Abstract
The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.
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References
Dubi, Y. & Di Ventra, M. Heat flow and thermoelectricity in atomic and molecular junctions. Rev. Mod. Phys. 83, 131–155 (2011).
Schwab, K., Henriksen, E. A., Worlock, J. M. & Roukes, M. L. Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000).
Meschke, M., Guichard, W. & Pekola, J. P. Single-mode heat conduction by photons. Nature 444, 187–190 (2006).
Jezouin, S. et al. Quantum limit of heat flow across a single electronic channel. Science 342, 601–604 (2013).
Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nat. Mater. 11, 391–399 (2012).
Giazotto, F., Heikkilä, T. T., Luukanen, A., Savin, A. M. & Pekola, J. P. Opportunities for mesoscopics in thermometry and refrigeration: physics and applications. Rev. Mod. Phys. 78, 217–274 (2006).
Muhonen, J. T., Meschke, M. & Pekola, J. P. Micrometre-scale refrigerators. Rep. Prog. Phys. 75, 046501 (2012).
Tan, K. Y. et al. Quantum circuit refrigerator. Nat. Commun. 8, 15189 (2017).
Li, N. et al. Phononics: manipulating heat flow with electronic analogs and beyond. Rev. Mod. Phys. 84, 1045–1066 (2012).
Chang, C. W., Okawa, D., Majumdar, A. & Zettl, A. Solid-state thermal rectifier. Science 314, 1121–1124 (2006).
Tian, H. et al. A novel solid-state thermal rectifier based on reduced graphene oxide. Sci. Rep. 2, 523 (2012).
Eom, J., Chien, C. J. & Chandrasekhar, V. Phase dependent thermopower in Andreev interferometers. Phys. Rev. Lett. 81, 437–440 (1998).
Dikin, D. A., Jung, S. & Chandrasekhar, V. Low-temperature thermal properties of mesoscopic normal-metal/superconductor heterostructures. Phys. Rev. B 65, 012511 (2001).
Jiang, Z. & Chandrasekhar, V. Quantitative measurements of the thermal resistance of Andreev interferometers. Phys. Rev. B 72, 020502 (2005).
Jiang, Z. & Chandrasekhar, V. Thermal conductance of Andreev interferometers. Phys. Rev. Lett. 94, 147002 (2005).
Bezuglyi, E. V. & Vinokur, V. Heat transport in proximity structures. Phys. Rev. Lett. 91, 137002 (2003).
Giazotto, F. & Martínez-Pérez, M. J. The Josephson heat interferometer. Nature 492, 401–405 (2012).
Martínez-Pérez, M. J., Solinas, P. & Giazotto, F. Coherent caloritronics in Josephson-based nanocircuits. J. Low Temp. Phys. 175, 813–837 (2014).
Maki, K. & Griffin, A. Entropy transport between two superconductors by electron tunneling. Phys. Rev. Lett. 15, 921–923 (1965).
Giazotto, F. & Martínez-Pérez, M. J. Phase-controlled superconducting heat-flux quantum modulator. Appl. Phys. Lett. 101, 102601 (2012).
Martínez-Pérez, M. J. & Giazotto, F. A quantum diffractor for thermal flux. Nat. Commun. 5, 3579 (2014).
Martínez-Pérez, M. J., Fornieri, A. & Giazotto, F. Rectification of electronic heat current by a hybrid thermal diode. Nat. Nanotech. 10, 303–307 (2015).
Fornieri, A., Blanc, C., Bosisio, R., D'Ambrosio, S. & Giazotto, F. Nanoscale phase engineering of thermal transport with a Josephson heat modulator. Nat. Nanotech. 11, 258–262 (2016).
Fornieri, A., Timossi, G., Virtanen, P., Solinas, P. & Giazotto, F. 0–π phase-controllable thermal Josephson junction. Nat. Nanotech. 12, 425–429 (2017).
Giazotto, F., Peltonen, J. T., Meschke, M. & Pekola, J. P. Superconducting quantum interference proximity transistor. Nat. Phys. 6, 254–259 (2010).
