- Open Access
Microwave radiometry of a quantum-critical hybrid Josephson array
Phys. Rev. Applied 26, 014031 – Published 10 July, 2026
DOI: https://doi.org/10.1103/75bl-mm3b
Abstract
Arrays of Josephson junctions can be tuned through anomalous metallic, quantum-critical, and insulating regimes. We introduce an alternative experimental probe, capturing microwave radiation across all three regimes, using a two-dimensional array of superconductor-semiconductor hybrid Josephson junctions as a model system. Our approach allows in situ calibration of the sample’s circuit parameters and provides isolation from measurement back-action effects. We measure the radiation temperature of the anomalous metal and find that it is hotter than both the quantum-critical and insulating regimes. We further show that the anomalous metallic regime is more susceptible to additional heating than other regimes, explaining its emergence in otherwise thermalized systems. Turning to the quantum-critical regime, we discover nonlinear scaling of radiative noise with applied bias, consistent with theoretical predictions of universal nonequilibrium behavior at quantum-critical points.
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References (47)
- B. Sacépé, M. Feigel’man, and T. M. Klapwijk, Quantum breakdown of superconductivity in low-dimensional materials, Nat. Phys. 16, 734 (2020).
- H. M. Jaeger, D. B. Haviland, B. G. Orr, and A. M. Goldman, Onset of superconductivity in ultrathin granular metal films, Phys. Rev. B 40, 182 (1989).
- D. Ephron, A. Yazdani, A. Kapitulnik, and M. R. Beasley, Observation of quantum dissipation in the vortex state of a highly disordered superconducting thin film, Phys. Rev. Lett. 76, 1529 (1996).
- O. Crauste, C. A. Marrache-Kikuchi, L. Bergé, D. Stanescu, and L. Dumoulin, Thickness dependence of the superconductivity in thin disordered NBSI films, J. Phys. Conf. Ser. 150, 042019 (2009).
- S. Eley, S. Gopalakrishnan, P. M. Goldbart, and N. Mason, Approaching zero-temperature metallic states in mesoscopic superconductor–normal–superconductor arrays, Nat. Phys. 8, 59 (2012).
- Z. Han, A. Allain, H. Arjmandi-Tash, K. Tikhonov, M. Feigel’man, B. Sacépé, and V. Bouchiat, Collapse of superconductivity in a hybrid tin–graphene Josephson junction array, Nat. Phys. 10, 380 (2014).
- C. G. L. Bøttcher, F. Nichele, M. Kjaergaard, H. J. Suominen, J. Shabani, C. J. Palmstrøm, and C. M. Marcus, Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array, Nat. Phys. 14, 1138 (2018).
- C. G. L. Bøttcher, F. Nichele, J. Shabani, C. J. Palmstrøm, and C. M. Marcus, Dynamical vortex transitions in a gate-tunable two-dimensional Josephson junction array, Phys. Rev. B 108, 134517 (2023).
- K. Ienaga, Y. Tamoto, M. Yoda, Y. Yoshimura, T. Ishigami, and S. Okuma, Broadened quantum critical ground state in a disordered superconducting thin film, Nat. Commun. 15, 2388 (2024).
- E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).
- A. Kapitulnik, S. A. Kivelson, and B. Spivak, Colloquium: Anomalous metals—failed superconductors, Rev. Mod. Phys. 91, 011002 (2019).
- C. G. L. Bøttcher, F. Nichele, J. Shabani, C. J. Palmstrøm, and C. M. Marcus, Berezinskii-Kosterlitz-Thouless transition and anomalous metallic phase in a hybrid Josephson junction array, Phys. Rev. B 110, L180502 (2024).
- I. Tamir, A. Benyamini, E. J. Telford, F. Gorniaczyk, A. Doron, T. Levinson, D. Wang, F. Gay, B. Sacépé, J. Hone, K. Watanabe, T. Taniguchi, C. R. Dean, A. N. Pasupathy, and D. Shahar, Sensitivity of the superconducting state in thin films, Sci. Adv. 5, eaau3826 (2019).
