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

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. Access through your institution Buy or subscribe This is a preview of subscription content, access via

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subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS QUASIPARTICLE AND SUPERFLUID DYNAMICS IN MAGIC-ANGLE GRAPHENE Article Open access 08 May 2025

EVOLUTION OF THE FLAT BAND AND THE ROLE OF LATTICE RELAXATIONS IN TWISTED BILAYER GRAPHENE Article 24 April 2024 UNCONVENTIONAL NON-LOCAL RELAXATION DYNAMICS IN A TWISTED TRILAYER GRAPHENE

MOIRÉ SUPERLATTICE Article Open access 08 December 2022 DATA AVAILABILITY All data in the main text and extended figures, as well as the code for data analysis, are available from Open

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graphene. OSF https://osf.io/8kqh3 (2024). Download references 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 * Department of Physics, University of California at Santa Barbara, Santa

Barbara, CA, USA Tian Xie, Siyuan Xu, Zhiyuan Cui & Chenhao Jin * Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena,

CA, USA Zhiyu Dong * 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 * Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan Kenji Watanabe * Research Center for Materials Nanoarchitectonics,

National Institute for Materials Science, Tsukuba, Japan Takashi Taniguchi * Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA Leonid S. Levitov Authors * Tian

Xie View author publications You can also search for this author inPubMed Google Scholar * Siyuan Xu View author publications You can also search for this author inPubMed Google Scholar *

Zhiyu Dong View author publications You can also search for this author inPubMed Google Scholar * Zhiyuan Cui View author publications You can also search for this author inPubMed Google

Scholar * Yunbo Ou View author publications You can also search for this author inPubMed Google Scholar * Melike Erdi View author publications You can also search for this author inPubMed 

Google Scholar * Kenji Watanabe View author publications You can also search for this author inPubMed Google Scholar * Takashi Taniguchi View author publications You can also search for this

author inPubMed Google Scholar * Seth A. Tongay View author publications You can also search for this author inPubMed Google Scholar * Leonid S. Levitov View author publications You can

also search for this author inPubMed Google Scholar * Chenhao Jin View author publications You can also search for this author inPubMed Google Scholar 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. CORRESPONDING AUTHOR Correspondence to Chenhao Jin. ETHICS

DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Nature_ thanks Minhao He and the other, anonymous, reviewer(s) for their

contribution to the peer review of this work. Peer reviewer reports are available. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional

claims in published maps and institutional affiliations. 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 _R_xx 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 _R_xx. 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

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 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 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 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 Transient RC of

device D2 on electron-doing side at pump probe delays from −4.667 ps to 55.333 ps. SUPPLEMENTARY VIDEO 6 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. PEER REVIEW FILE RIGHTS AND PERMISSIONS Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to

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terms of such publishing agreement and applicable law. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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 Download citation * Received: 12 March 2024 * Accepted: 25 July 2024 * Published:

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