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Twisted Bilayer Graphene Reveals its Flat Bands under Spin Pumping

PI of Joint-use project: S. Haddad
Host lab: Kato and Osada Groups

Stacking two graphene layers with a relative twist angle θ results in a moiré superstructure which is found to host, in the vicinity of the so-called magic angle θM 1.1˚, unconventional superconductivity and strongly correlated insulating states [1,2]. Such strong electronic correlations originate from the moiré flat bands emerging at the magic angle around the charge neutrality point. The tantalizing signature of the flat bands have been experimentally demonstrated by probing the corresponding peaks of the density of states using transport, electronic compressibility measurements, scanning tunneling microscopy (STM) and spectroscopy (STS). The direct evidence of these flat bands has been reported by angle resolved photoemission spectroscopy (ARPES). However, spectroscopic measurements on magic-angle twisted bilayer graphene (TBG) raise many technical challenges related to the need of an accurate control of the twist angle, and the necessity to have non-encapsulated samples which can degrade in air.

Recently, we proposed a noninvasive method to probe the flat bands of TBG and accurately determine the magic angle [3]. This method is based on spin pumping induced by ferromagnetic resonance, where the increase in the FMR linewidth provides insight into the spin excitations of the nonmagnetic material adjacent to the ferromagnet. The linewidth increase is given by the Gilbert damping (GD) coefficient.

We theoretically study a planar junction of a ferromagnetic insulator (FI) and a TBG adjacent to a monolayer of transition metal dichalcogenides (TMD), as WSe2 (TBG/WSe2). We show a schematic figure of a FI/TBG planar junction adjacent to WSe2 under a microwave of a frequency Ω in Fig. 1 (a). We consider the case where a microwave of a frequency Ω is applied to this junction and focus on the twist angle dependence of the FMR linewidth. We calculated the correction to the Gilbert damping (GD) coefficient, induced by the adjacent heterostructure TBG/WSe2. We take into account the relatively strong spin-orbit interaction (SOI) induced by the WSe2 in TBG.

We formulated the FMR linewidth based on the perturbation method with respect to an interfacial exchange coupling in this setup and discussed its twist angle dependence. We described the heterostructure TBG/WSe2 by the continuum model including the SOI based on Ref. [4] and evaluated the increase of the effective Gilbert damping coefficient of the FMR linewidth.

In Fig. 1(b) we depicted the behavior of δαG as a function of the twist angle θ for several temperatures for a clean interface. This figure shows that regardless of the temperature range, δαG increases by decreasing θ but drops sharply at the magic angle, where it exhibits a relatively small peak which is smeared out at low temperature. We also discussed the case of a dirty interface and showed that the Gilbert damping correction drops at the magic angle as found in the case of a clean interface.

Our result provides an accurate determination method of the magic angle and an estimation of the SOC induced in TBG by its proximity to the TMD layer. Our proposed setup can be readily implemented regarding the state-of-the art of the experimental realizations of spin pumping in 2D materials and TBG-based heterostructure. Our work opens the gate to a twist tunable spintronics in twisted layered heterostructures.

This project has been performed as a joint study with Sonia Haddad, who was a visiting professor of ISSP in the academic year 2022.


References
  • [1] Y. Cao et al., Nature, 556, 80 (2018).
  • [2] M. Yankowitz et al., Science 363, 1059 (2019).
  • [3] S. Haddad, T. Kato, J. Zhu, and L. Mandhour, Phys. Rev. B 108, L121101 (2023).
  • [4] H. S. Arora et al., Nature 583, 379 (2020).
Authors
  • S. Haddada,b, T. Kato, J. Zhub, and L. Mandhoura
  • aUniversité Tunis El Manar
  • bMax Planck Institute for the Physics of Complex Systems