- Open Access
Cooper-Pair Splitters as Circuit Elements for Realizing Topological Superconductors
PRX Quantum 6, 030318 – Published 31 July, 2025
DOI: https://doi.org/10.1103/3c6m-x28w
Abstract
Advances in materials and fabrication of superconducting devices allows the exploration of novel quantum effects in synthetic superconducting systems beyond conventional Josephson-junction arrays. As an example, we introduce a new circuit element, the Y splitter, a superconducting loop with three leads and three Josephson junctions, smaller or comparable in size to the superconducting coherence length of the material. By tuning magnetic flux through an array of Y splitters, Cooper-pair transport can be made to interfere destructively, while spatially separated split Cooper pairs propagate coherently. We consider an array of Y splitters connected in a two-dimensional star [Archimedean (3,)] geometry, deformable into the kagome lattice, and find a rich phase diagram that includes topological superconducting phases with Chern numbers . Experimental realization appears feasible.
Physics Subject Headings (PhySH)
Popular Summary
The ability of superconductors to carry electricity without loss is key to building circuits that follow the laws of quantum mechanics, making them leading contenders for quantum computing architectures. To date, the main components of such circuits are capacitors, inductors, and Josephson junctions. While superconductivity arises from electrons moving in pairs, this pairing is typically hidden in the theoretical analysis of superconducting circuits and only becomes relevant when pairs break apart, which is often regarded as an undesirable feature that can disrupt the quantum behavior of the circuit.
What if, instead, one could harness the pair breaking? This paper introduces a new component for superconducting circuits: the Y splitter. It consists of a superconducting ring with three arms, each connected by Josephson junctions. The Y splitter is designed to split Cooper pairs—the bound electrons responsible for superconductivity—and recombine them in a controlled way that spreads quantum correlations across the circuit. By combining many Y splitters into a network, the authors show how to create the conditions necessary for topological superconductivity, a phase of matter with potential applications in quantum information.
The work combines theory with realistic circuit design, setting a path toward experimental realization. This approach introduces a new superconducting circuit element to the existing toolkit for constructing topological quantum states.
Article Text
References (57)
- M. H. Devoret, A. Wallraff, and J. M. Martinis, Superconducting qubits: A short review, arXiv:cond-mat/0411174 [cond-mat.mes-hall].
- G. Wendin, Quantum information processing with superconducting circuits: A review, Rep. Prog. Phys. 80, 106001 (2017).
- M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
- A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
- O. Lesser, A. Stern, and Y. Oreg, Josephson junction arrays as a platform for topological phases of matter, Phys. Rev. B 109, 144519 (2024).
- R.-P. Riwar, M. Houzet, J. S. Meyer, and Y. V. Nazarov, Multi-terminal Josephson junctions as topological matter, Nat. Commun. 7, 11167 (2016).
- G. B. Lesovik, T. Martin, and G. Blatter, Electronic entanglement in the vicinity of a superconductor, Eur. Phys. J. B 24, 287 (2001).
- P. Recher, E. V. Sukhorukov, and D. Loss, Andreev tunneling, Coulomb blockade, and resonant transport of nonlocal spin-entangled electrons, Phys. Rev. B 63, 165314 (2001).
- L. Hofstetter, S. Csonka, J. Nygard, and C. Schonenberger, Cooper pair splitter realized in a two-quantum-dot Y-junction, Nature 461, 960 (2009).
- L. G. Herrmann, F. Portier, P. Roche, A. L. Yeyati, T. Kontos, and C. Strunk, Carbon nanotubes as Cooper-pair beam splitters, Phys. Rev. Lett. 104, 026801 (2010).
- L. Hofstetter, S. Csonka, A. Baumgartner, G. Fülöp, S. d’Hollosy, J. Nygård, and C. Schönenberger, Finite-bias Cooper pair splitting, Phys. Rev. Lett. 107, 136801 (2011).
- J. Schindele, A. Baumgartner, and C. Schönenberger, Near-unity Cooper pair splitting efficiency, Phys. Rev. Lett. 109, 157002 (2012).
- L. G. Herrmann, P. Burset, W. J. Herrera, F. Portier, P. Roche, C. Strunk, A. Levy Yeyati, and T. Kontos, Spectroscopy of non-local superconducting correlations in a double quantum dot, arXiv:1205.1972.
- A. Das, R. Ronen, M. Heiblum, D. Mahalu, A. V. Kretinin, and H. Shtrikman, High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation, Nat. Commun. 3, 1165 (2012).
- G. Fülöp, S. d’Hollosy, A. Baumgartner, P. Makk, V. A. Guzenko, M. H. Madsen, J. Nygård, C. Schönenberger, and S. Csonka, Local electrical tuning of the nonlocal signals in a Cooper pair splitter, Phys. Rev. B 90, 235412 (2014).
