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Advertisement Advertisement Nature * View all journals * Search * Log in * Explore content * About the journal * Publish with us * Subscribe * Sign up for alerts * RSS feed 1. nature 2. articles 3. article * Article * Published: 15 February 2023 Evidence for Dirac flat band superconductivity enabled by quantum geometry * Haidong Tian^1, * Xueshi Gao^1, * Yuxin Zhang^1, * Shi Che^1, * Tianyi Xu^2, * Patrick Cheung^2, * Kenji Watanabe ORCID: orcid.org/0000-0003-3701-8119^3, * Takashi Taniguchi ORCID: orcid.org/0000-0002-1467-3105^4, * Mohit Randeria^1, * Fan Zhang ORCID: orcid.org/0000-0003-4623-4200^2, * Chun Ning Lau ORCID: orcid.org/0000-0003-2159-6723^1 & * ... * Marc W. Bockrath^1 Show authors Nature volume 614, pages 440-444 (2023)Cite this article * 6206 Accesses * 62 Altmetric * Metrics details Subjects * Electronic properties and devices * Superconducting properties and materials Abstract In a flat band superconductor, the charge carriers' group velocity v [F] is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors^1 and heavy-fermion systems^2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small v[F] in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene^3,4,5,6,7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system^8,9,10,11,12,13. Using Schwinger-limited non-linear transport studies^14,15, we demonstrate an extremely slow normal state drift velocity v[n] [?] 1,000 m s^-1 for filling fraction n between -1/2 and -3/4 of the moire superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid^16. Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution^8,9,10,11,12. We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover^17,18,19, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution Access options Access through your institution Access through your institution Change institution Buy or subscribe Subscribe to Nature+ Get immediate online access to Nature and 55 other Nature journal $29.99 monthly Subscribe Subscribe to Journal Get full journal access for 1 year $199.00 only $3.90 per issue Subscribe All prices are NET prices. VAT will be added later in the checkout. Tax calculation will be finalised during checkout. Buy article Get time limited or full article access on ReadCube. $32.00 Buy All prices are NET prices. Additional access options: * Log in * Learn about institutional subscriptions Fig. 1: Normal state transport of tBLG with th =1.08deg at B = 0.2 T and T = 0.3 K (unless specified otherwise). [41586_2022_5576_Fig1_HTML] Fig. 2: Zero-bias transport data at B = 0. [41586_2022_5576_Fig2_HTML] Fig. 3: Nonlinear transport data in the superconducting regime. [41586_2022_5576_Fig3_HTML] Fig. 4: Superfluid stiffness and characteristic temperatures of the flat band. [41586_2022_5576_Fig4_HTML] Data availability The data that support the findings of this study are available from the corresponding authors on reasonable request. Source data are provided with this paper. Code availability The code that supports the findings of this study is available from the corresponding authors upon reasonable request. References 1. Lee, P. A., Nagaosa, N. & Wen, X.-G. 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T.X., P.C. and F.Z. acknowledge the Texas Advanced Computing Center for providing resources that have contributed to the research results reported in this work. Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233). Author information Authors and Affiliations 1. Department of Physics, The Ohio State University, Columbus, OH, USA Haidong Tian, Xueshi Gao, Yuxin Zhang, Shi Che, Mohit Randeria, Chun Ning Lau & Marc W. Bockrath 2. Department of Physics, The University of Texas at Dallas, Richardson, TX, USA Tianyi Xu, Patrick Cheung & Fan Zhang 3. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan Kenji Watanabe 4. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan Takashi Taniguchi Authors 1. Haidong Tian View author publications You can also search for this author in PubMed Google Scholar 2. Xueshi Gao View author publications You can also search for this author in PubMed Google Scholar 3. Yuxin Zhang View author publications You can also search for this author in PubMed Google Scholar 4. Shi Che View author publications You can also search for this author in PubMed Google Scholar 5. Tianyi Xu View author publications You can also search for this author in PubMed Google Scholar 6. Patrick Cheung View author publications You can also search for this author in PubMed Google Scholar 7. Kenji Watanabe View author publications You can also search for this author in PubMed Google Scholar 8. Takashi Taniguchi View author publications You can also search for this author in PubMed Google Scholar 9. Mohit Randeria View author publications You can also search for this author in PubMed Google Scholar 10. Fan Zhang View author publications You can also search for this author in PubMed Google Scholar 11. Chun Ning Lau View author publications You can also search for this author in PubMed Google Scholar 12. Marc W. Bockrath View author publications You can also search for this author in PubMed Google Scholar Contributions H.T., C.N.L. and M.W.B. conceived the project. H. T., X.G., Y.Z. and S.C. fabricated samples. H.T. X.G. and Y.Z. performed transport measurements. T.X. and P.C. performed theoretical calculations under the supervision of F.Z. K.W. and T.T. provided hBN crystals. H.T., C.N.L. and M.W.B. analysed the data. M.W.B., C.N.L., M.R. and F.Z. interpreted the data and co-wrote the manuscript. All authors discussed and commented on the manuscript. Corresponding authors Correspondence to Chun Ning Lau or Marc W. Bockrath. Ethics declarations Competing interests The authors declare no competing interests. Peer review Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work. 