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Superfluid stiffness of magic-angle twisted bilayer graphene

  • Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528–542 (2022).

    Article 
    MATH 

    Google Scholar
     

  • Tian, H. et al. Evidence for Dirac flat band superconductivity enabled by quantum geometry. Nature 614, 440–444 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Cao, Y. et al. Correlated insulator behavior at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240–245 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Peotta, S. & Törmä, P. Superfluidity in topologically nontrivial flat bands. Nat. Commun. 6, 8944 (2015).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Hu, X., Hyart, T., Pikulin, D. I. & Rossi, E. Geometric and conventional contribution to the superfluid weight in twisted bilayer graphene. Phys. Rev. Lett. 123, 237002 (2019).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Julku, A., Peltonen, T. J., Liang, L., Heikkilä, T. T. & Törmä, P. Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene. Phys. Rev. B 101, 060505 (2020).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Xie, F., Song, Z., Lian, B. & Bernevig, B. A. Topology-bounded superfluid weight in twisted bilayer graphene. Phys. Rev. Lett. 124, 167002 (2020).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Hofmann, J. S., Chowdhury, D., Kivelson, S. A. & Berg, E. Heuristic bounds on superconductivity and how to exceed them. npj Quantum Mater. 7, 83 (2022).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Ma, C. et al. Moiré band topology in twisted bilayer graphene. Nano Lett. 20, 6076–6083 (2020).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Tinkham, M. Introduction to Superconductivity: Second Edition (Dover Publications, 2004).

  • Prozorov, R. & Giannetta, R. W. Magnetic penetration depth in unconventional superconductors. Supercond. Sci. Technol. 19, R41 (2006).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Hardy, W., Kamal, S. & Bonn, D. Magnetic Penetration Depths in Cuprates: A Short Review of Measurement Techniques and Results (Springer, 2002).

  • Bøttcher, C. et al. Circuit quantum electrodynamics detection of induced two-fold anisotropic pairing in a hybrid superconductor–ferromagnet bilayer. Nat. Phys. 20, 1609–1615 (2024).

  • Phan, D. et al. Detecting induced p ± ip pairing at the Al-InAs interface with a quantum microwave circuit. Phys. Rev. Lett. 128, 107701 (2022).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Weitzel, A. et al. Sharpness of the Berezinskii-Kosterlitz-Thouless transition in disordered NbN films. Phys. Rev. Lett. 131, 186002 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Penttilä, R. P. S., Huhtinen, K.-E. & Törmä, P. Flat-band ratio and quantum metric in the superconductivity of modified Lieb lattices. Preprint at https://arxiv.org/abs/2404.12993 (2024).

  • Probst, S., Song, F. B., Bushev, P. A., Ustinov, A. V. & Weides, M. Efficient and robust analysis of complex scattering data under noise in microwave resonators. Rev. Sci. Instrum. 86, 024706 (2015).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Emery, V. & Kivelson, S. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Kosterlitz, J. M. & Thouless, D. J. in Basic Notions Of Condensed Matter Physics 493–515 (CRC Press, 1973).

  • Berdyugin, A. I. et al. Out-of-equilibrium criticalities in graphene superlattices. Science 375, 430–433 (2022).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Wu, F. Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene. Phys. Rev. B 99, 195114 (2019).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Törmä, P. Essay: where can quantum geometry lead us? Phys. Rev. Lett. 131, 240001 (2023).

    Article 
    ADS 
    MathSciNet 
    PubMed 
    MATH 

    Google Scholar
     

  • Hirschfeld, P. J. & Goldenfeld, N. Effect of strong scattering on the low-temperature penetration depth of a d-wave superconductor. Phys. Rev. B 48, 4219 (1993).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Roppongi, M. et al. Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5. Nat. Commun. 14, 667 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 
    MATH 

    Google Scholar
     

  • Teknowijoyo, S. et al. Nodeless superconductivity in the type-II Dirac semimetal PdTe2: London penetration depth and pairing-symmetry analysis. Phys. Rev. B 98, 024508 (2018).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Khvalyuk, A. V., Charpentier, T., Roch, N., Sacépé, B. & Feigel’Man, M. V. Near power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors. Phys. Rev. B 109, 144501 (2024).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Mishra, V. et al. Lifting of nodes by disorder in extended-s-state superconductors: application to ferropnictides. Phys. Rev. B 79, 094512 (2009).

