Abstract
Peculiar electron–phonon interaction characteristics underpin the ultrahigh mobility1, electron hydrodynamics2,3,4, superconductivity5 and superfluidity6,7 observed in graphene heterostructures. The Lorenz ratio between the electronic thermal conductivity and the product of the electrical conductivity and temperature provides insight into electron–phonon interactions that is inaccessible to past graphene measurements. Here we show an unusual Lorenz ratio peak in degenerate graphene near 60 kelvin and decreased peak magnitude with increased mobility. When combined with ab initio calculations of the many-body electron–phonon self-energy and analytical models, this experimental observation reveals that broken reflection symmetry in graphene heterostructures can relax a restrictive selection rule8,9 to allow quasielastic electron coupling with an odd number of flexural phonons, contributing to the increase of the Lorenz ratio towards the Sommerfeld limit at an intermediate temperature sandwiched between the low-temperature hydrodynamic regime and the inelastic electron–phonon scattering regime above 120 kelvin. In contrast to past practices of neglecting the contributions of flexural phonons to transport in two-dimensional materials, this work suggests that tunable electron–flexural phonon coupling can provide a handle to control quantum matter at the atomic scale, such as in magic-angle twisted bilayer graphene10 where low-energy excitations may mediate Cooper pairing of flat-band electrons11,12.
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Acknowledgements
We thank B. Fallahazad, K. Kim and Y. Wang for discussions on dry transfer of two-dimensional heterostructures. The experimental and DFT computational efforts were respectively supported by an award (DE-FG02-07ER46377) from the Physical Properties of Materials Program and an award (DE-SC0020129) from the Computational Materials Sciences Program of US Department of Energy Office of Basic Energy Science. Development of the analytical models was supported by a Multidisciplinary University Research Initiative (MURI) award (N00014-21-1-2377) from the US Office of Naval Research. Development of the heterostructure transfer technique was supported by the Army Research Office under grant no. W911NF-17-1-0312. The measurement device was fabricated at the Texas Nanofabrication Facility supported by US National Science Foundation (NSF) grant NNCI-1542159. The computation used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231, and the Texas Advanced Computing Center (TACC) at The University of Texas at Austin. Growth of hBN crystals was supported by JSPS KAKENHI (Grant Numbers 19H05790, 20H00354 and 21H05233).
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L.S. initiated the study. M.M.S. and L.S. designed the experiment for the bottom-contacted sample. Y.H. and L.S. designed the experiment for the edge-contacted and hybrid-contacted samples. E.T. designed the 2D heterostructure transfer method. M.M.S. and Y.H. designed and fabricated the measurement devices, and conducted the measurements, data analysis and numerical simulations for the bottom-contacted and the other three samples, respectively. C.L. and F.G. carried out density functional theoretical calculations. A.H.M. and L.S. developed the analytical models. T.T. and K.W. synthesized the hBN crystals. L.S., M.M.S., Y.H., C.L., F.G., A.H.M. and E.T. wrote the paper with input from T.T. and K.W.
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This Supplementary Information file has 4 sections: 1. Experimental Methods; 2. Theoretical Analysis; 3 Density Functional Theory (DFT) Calculations; 4. Simplified Models. There are 23 Supplementary figures, 2 Supplementary tables and additional references.
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Sadeghi, M.M., Huang, Y., Lian, C. et al. Tunable electron–flexural phonon interaction in graphene heterostructures. Nature 617, 282–286 (2023). https://doi.org/10.1038/s41586-023-05879-y
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DOI: https://doi.org/10.1038/s41586-023-05879-y
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