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 R[xx] (V[bg], B) of the device at T = 0.3 K. The numbers on the right indicate the filling factors of the peaks (where the full-filling of the minibands correspond to filling factors \(\widetilde{\nu }\) = +-4). Using the convention that the full-filling of the minibands correspond to filling factor \(\ widetilde{\nu }\) = +-4, we identify a number of peaks at fractional fillings of \(\widetilde{\nu }\) = -0.5, 1.5 and N +- 1/3, where N is an integer. Source data Extended Data Fig. 2 Hall resistance and inferred charge densities. Left: Symmetrized R[xy] versus density. Right: Measured Hall density compared to inferred density from capacitance; the red line has a unit slope to show the agreement between the two. Source data Extended Data Fig. 3 Non-linear transport at B = 0 and higher temperatures. a-b dV/dI versus J and n at T = 5 K, and dV/dI in kO versus J at n = -1 (blue), -2 (green) and -3 (red) x 10^11 cm^-2, respectively. c-d dV/dI in kO versus J and T at n ~ -2.8 and -1.7 x 10^11 cm^-2, respectively. The dV/dI peaks disappear at higher temperatures, which is consistent with an ultra-small Fermi energy of ~1 meV. Source data Extended Data Fig. 4 The shape of Fermi surface in the lab frame for various rescaled drift velocity \({\boldsymbol{\beta }}={{\boldsymbol {v}}}_{{\bf{n}}}/{{\boldsymbol{v}}}_{{\bf{F}}}\). Plot of the Fermi surface for various b versus x and y momentum components p[x] and p[y]. Extended Data Fig. 5 Theoretical modelling of Fermi velocity v[F] and the critical drift velocity v[n]. a \({v}_{{\rm{F}}}\) and \({v}_{{\rm{n}}}\) in units of the Fermi velocity at the Dirac point \({v}_{{\rm{DP}}}\), as well as \({v}_{{\ rm{n}}}/{v}_{{\rm{F}}}\), versus electron density \({n}_{e}\). b the effective masses at Fermi energy, \(\hbar {k}_{{\rm{F}}}/{v}_{{\rm {F}}}\) in theory and \(\hbar {k}_{{\rm{F}}}/{v}_{{\rm{n}}}\) in measurements, in units of the bare electron mass \({m}_{e}\) as functions of the electron density \({n}_{e}\). Source data Extended Data Fig. 6 Comparison between velocity measured from quantum Hall effect, Shubnikov-de Hass oscillations and non-linear transport measurements near charge neutrality. a dV/dI versus density n and bias current I for device D2 with th = 1.06o. Peaks due to the Schwinger effect are indicated by the red dashed lines. b R[xx] versus n at T = 30, 25, 20, 18, 12, 10, 7, 5 and 2.02 K, respectively (blue to black). Inset: Activation plot of R [xx] measured in the quantum Hall n[q] = 4 valley indicated by the arrow in the main panel taken at B = 4 T. c-d Same as a-b but for device D3. Inset in c: Zoom-in of same data in main panel with background subtracted. Colour scale: black: -1 kO; white: 3 kO. From blue to black, temperatures in d are T = 10, 6, 4, 2.5, 1.8, 1.2, 0.8, 0.4, 0.1 and 0.03 K. e Plot of v[QH] versus v[NLT] for D2 and D3. The dotted line indicates v[QH] = v[NLT]. Source data Extended Data Fig. 7 Non-linear transport data near charge neutrality and half-filling for device D4. a dV/dI (n, I) near charge neutrality. Velocity obtained from slope of features near zero density such as shown by the red dashed line, yielding v[NL] = ~ 1.7 x 10^4 m s^-1; averaging the slopes of features over four quadrants yields v[NL] = ~ 1.5 x 10^4 m s^-1. b dV /dI data near half-filling. Features indicated by red dashed lines follow nearly equal slopes, yielding v[NL] = 2.3 x 10^3 m s^-1. Source data Extended Data Fig. 8 Comparison of ac and dc measurements. a R(n) at B = 0, T = 0.3 K and zero bias, measured using ac lock-in techniques with a large dynamic range. The superconducting region displays a "residual" resistance of ~20-30 O. b DC voltage-current curve at n = -1.65 x 10^11 cm^-2, B = 0 and T = 0.3 K. The blue line is a line fit to the zero-bias region, which has a slope of -0.2 +- 1.4 O. Source data Extended Data Fig. 9 Transport data over extended range. Nonlinear transport data dV/dI ( J,n) in kO over a large density range at B = 0 and T = 0.3 K. Source data Source data Source Data Fig. 1 Source Data Fig. 2 Source Data Fig. 3 Source Data Fig. 4 Source Data Extended Data Fig. 1 Source Data Extended Data Fig. 2 Source Data Extended Data Fig. 3 Source Data Extended Data Fig. 5 Source Data Extended Data Fig. 6 Source Data Extended Data Fig. 7 Source Data Extended Data Fig. 8 Source Data Extended Data Fig. 9 Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and Permissions About this article Verify currency and authenticity via CrossMark Cite this article Tian, H., Gao, X., Zhang, Y. et al. Evidence for Dirac flat band superconductivity enabled by quantum geometry. Nature 614, 440-444 (2023). https://doi.org/10.1038/s41586-022-05576-2 Download citation * Received: 24 November 2021 * Accepted: 18 November 2022 * Published: 15 February 2023 * Issue Date: 16 February 2023 * DOI: https://doi.org/10.1038/s41586-022-05576-2 Share this article Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Comments By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. 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