This work is supported primarily by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract number DE-AC02-76SF00515, the Stanford Linear Accelerator (SLAC) National Accelerator Laboratory, the Stanford Institute for Materials and Energy Sciences (E.J.S., C.M.N., C.D.P., E.M., T.P.D., T.F.H., A.M.L.). E.J.S. acknowledges additional support from Stanford GLAM Postdoctoral Fellowship Program. C.M.N. acknowledges additional support from the National Science Foundation (NSF) through a Graduate Research Fellowship (DGE-114747). T.F.H. acknowledges additional funding for analysis from the Gordon and Betty Moore Foundation EPiQS Initiative through grant number GBMF4545. S.J.P. is supported by the US Department of Energy (DE-SC0012375). M.C.H. is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number 2015-SLAC-100238-Funding. B.K.O.-O. acknowledges support from the DOE Office of Science, Fusion Energy Science, under grant number FWP 100182. N.F. acknowledges support from the Stewardship Science Graduate Fellowship programme, provided under cooperative agreement number DE-NA0002135. Synthesis of MoTe 2 and sample preparation were supported by the US Department of Energy, DE-SC0016703 (D.R., D.C., A.A., J.H.). L.B. acknowledges the US Army Research Office MURI grant W911NF-11-1-0362. The National High Magnetic Field Laboratory is supported by the NSF through NSF/DMR-1157490, NSF/DMR-1644779 and the State of Florida. First-principles calculations by C.D.P. were supported by the TIMES programme at SLAC. Numerical simulations were performed using computational resources at the National Energy Research Scientific Computing Center (NSERC). The UED work was performed at SLAC MeV-UED, which is supported in part by the DOE BES SUF Division Accelerator & Detector R&D programme, the LCLS Facility and SLAC under contracts DE-AC02-05-CH11231 and DE-AC02-76SF00515. The authors thank D. Pikulin and B. Moritz for discussions and G. Stewart for the illustration of the UED setup.

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Nature thanks C. Ropers and the other anonymous reviewer(s) for their contribution to the peer review of this work.