Ronzani, A., Altimiras, C. & Giazotto, F. Highly sensitive superconducting quantum interference proximity transistor. Phys. Rev. Appl. 2, 024005 (2014).
D'Ambrosio, S., Meissner, M., Blanc, C., Ronzani, A. & Giazotto, F. Normal metal tunnel junction-based superconducting quantum interference proximity transistor. Appl. Phys. Lett. 107, 113110 (2015).
Zhou, F., Charlat, P., Spivak, B. & Pannetier, B. Density of states in superconductor-normal metal-superconductor junctions. J. Low Temp. Phys. 110, 841–850 (1998).
le Sueur, H., Joyez, P., Pothier, H., Urbina, C. & Esteve, D. Phase controlled superconducting proximity effect probed by tunneling spectroscopy. Phys. Rev. Lett. 100, 197002 (2008).
Strambini, E., Bergeret, F. S. & Giazotto, F. Proximity nanovalve with large phase-tunable thermal conductance. Appl. Phys. Lett. 105, 082601 (2014).
Ojanen, T. & Jauho, A. P. Mesoscopic photon heat transistor. Phys. Rev. Lett. 100, 155902 (2008).
Pascal, L. M. A., Courtois, H. & Hekking, F. W. J. Circuit approach to photonic heat transport. Phys. Rev. B 83, 125113 (2011).
Wellstood, F. C., Urbina, C. & Clarke, J. Hot-electron effects in metals. Phys. Rev. B 49, 5942–5955 (1994).
Timofeev, A. V. et al. Recombination-limited energy relaxation in a Bardeen–Cooper–Schrieffer superconductor. Phys. Rev. Lett. 102, 017003 (2009).
Taskinen, L. J. & Maasilta, I. J. Improving the performance of hot-electron bolometers and solid state coolers with disordered alloys. Appl. Phys. Lett. 89, 143511 (2006).
Josephson, B. D. Possible new effects in superconductive tunneling. Phys. Lett. 1, 251–253 (1962).
Guttman, G. D., Nathanson, B., Ben-Jacob, E. & Bergman, D. J. Phase-dependent thermal transport in Josephson junctions. Phys. Rev. B 55, 3849–3855 (1997).
Zhao, E., Löfwander, T. & Sauls, J. A. Heat transport through Josephson point contacts. Phys. Rev. B 69, 134503 (2004).
Tinkham, M. Introduction to Superconductivity (McGraw-Hill, 1996).
Barone, A. & Paternò, G. Physics and Applications of the Josephson Effect (Wiley, 1982).
Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014).
Giazotto, F., Martínez-Pérez, M. J. & Solinas, P. Coherent diffraction of thermal currents. Phys. Rev. B 88, 094506 (2013).
Martínez-Pérez, M. J. & Giazotto, F. Fully balanced heat interferometer. Appl. Phys. Lett. 102, 092602 (2013).
Bosisio, R. et al. A magnetic thermal switch for heat management at the nanoscale. Phys. Rev. B 91, 205420 (2015).
Ben-Abdallah, P., Belarouci, A., Frechette, L. & Biehs, S.A. Heat flux splitter for near-field thermal radiation. Appl. Phys. Lett. 107, 053109 (2015).
Martínez-Pérez, M. J. & Giazotto, F. Efficient phase-tunable Josephson thermal rectifier. Appl. Phys. Lett. 102, 182602 (2013).
Ren, J., Hänggi, P. & Li, B. Berryphaseinduced heat pumping and its impact on the fluctuation theorem. Phys. Rev. Lett. 104, 170601 (2010).
Valenzuela, S. O. et al. Microwave-induced cooling of a superconducting qubit. Science 314, 1589–1592 (2006).
Solinas, P., Bosisio, R. & Giazotto, F. Microwave quantum refrigeration based on the Josephson effect. Phys. Rev. B 93, 224521 (2016).
Campisi, M., Pekola, J. & Fazio, R. Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments. New J. Phys. 17, 035012 (2015).