- J. Shin, S. Park, and E. Kim, Effect of external electromagnetic radiation on the anomalous metallic behavior in superconducting Ta thin films, Phys. Rev. B 102, 184501 (2020).
- A. Haug and D. Shahar, Excess noise in the anomalous metallic phase in amorphous indium oxide, Phys. Rev. B 109, 014514 (2024).
- D. Dalidovich and P. Phillips, Nonlinear transport near a quantum phase transition in two dimensions, Phys. Rev. Lett. 93, 027004 (2004).
- A. G. Green and S. L. Sondhi, Nonlinear quantum critical transport and the Schwinger mechanism for a superfluid-Mott-insulator transition of bosons, Phys. Rev. Lett. 95, 267001 (2005).
- A. G. Green, J. E. Moore, S. L. Sondhi, and A. Vishwanath, Current noise in the vicinity of the 2D superconductor-insulator quantum critical point, Phys. Rev. Lett. 97, 227003 (2006).
- J. Sonner and A. G. Green, Hawking radiation and nonequilibrium quantum critical current noise, Phys. Rev. Lett. 109, 091601 (2012).
- R. H. Dicke, R. Beringer, R. L. Kyhl, and A. B. Vane, Atmospheric absorption measurements with a microwave radiometer, Phys. Rev. 70, 340 (1946).
- M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Amplification and squeezing of quantum noise with a tunable Josephson metamaterial, Nat. Phys. 4, 929 (2008).
- B. M. Brubaker, L. Zhong, Y. V. Gurevich, S. B. Cahn, S. K. Lamoreaux, M. Simanovskaia, J. R. Root, S. M. Lewis, S. Al Kenany, K. M. Backes, I. Urdinaran, N. M. Rapidis, T. M. Shokair, K. A. van Bibber, D. A. Palken, M. Malnou, W. F. Kindel, M. A. Anil, K. W. Lehnert, and G. Carosi, First results from a microwave cavity axion search at , Phys. Rev. Lett. 118, 061302 (2017).
- A. Majumdar, N. Chadha, P. Pal, A. Gugnani, B. Ghawri, K. Watanabe, T. Taniguchi, S. Mukerjee, and A. Ghosh, Universality in quantum critical flow of charge and heat in ultraclean graphene, Nat. Phys. 21, 1374 (2025).
- L. Chen, D. T. Lowder, E. Bakali, A. M. Andrews, W. Schrenk, M. Waas, R. Svagera, G. Eguchi, L. Prochaska, Y. Wang, C. Setty, S. Sur, Q. Si, S. Paschen, and D. Natelson, Shot noise in a strange metal, Science 382, 907(2023).
- J. Shabani, M. Kjaergaard, H. J. Suominen, Y. Kim, F. Nichele, K. Pakrouski, T. Stankevic, R. M. Lutchyn, P. Krogstrup, R. Feidenhans’l, S. Kraemer, C. Nayak, M. Troyer, C. M. Marcus, and C. J. Palmstrøm, Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks, Phys. Rev. B 93, 155402 (2016).
- W. Mayer, J. Yuan, K. S. Wickramasinghe, T. Nguyen, M. C. Dartiailh, and J. Shabani, Superconducting proximity effect in epitaxial Al-InAs heterostructures, Appl. Phys. Lett. 114, 103104 (2019).
- S. Sasmal, M. Efthymiou-Tsironi, G. Nagda, E. Fugl, L. L. Olsen, F. Krizek, C. M. Marcus, and S. Vaitiekėnas, Voltage-tuned anomalous-metal to metal transition in hybrid Josephson junction arrays, Phys. Rev. Lett. 135, 156301 (2025).arXiv:2505.12536
- M.-C. Cha, M. P. A. Fisher, S. M. Girvin, M. Wallin, and A. P. Young, Universal conductivity of two-dimensional films at the superconductor-insulator transition, Phys. Rev. B 44, 6883 (1991).
