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Dirac revivals drive a resonance response in twisted bilayer graphene


Collective excitations contain key information regarding the electronic order of the ground state of strongly correlated systems. Various collective modes in the spin and valley isospin channels of magic-angle graphene moiré bands have been alluded to by a series of recent experiments. However, a direct observation of collective excitations has been impossible due to the lack of a spin probe. Here we observe low-energy collective excitations in twisted bilayer graphene near the magic angle, using a resistively detected electron spin resonance technique. Two independent observations show that the generation and detection of microwave resonance relies on the strong correlations within the flat moiré energy band. First, the onset of the resonance response coincides with the spontaneous flavour polarization at moiré half-filling, but is absent in the isospin unpolarized density range. Second, we perform the same measurement on various systems that do not have flat bands and observe no indication of a resonance response in these samples. Our explanation is that the resonance response near the magic angle originates from Dirac revivals and the resulting isospin order.

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Fig. 1: Microwave-induced transport response in TBG.
Fig. 2: Density dependence and magnetic anisotropy.
Fig. 3: Antiferromagnetic intervalley coupling and the value of JH.
Fig. 4: Spin stiffness and dispersion.

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Source data are available for this paper. All other data that support the findings of this study are available from the corresponding authors upon reasonable request.


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A.M and J.I.A.L. thank R. Cong for the critical review of the manuscript. E.M. acknowledges funding from the National Defense Science and Engineering Graduate (NDSEG) Fellowship. J.-X.L. and J.I.A.L. acknowledge funding from NSF DMR-2143384. The device fabrication was performed at the Institute for Molecular and Nanoscale Innovation at Brown University. J.P. and L.Z. acknowledge support from the Cowen Family Endowment at MSU. K.W. and T.T. acknowledge support from the EMEXT Element Strategy Initiative to Form Core Research Center by grant no. JPMXP0112101001 and the CREST(JPMJCR15F3), JST. Sandia National Laboratories is a multi-mission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy (DOE)’s National Nuclear Security Administration under contract DE-NA0003525. This work was funded, in part, by the Laboratory Directed Research and Development Program and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the US DOE, Office of Science. This paper describes the objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the US DOE or the US government.

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Authors and Affiliations



J.-X.L. and E.M. fabricated the device. E.M, A.M., D.S., L.Z. and J.P. performed the measurements. E.M., A.M. and J.I.A.L. analysed the data. E.M., M.S.S., A.M. and J.I.A.L. wrote the manuscript. S.L., D.R. and J.H. provided the WSe2 crystals. K.W. and T.T. provided the hexagonal boron nitride crystals.

Corresponding authors

Correspondence to Andrew Mounce or J. I. A. Li.

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Competing interests

A provisional patent application has been filed in the USA. by Brown University under serial no. 18/103,290. The inventors include J.I.A.L., A.M., E.M. and J.-X.L. The application, which is pending, contains proposals of two-dimensional material architectures with controllable magnetic states and microwave resonance.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20, Table 1 and discussion.

Source data

Source Data Fig. 1

Source data for the transport measurements in Fig. 1c,e,g.

Source Data Fig. 2

Source data for the transport measurements in Fig. 2a.

Source Data Fig. 3

Source data for the transport measurements in Fig. 3a.

Source Data Fig. 4

Source data for the transport measurements in Fig. 4a,d.

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Morissette, E., Lin, JX., Sun, D. et al. Dirac revivals drive a resonance response in twisted bilayer graphene. Nat. Phys. 19, 1156–1162 (2023).

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