Niskanen, A. O., Nakamura, Y. & Pekola J. Information entropic superconducting microcooler. Phys. Rev. B 76, 174523 (2007).
Quan, H. T., Wang, Y. D., Liu, Y.-x., Sun, C. P. & Nori, F. Maxwell's Demon assisted thermodynamic cycle in superconducting quantum circuits. Phys. Rev. Lett. 97, 180402 (2006).
Fornieri, A., Timossi, G., Bosisio, R., Solinas, P. & Giazotto, F. Negative differential thermal conductance and heat amplification in superconducting hybrid devices. Phys. Rev. B 93, 134508 (2016).
Fornieri, A., Martínez-Pérez, M. J. & Giazotto, F. Electronic heat current rectification in hybrid superconducting devices. AIP Adv. 5, 053301 (2015).
Paolucci, F., Marchegiani, G., Strambini, E. & Giazotto, F. Phase-tunable temperature amplifier. Europhys. Lett. 118, 68004 (2017).
Fornieri, A., Martínez-Pérez, M. J. & Giazotto, F. A normal metal tunnel-junction heat diode. Appl. Phys. Lett. 104, 183108 (2014).
Giazotto, F. & Bergeret, F. S. Thermal rectification of electrons in hybrid normal metal–superconductor nanojunctions. Appl. Phys. Lett. 103, 242602 (2013).
de Gennes, P. G. & Saint-James, D. Elementary excitations in the vicinity of a normal metal–superconducting metal contact. Phys. Lett. 4, 151–152 (1963).
Usadel, K. D. Generalized diffusion equation for superconducting alloys. Phys. Rev. Lett. 25, 507–509 (1970).
Virtanen, P., Ronzani, A. & Giazotto, F. Spectral characteristics of a fully-superconducting SQUIPT. Phys. Rev. B 95, 144512 (2017).
Rabani, H., Taddei, F., Bourgeois, O., Fazio, R. & Giazotto, F. Phase-dependent electronic specific heat of mesoscopic Josephson junctions. Phys. Rev. B 78, 012503 (2008).
Rabani, H., Taddei, F., Giazotto, F. & Fazio, R. Influence of interface transmissivity and inelastic scattering on the electronic entropy and specific heat of diffusive superconductor–normal metal–superconductor Josephson junctions. J. Appl. Phys. 105, 093904 (2009).
Heikkilä, T. T. & Giazotto, F. Phase sensitive electron–phonon coupling in a superconducting proximity structure. Phys. Rev. B 79, 094514 (2009).
Schmidt, D. R., Schoelkopf, R. J. & Cleland, A. N. Photon-mediated thermal relaxation of electrons in nanostructures. Phys. Rev. Lett. 93, 045901 (2004).
Paolucci, F., Timossi, G., Solinas, P. & Giazotto, F. Coherent manipulation of thermal transport by tunable electron–photon and electron–phonon interaction. J. Appl. Phys. 121, 244305 (2017).
Bosisio, R., Solinas, P., Braggio, A. & Giazotto, F. Photonic heat conduction in Josephson-coupled Bardeen–Cooper–Schrieffer superconductors. Phys. Rev. B 93, 144512 (2016).
Partanen, M. et al. Quantum-limited heat conduction over macroscopic distances. Nat. Phys. 12, 460–464 (2016).
Ruokola, T., Ojanen, T. & Jauho, A.-P. Thermal rectification in nonlinear quantum circuits. Phys. Rev. B 79, 144306 (2009).
Wei, J. et al. Ultrasensitive hot-electron nanobolometers for terahertz astrophysics. Nat. Nanotech. 3, 496–500 (2008).
Govenius, J., Lake, R. E., Tan, K. Y. & Möttönen, M. Detection of zeptojoule microwave pulses using electrothermal feedback in proximity-induced Josephson junctions. Phys. Rev. Lett. 117, 030802 (2016).
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information, (Cambridge Univ. Press, 2002).
Guarcello, C., Solinas, P., Di Ventra, M. & Giazotto, F. Hysteretic superconducting heat-flux quantum modulator. Phys. Rev. Appl. 7, 044021 (2017).