- M. Swanson, Y. L. Loh, M. Randeria, and N. Trivedi, Dynamical conductivity across the disorder-tuned superconductor-insulator transition, Phys. Rev. X 4, 021007 (2014).
- D. B. Haviland, Y. Liu, and A. M. Goldman, Onset of superconductivity in the two-dimensional limit, Phys. Rev. Lett. 62, 2180 (1989).
- P. Dieleman, H. G. Bukkems, T. M. Klapwijk, M. Schicke, and K. H. Gundlach, Observation of Andreev reflection enhanced shot noise, Phys. Rev. Lett. 79, 3486 (1997).
Since the determination of [e.g., in Fig. 3] from the measured data requires knowledge of , this analysis enables a self-consistent extraction of . Specifically, the value of obtained from the fits in Fig. 3 should match the initially assumed used in the calculation of in Fig. 3.
- P. Barbara, A. B. Cawthorne, S. V. Shitov, and C. J. Lobb, Stimulated emission and amplification in Josephson junction arrays, Phys. Rev. Lett. 82, 1963 (1999).
- A. B. Cawthorne, P. Barbara, S. V. Shitov, C. J. Lobb, K. Wiesenfeld, and A. Zangwill, Synchronized oscillations in Josephson junction arrays: The role of distributed coupling, Phys. Rev. B 60, 7575 (1999).
- Y. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000).
- V. D. Kurilovich, B. Remez, and L. I. Glazman, Quantum theory of Bloch oscillations in a resistively shunted transmon, Nat. Commun. 16, 1384 (2025).
- B. Karimi, G. O. Steffensen, A. P. Higginbotham, C. M. Marcus, A. Levy Yeyati, and J. P. Pekola, Bolometric detection of Josephson radiation, Nat. Nanotechnol. 19, 1613 (2024).
- A. Denisov, A. Bubis, S. Piatrusha, N. Titova, A. Nasibulin, J. Becker, J. Treu, D. Ruhstorfer, G. Koblmüller, E. Tikhonov, and V. Khrapai, Heat-mode excitation in a proximity superconductor, Nanomaterials 12, 1461 (2022).
- Y. Ronen, Y. Cohen, J.-H. Kang, A. Haim, M.-T. Rieder, M. Heiblum, D. Mahalu, and H. Shtrikman, Charge of a quasiparticle in a superconductor, Proc. Natl. Acad. Sci. U.S.A. 113, 1743 (2016).
- T. Hoss, C. Strunk, T. Nussbaumer, R. Huber, U. Staufer, and C. Schönenberger, Multiple Andreev reflection and giant excess noise in diffusive superconductor/normal-metal/superconductor junctions, Phys. Rev. B 62, 4079 (2000).
- H. Courtois, M. Meschke, J. T. Peltonen, and J. P. Pekola, Origin of hysteresis in a proximity Josephson junction, Phys. Rev. Lett. 101, 067002 (2008).
- M. Feigel’man and A. Larkin, Quantum superconductor–metal transition in a 2D proximity-coupled array, Chem. Phys. 235, 107 (1998).
- B. Spivak, A. Zyuzin, and M. Hruska, Quantum superconductor-metal transition, Phys. Rev. B 64, 132502 (2001).
- B. Spivak, P. Oreto, and S. A. Kivelson, Theory of quantum metal to superconductor transitions in highly conducting systems, Phys. Rev. B 77, 214523 (2008).
- Data for “microwave radiometry of a quantum-critical, hybrid josephson array” (2026), Zenodo,10.5281/zenodo.19615009.
- F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications, Rev. Mod. Phys. 78, 217 (2006).
- V. F. Gantmakher and V. T. Dolgopolov, Superconductor–insulator quantum phase transition, Phys. Usp. 53, 1 (2010).