- Z. B. Tan, D. Cox, T. Nieminen, P. Lähteenmäki, D. Golubev, G. B. Lesovik, and P. J. Hakonen, Cooper pair splitting by means of graphene quantum dots, Phys. Rev. Lett. 114, 096602 (2015).
- G. Fülöp, F. Domínguez, S. d’Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygård, C. Schönenberger, A. Levy Yeyati, and S. Csonka, Magnetic field tuning and quantum interference in a Cooper pair splitter, Phys. Rev. Lett. 115, 227003 (2015).
- I. Borzenets, Y. Shimazaki, G. Jones, M. F. Craciun, S. Russo, M. Yamamoto, and S. Tarucha, High efficiency CVD graphene-lead (Pb) Cooper pair splitter, Sci. Rep. 6, 23051 (2016).
- L. E. Bruhat, T. Cubaynes, J. J. Viennot, M. C. Dartiailh, M. M. Desjardins, A. Cottet, and T. Kontos, Circuit QED with a quantum-dot charge qubit dressed by Cooper pairs, Phys. Rev. B 98, 155313 (2018).
- S. Baba, C. Junger, S. Matsuo, A. Baumgartner, Y. Sato, H. Kamata, K. Li, S. Jeppesen, L. Samuelson, H. Q. Xu, C. Schonenberger, and S. Tarucha, Cooper-pair splitting in two parallel nanowires, New J. Phys. 20, 063021 (2018).
- Z. B. Tan, A. Laitinen, N. S. Kirsanov, A. Galda, V. M. Vinokur, M. Haque, A. Savin, D. S. Golubev, G. B. Lesovik, and P. J. Hakonen, Thermoelectric current in a graphene Cooper pair splitter, Nat. Commun. 12, 138 (2021).
- A. Ranni, F. Brange, E. T. Mannila, C. Flindt, and V. F. Maisi, Real-time observation of Cooper pair splitting showing strong non-local correlations, Nat. Commun. 12, 6358 (2021).
- P. Pandey, R. Danneau, and D. Beckmann, Ballistic graphene Cooper pair splitter, Phys. Rev. Lett. 126, 147701 (2021).
- F. Brange, K. Prech, and C. Flindt, Dynamic Cooper pair splitter, Phys. Rev. Lett. 127, 237701 (2021).
- Z. Scherübl, G. m. H. Fülöp, J. Gramich, A. Pályi, C. Schönenberger, J. Nygård, and S. Csonka, From Cooper pair splitting to nonlocal spectroscopy of a Shiba state, Phys. Rev. Res. 4, 023143 (2022).
- O. Kurtoessy, Z. Scherubl, G. Fulop, I. E. Lukacs, T. Kanne, J. Nygard, P. Makk, and S. Csonka, Parallel nanowires for Cooper pair splitters with Coulomb repulsion, Npj Quantum Mater. 7, 88 (2022).
- A. Ranni, E. T. Mannila, A. Eriksson, D. S. Golubev, J. P. Pekola, and V. F. Maisi, Local and nonlocal two-electron tunneling processes in a Cooper pair splitter, Phys. Rev. Lett. 129, 207703 (2022).
- A. Bordoloi, V. Zannier, L. Sorba, C. Schonenberger, and A. Baumgartner, Spin cross-correlation experiments in an electron entangler, Nature 612, 454 (2022).
- G. Wang, T. Dvir, G. P. Mazur, C.-X. Liu, N. van Loo, S. L. D. ten Haaf, A. Bordin, S. Gazibegovic, G. Badawy, E. P. A. M. Bakkers, M. Wimmer, and L. P. Kouwenhoven, Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires, Nature 612, 448 (2022).
- D. de Jong, C. G. Prosko, L. Han, F. K. Malinowski, Y. Liu, L. P. Kouwenhoven, and W. Pfaff, Controllable single Cooper pair splitting in hybrid quantum dot systems, Phys. Rev. Lett. 131, 157001 (2023).
- Q. Wang, S. L. D. ten Haaf, I. Kulesh, D. Xiao, C. Thomas, M. J. Manfra, and S. Goswami, Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas, Nat. Commun. 14, 4876 (2023).
- A. Bordin, X. Li, D. van Driel, J. C. Wolff, Q. Wang, S. L. D. ten Haaf, G. Wang, N. van Loo, L. P. Kouwenhoven, and T. Dvir, Crossed Andreev reflection and elastic cotunneling in three quantum dots coupled by superconductors, Phys. Rev. Lett. 132, 056602 (2024).
- K. Vilkelis, A. Manesco, J. D. T. Luna, S. Miles, M. Wimmer, and A. Akhmerov, Fermionic quantum computation with Cooper pair splitters, SciPost Phys. 16, 135 (2024).
- F. Brange, R. Baruah, and C. Flindt, Adiabatic Cooper pair splitter, Phys. Rev. B 109, L081402 (2024).