Guarcello, C., Solinas, P., Braggio, A., Di Ventra, M. & Giazotto, F. A Josephson thermal memory. Preprint at https://arxiv.org/abs/1706.05323 (2017).
Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).
Mastomäki, J. et al. InAs nanowire superconducting tunnel junctions: quasiparticle spectroscopy, thermometry and nanorefrigeration. Nano Res. 10, 3468–3475 (2017).
Yokoyama, T., Linder, J. & Sudbø, A. Heat transport by Dirac fermions in nor- mal/superconducting graphene junctions. Phys. Rev. B 77, 132503 (2008).
Rainis, D., Taddei, F., Dolcini, F., Polini, M. & Fazio, R. Andreev reflection in graphene nanoribbons. Phys. Rev. B 79, 115131 (2009).
Kawabata, S., Ozaeta, A., Vasenko, A. S., Hekking, F. W. J. & Bergeret, F. S. Efficient electron refrigeration using superconductor/spin-filter devices. Appl. Phys. Lett. 103, 032602 (2013).
Bergeret, F. S. & Giazotto, F. Manifestation of a spin-splitting field in a thermally biased Josephson junction. Phys. Rev. B 89, 054505 (2014).
Bergeret, F. S. & Giazotto, F. Phase-dependent heat transport through magnetic Josephson tunnel junctions. Phys. Rev. B 88, 014515 (2013).
Giazotto, F. & Bergeret, F. S. Phase-tunable colossal magnetothermal resistance in ferromagnetic Josephson valves. Appl. Phys. Lett. 102, 132603 (2013).
Wang, Z., Qi, X.-L. & Zhang, S.-C. Topological field theory and thermal responses of interacting topological superconductors. Phys. Rev. B 84, 014527 (2011).
Ren, J. & Zhu, J.-X. Anomalous energy transport across topological insulator superconductor junctions. Phys. Rev. B 87, 165121 (2013).
Ren, J. & Zhu, J.-X. Asymmetric Andreev reflection induced electrical and thermal Hall-like effects in metal/anisotropic superconductor junctions. Phys. Rev. B 89, 064512 (2014).
Sothmann, B. & Hankiewicz, E. M. Fingerprint of topological Andreev bound states in phase- dependent heat transport. Phys. Rev. B 94, 081407(R) (2016).
Sothmann, B., Giazotto, F. & Hankiewicz, E. M. High-efficiency thermal switch based on topological Josephson junctions. New J. Phys. 19, 023056 (2017).
Pekola, J. Towards quantum thermodynamics in electronic circuits. Nat. Phys. 11, 118–123 (2015).
Giazotto, F., Heikkilä, T. T. & Bergeret, F. S. Very large thermophase in ferromagnetic Josephson junctions. Phys. Rev. Lett. 114, 067001 (2015).
Giazotto, F., Robinson, J. W. A., Moodera, J. S. & Bergeret, F. S. Proposal for a phase-coherent thermoelectric transistor. Appl. Phys. Lett. 105, 062602 (2014).
Kleeorin, Y., Meir, Y., Giazotto, F. & Dubi, Y. Large tunable thermophase in superconductor–quantum dot–superconductor Josephson junctions. Sci. Rep. 6, 35116 (2016).
Dynes, R. C., Narayanamurty, V. & Garno, J. P. Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor. Phys. Rev. Lett. 41, 1509–1512 (1978).
Acknowledgements
We thank J. P. Pekola and M. Meschke for providing experimental data. We also thank F. Paolucci, G. Timossi, E. Strambini and L. Casparis for discussions. The MIUR-FIRB2013–Project Coca (grant no. RBFR1379UX) and the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 615187—COMANCHE are acknowledged for partial financial support.
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Fornieri, A., Giazotto, F. Towards phase-coherent caloritronics in superconducting circuits. Nature Nanotech 12, 944–952 (2017). https://doi.org/10.1038/nnano.2017.204
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DOI: https://doi.org/10.1038/nnano.2017.204
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