    Article 
    ADS 

    Google Scholar
     

  • Cho, K. et al. Energy gap evolution across the superconductivity dome in single crystals of (Ba1–xKx) Fe2As2. Sci. Adv. 2, e1600807 (2016).

    Article 
    ADS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Gittleman, J., Rosenblum, B., Seidel, T. & Wicklund, A. Nonlinear reactance of superconducting films. Phys. Rev. 137, A527 (1965).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Enpuku, K., Hoashi, M., Doi, H. D. H. & Kisu, T. K. T. Modulation of kinetic inductance of high Tc superconducting thin films with bias current. Jpn. J. Appl. Phys. 32, 3804 (1993).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Kubo, T. Superfluid flow in disordered superconductors with Dynes pair-breaking scattering: depairing current, kinetic inductance, and superheating field. Phys. Rev. Res. 2, 033203 (2020).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Anthore, A., Pothier, H. & Esteve, D. Density of states in a superconductor carrying a supercurrent. Phys. Rev. Lett. 90, 127001 (2003).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Luomahaara, J., Vesterinen, V., Grönberg, L. & Hassel, J. Kinetic inductance magnetometer. Nat. Commun. 5, 4872 (2014).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ku, J., Manucharyan, V. & Bezryadin, A. Superconducting nanowires as nonlinear inductive elements for qubits. Phys. Rev. B 82, 134518 (2010).

    Article 
    ADS 

    Google Scholar
     

  • Claassen, J., Adrian, S. & Soulen, R. Large non-linear kinetic inductance in superconductor/normal metal bilayer films. IEEE Trans. Appl. Supercond. 9, 4189–4192 (1999).

    Article 
    ADS 

    Google Scholar
     

  • Thomas, C. N., Withington, S., Sun, Z., Skyrme, T. & Goldie, D. J. Nonlinear effects in superconducting thin film microwave resonators. New J. Phys. 22, 073028 (2020).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Vissers, M. R. et al. Frequency-tunable superconducting resonators via nonlinear kinetic inductance. Appl. Phys. Lett. 107, 062601 (2015).

  • Kirsh, N. et al. Linear and nonlinear properties of a compact high-kinetic-inductance WSi multimode resonator. Phys. Rev. A 16, 044017 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Zhao, S., Withington, S., Goldie, D. J. & Thomas, C. N. Nonlinear properties of supercurrent-carrying single-and multi-layer thin-film superconductors. J. Low Temp. Phys. 199, 34–44 (2020).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Carrington, A., Giannetta, R., Kim, J. & Giapintzakis, J. Absence of nonlinear Meissner effect in YBa2Cu3O6.95. Phys. Rev. B 59, R14173 (1999).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Li, M.-R., Hirschfeld, P. & Wölfle, P. Is the nonlinear Meissner effect unobservable? Phys. Rev. Lett. 81, 5640 (1998).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Banerjee, A. et al. Superfluid stiffness of twisted trilayer graphene superconductors. Nature https://doi.org/10.1038/s41586-024-08444-3 (2025).

  • Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nat. Commun. 7, 12964 (2016).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Wang, J. I.-J. et al. Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures. Nat. Nanotechnol. 14, 120–125 (2019).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Pozar, D. M. Microwave Engineering (John Wiley & Sons, 2011).

  • Schmidt, F. E., Jenkins, M. D., Watanabe, K., Taniguchi, T. & Steele, G. A. A ballistic graphene superconducting microwave circuit. Nat. Commun. 9, 4069 (2018).

    Article 
    ADS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Bretheau, L. et al. Tunnelling spectroscopy of Andreev states in graphene. Nat. Phys. 13, 756–760 (2017).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Schwinger, J. On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951).

    Article 
    ADS 
    MathSciNet 
    MATH 

    Google Scholar
     

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