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Long-lived isospin excitations in magic-angle twisted bilayer graphene

Nature volume 633, pages 77–82 (2024)Cite this article

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Abstract

Numerous correlated many-body phases, both conventional and exotic, have been reported in magic-angle twisted bilayer graphene (MATBG)1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24. However, the dynamics associated with these correlated states, crucial for understanding the underlying physics, remain unexplored. Here we combine exciton sensing and optical pump–probe spectroscopy to investigate the dynamics of isospin orders in MATBG with WSe2 substrate across the entire flat band, achieving sub-picosecond resolution. We observe remarkably slow isospin dynamics in a broad filling range around ν = 2 and between ν = −3 and −2, with lifetimes of up to 300 ps that decouple from the much faster cooling of electronic temperature (about 10 ps). This non-thermal behaviour demonstrates the presence of abnormally long-lived modes in the isospin degrees of freedom. This observation, not anticipated by theory, implies the existence of long-range propagating collective modes, strong isospin fluctuations and memory effects and is probably associated with an intervalley coherent or incommensurate Kekulé spiral ground state. We further demonstrate non-equilibrium control of the isospin orders previously found around integer fillings. Specifically, through ultrafast manipulation, it can be transiently shifted away from integer fillings. Our study demonstrates a unique probe of collective excitations in MATBG and paves the way for actively controlling non-equilibrium phenomena in moiré systems.

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Fig. 1: Exciton sensing of isospin orders and dynamics in MATBG.
Fig. 2: Filling-dependent dynamics in MATBG.
Fig. 3: Decoupling between the charge and isospin dynamics.
Fig. 4: Ultrafast manipulation of the cascade features.

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Data availability

All data in the main text and extended figures, as well as the code for data analysis, are available from Open Science Framework60.

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Acknowledgements

We acknowledge discussions with A. Young and L. Balents. C.J. acknowledges support from the Air Force Office of Scientific Research under award FA9550-23-1-0117. The sample fabrication is supported by the National Science Foundation through a CAREER award DMR-2337606. T.X. acknowledges the support from the National Science Foundation Graduate Research Fellowship under grant no. 2139319. L.S.L. acknowledges the support from the Science and Technology Center for Integrated Quantum Materials, National Science Foundation grant no. DMR1231319. S.A.T. acknowledges primary support from DOE-SC0020653 (materials synthesis), DMR 2111812, DMR 2206987 and CMMI 2129412 (manufacturing). S.A.T. acknowledges support from the Lawrence Semiconductor Labs. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 20H00354 and 23H02052) and the World Premier International Research Center Initiative (WPI), MEXT, Japan.

Author information

Authors and Affiliations

  1. Department of Physics, University of California at Santa Barbara, Santa Barbara, CA, USA

    Tian Xie, Siyuan Xu, Zhiyuan Cui & Chenhao Jin

  2. Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    Zhiyu Dong

  3. Materials Science and Engineering, School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA

    Yunbo Ou, Melike Erdi & Seth A. Tongay

  4. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  5. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  6. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Leonid S. Levitov

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Contributions

C.J. conceived and supervised the project. S.X., Z.C. and T.X. fabricated the device. T.X. performed the measurements and analysed the data. Z.D. and L.S.L. contributed to the theoretical interpretation. Y.O., M.E. and S.A.T. grew the WSe2 crystals. K.W. and T.T. grew the hBN crystals. C.J. wrote the paper with input from all the authors.

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Correspondence to Chenhao Jin.

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Extended data figures and tables

Extended Data Fig. 1 Dynamics in MATBG device D2 (1.06° twisted).

(a) Equilibrium RC. (b) Pump-induced RC change (ΔRC) at representative filling factors and temperature of 2.5 K. Prominent slowing-down in relaxation is observed over a broad range of fillings near v = 2. (c) ΔRC at the WSe2 2 s exciton resonance across the entire flatband and (d) the filling-dependent lifetime from single exponential fitting. The slowing-down is maximized around v = 2.1 and −2.3, consistent with the observation in device D1. Vertical dashed lines label even fillings between v = ±4 as guide to the eye. (e) (f) ΔRC at v = 2.04 (e) and v = 3.99 (f) over a larger delay range of 300 ps. Their relaxation dynamics are compared in (g). The dynamics at v = 3.99 is well-described by a single-component decay with a lifetime of 60 ps (blue symbols and lines); while the dynamics at v = 2.04 shows two fully separable timescales with lifetime of 15 ps and 315 ps, respectively.

