 ^[6] O. F. Namarvar et al., Phys. Rev. B 101, 245407 (2020).
 ^[7] V. Vahedi et al., SciPost Phys. 11, 083 (2021).