- C. Chamon, M. Oshikawa, and I. Affleck, Junctions of three quantum wires and the dissipative Hofstadter model, Phys. Rev. Lett. 91, 206403 (2003).
- M. Oshikawa, C. Chamon, and I. Affleck, Junctions of three quantum wires, J. Stat. Mech.: Theory Exp. 2006, P02008 (2006).
- S. Iimura and Y. Imai, Thermal Hall conductivity in superconducting phase on kagome lattice, J. Phys. Soc. Jpn. 87, 094715 (2018).
- D. Green, L. Santos, and C. Chamon, Isolated flat bands and spin-1 conical bands in two-dimensional lattices, Phys. Rev. B 82, 075104 (2010).
- R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, PNAS 108, 12233 (2011).
- T. Morgan-Wall, B. Leith, N. Hartman, A. Rahman, and N. Marković, Measurement of critical currents of superconducting aluminum nanowires in external magnetic fields: Evidence for a Weber blockade, Phys. Rev. Lett. 114, 077002 (2015).
- A. F. Mayadas, Intrinsic resistivity and electron mean free path in aluminum films, J. Appl. Phys. 39, 4241 (1968).
- A. F. Mayadas, R. Feder, and R. Rosenberg, Resistivity and structure of evaporated aluminum films, J. Vac. Sci. Technol. 6, 690 (1969).
- J. Lee, M. Kang, B.-S. Kim, B. Hong, D. Whang, and S. Hwang, Single crystalline aluminum nanowires with ideal resistivity, Scr. Mater. 63, 1009 (2010).
- W. Mayer, J. Yuan, K. S. Wickramasinghe, T. Nguyen, M. C. Dartiailh, and J. Shabani, Superconducting proximity effect in epitaxial - heterostructures, Appl. Phys. Lett. 114, 103104 (2019).
- A. Pöschl, A. Danilenko, D. Sabonis, K. Kristjuhan, T. Lindemann, C. Thomas, M. J. Manfra, and C. M. Marcus, Nonlocal conductance spectroscopy of Andreev bound states in gate-defined / nanowires, Phys. Rev. B 106, L241301 (2022).
- A. M. Whiticar, A. Fornieri, E. O’Farrell, A. C. Drachmann, T. Wang, C. Thomas, S. Gronin, R. Kallaher, G. C. Gardner, and M. J. Manfra et al., Coherent transport through a Majorana island in an Aharonov–Bohm interferometer, Nat. Commun. 11, 3212 (2020).
- L. Banszerus, W. Marshall, C. W. Andersson, T. Lindemann, M. J. Manfra, C. M. Marcus, and S. Vaitiekėnas, Voltage-controlled synthesis of higher harmonics in hybrid Josephson junction circuits, Phys. Rev. Lett. 133, 186303 (2024).
- H. Sumiyoshi and S. Fujimoto, Quantum thermal Hall effect in a time-reversal-symmetry-broken topological superconductor in two dimensions: Approach from bulk calculations, J. Phys. Soc. Jpn. 82, 023602 (2013).
- S. Głodzik and N. Sedlmayr, Quantized thermal Hall conductance and the topological phase diagram of a superconducting bismuth bilayer, Phys. Rev. B 108, 184502 (2023).
- Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Majorana quantization and half-integer thermal quantum hall effect in a Kitaev spin liquid, Nature 559, 227 (2018).
- C. Kurter, A. Finck, Y. S. Hor, and D. J. V. Harlingen, Evidence for an anomalous current–phase relation in topological insulator Josephson junctions, Nat. Commun. 6, 7130 (2015).
- S. Li, A. V. Andreev, and B. Z. Spivak, Anomalous transport phenomena in superconductors, Phys. Rev. B 92, 100506 (2015).
- Z. Cao, T.-F. Fang, L. Li, and H.-G. Luo, Thermoelectric-induced unitary Cooper pair splitting efficiency, Appl. Phys. Lett. 107, 212601 (2015).
- A. Arora, S. Midha, A. Zyuzin, P. Hakonen, and B. Muralidharan, Steady-state dynamics and non-local correlations in thermoelectric Cooper pair splitters, npj Quantum Inf. 11, 40 (2025).
- C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: A software package for quantum transport, New J. Phys. 16, 063065 (2014).
- Z. Wang and X. Hu, Interference and switching of Josephson current carried by nonlocal spin-entangled electrons in a SQUID-like system with quantum dots, Phys. Rev. Lett. 106, 037002 (2011).
- R. Deacon, A. Oiwa, J. Sailer, S. Baba, Y. Kanai, K. Shibata, K. Hirakawa, and S. Tarucha, Cooper pair splitting in parallel quantum dot Josephson junctions, Nat. Commun. 6, 7446 (2015).