Extended Data Fig. 2 Dynamics in non-magic-angle TBG device D3 (1.14° twisted).

(a) Equilibrium RC. (b) Pump-induced RC change at temperature of 2.5 K and representative fillings. No apparent slowing-down is observed near v = 2.

Extended Data Fig. 3 Pump fluence dependence.

(a) Pump-induced RC change for device D1 at v = 2.07 under three representative pump fluences. (b) Comparison between the relaxation dynamics. The fast component shows sensitive pump fluence dependence due to different initial electronic temperature, as expected from the charge dynamics. In contrast, the slow component is insensitive to the pump fluence, indicating a complete decoupling between the isospin and charge dynamics.

Extended Data Fig. 4 Temperature dependence of Equilibrium RC.

The cascade features become weaker and broader at higher temperatures but do not show apparent shift in fillings.

Extended Data Fig. 5 Extraction of 2 s exciton energy.

(a) Representative RC of device D1 with the extracted 2 s exciton energy overlaid on top (green line). (b) Filling-dependent 2 s exciton energy (blue) and a fitted 3rd-order polynomial accounting for the smooth background redshift (orange). (c) The background-subtracted 2 s exciton energy (blue line) shows clear peaks from the cascade features, whose locations are obtained by a peak finding algorithm (orange arrows).

Extended Data Fig. 6 Probe fluence and pump wavelength dependence.

(a) RC of device D4 without pump and under representative probe fluences. The cascade features are blurred at higher probe fluence. On the other hand, the impacts from the probe light are negligible at probe fluence of 46.7 nJ/cm2, which we have used throughout our measurements. (b) (c) Pump-induced RC change at v = −2.36 (b) and v = 2.05 (c) with pump wavelengths of 800, 900, and 1000 nm and pump fluence of 1.84 μJ/cm2. The signal remains largely unchanged across these pump wavelengths, confirming that the pump is selectively exciting MATBG and the WSe2 layer remains a passive sensor.

Extended Data Fig. 7 Dynamics in MATBG device D4 (0.95° twisted).

(a) Equilibrium RC. (b) Pump-induced RC change of device D4 at representative filling factors and temperature of 2.5 K. Prominent slowing-down in relaxation is observed over a broad range of fillings between v = −3 and −2. (c) ΔRC at the WSe2 2 s exciton resonance across the entire flatband. (d) Filling-dependent lifetime from single exponential fitting (blue curve) and longitudinal resistance Rxx from in-situ four-point transport measurement (orange curve). The slowing-down on the hole-doping side is maximized around v = −2.4, a gapless metallic state, consistent with the observation in device D1 and D3. (e) Temperature dependence of longitudinal resistance Rxx.

Extended Data Fig. 8 Illustration of weakly damped isospin Goldstone mode in a metallic state.

The energy-momentum dispersion of the isospin particle-hole continuum can have a finite gap at q = 0, allowing the Goldstone mode to remain weakly damped.

Supplementary information

Supplementary Video 1 (download AVI )

Transient RC of device D1 on the electron-doped side at pump–probe delays from −3.667 ps to 136.333 ps.

Supplementary Video 2 (download AVI )

Transient RC of device D1 on the hole-doped side at pump–probe delays from −3.667 ps to 141.8 33 ps.

Supplementary Video 3 (download AVI )

Pump-induced RC change (ΔRC) of device D1 (about 1.04° twist) at filling factors from ν = −5.19 to ν = 5.19.

Supplementary Video 4 (download AVI )

Pump-induced RC change (ΔRC) of non-magic-angle device D3 (about 1.14° twist) at different filling factors from ν = −4.87 to ν = 5.07.

Supplementary Video 5 (download AVI )

Transient RC of device D2 on electron-doing side at pump probe delays from −4.667 ps to 55.333 ps.

Supplementary Video 6 (download AVI )

Pump-induced RC change (ΔRC) of non-magic-angle device D4 (about 0.95° twist) at different filling factors from ν = −4.76 to ν = 5.13.

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Xie, T., Xu, S., Dong, Z. et al. Long-lived isospin excitations in magic-angle twisted bilayer graphene. Nature 633, 77–82 (2024). https://doi.org/10.1038/s41586-024-07880-5

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