JAMP  Vol.5 No.3 , March 2017
Superconductor Hybrids-Electronic Paths to Quantum Computing
Abstract: We review several recent theoretical and experimental results in the study of superconductor hybrids. This includes the recent experimental advances in the study of superconducting beamsplitters as well as more advanced superconductor hybrid systems including ferromagnets or Majorana fermions. In the same manner, theoretical studies have revealed that such superconductor hybrid systems pave the way towards electronic generation and detection of entanglement as well as possible use cases in quantum computing. We will review the aspects in detail and illustrate the possible next steps to be taken.
Cite this paper: Soller, H. (2017) Superconductor Hybrids-Electronic Paths to Quantum Computing. Journal of Applied Mathematics and Physics, 5, 606-622. doi: 10.4236/jamp.2017.53052.

[1]   Onnes, H.K. (1911) The Superconductivity of Mercury. Comm. Phys. Lab. Univ., Leiden, 122-124.
Breyel, D., Schmidt, T.L. and Komnik, A. (2012) Rydberg Crystallization Detection by Statistical Means. Physical Review A, 86, Article ID: 023405.

[2]   Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957) Theory of Superconductivity. Physical Review, 108, 1175-1204.

[3]   Tinkham, M. (1996) Introduction to Superconductivity. Courier Corporation, North Chelmsford.

[4]   De Franceschi, S., Kouwenhoven, L., Schönenberger, C. and Wernsdorfer, W. (2010) Hybrid Superconductor-Quantum Dot Devices. Nature Nanotechnology, 5, 703-711.

[5]   Mourik, V., Zuo, K., Frolov, S.M., Plissard, S.R., Bakkers, E.P.A.M. and Kouwenhoven, L.P. (2012) Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices. Science, 336, 1003-1007.

[6]   Hofstetter, L., Geresdi, A., Aagesen, M., Nygård, J., Schönenberger, C. and Csonka, S. (2010) Ferromagnetic Proximity Effect in a Ferromagnet-Quantum-Dot-Super-conductor Device. Physical Review Letters, 104, Article ID: 246804.

[7]   Kitaev, A.Y. (2001) Unpaired Majorana Fermions in Quantum Wires. Physics-Uspekhi, 44, 131-136.

[8]   Recher, P. and Loss, D. (2002) Creation of Nonlocal Spin-Entangled Electrons via Andreev Tunneling, Coulomb Blockade, and Resonant Transport. Journal of Super-conductivity, 15, 49-65.

[9]   Sköldberg, J., Löfwander, T., Shumeiko, V.S. and Fogelström, M. (2008) Spectrum of Andreev Bound States in a Molecule Embedded inside a Microwave-Excited Superconducting Junction. Physical Review Letters, 101, Article ID: 087002.

[10]   Nussbaumer, T. and Belzig, W. (2004) Quantum Dot Coupled to a Normal and a Superconducting Lead. Nanotechnology, 15, S479-S482.

[11]   Kondo, J. (1964) Resistance Minimum in Dilute Magnetic Alloys. Progress of Theoretical Physics, 32, 37-49.

[12]   Soller, H. (2009) FCS for Superconducting Quantum Point Contacts. Doctoral Dissertation.

[13]   Cohen, M.H., Falicov, L.M. and Phillips, J.C. (1962) Superconductive Tunneling. Physical Review Letters, 8, 316-318.

[14]   Yamada, Y., Tanaka, Y. and Kawakami, N. (2011) Interplay of Kondo and Superconducting Correlations in the Nonequilibrium Andreev Transport through a Quantum Dot. Physical Review B, 84, Article ID: 075484.

[15]   Soller, H. (2014) Proximity Effect in Normal-Superconductor Hybrids at the Nanoscale. Journal of Applied Mathematics and Physics, 2, 745-752.

[16]   Muzykantskii, B.A. and Khmelnitskii, D.E. (1994) Quantum Shot Noise in a Normal-Metal-Superconductor Point Contact. Physical Review B, 50, 3982-3987.

[17]   Cuevas, J.C., Martin-Rodero, A. and Yeyati, A.L. (1996) Hamiltonian Approach to the Transport Properties of Superconducting Quantum Point Contacts. Physical Review B, 54, 7366-7379.

[18]   Andreev, A.F. (1964) Thermal Conductivity of the Intermediate State of Superconductors. JETP Letters, 46, 1823-1828.

[19]   Grein, R., Löfwander, T., Metalidis, G. and Eschrig, M. (2010) Theory of Superconductor-Ferromagnet Point-Contact Spectra: The Case of Strong Spin Polarization. Physical Review B, 81, Article ID: 094508.

[20]   Soller, H., Hofstetter, L., Csonka, S., Yeyati, A. L., Schönenberger, C. and Komnik, A. (2012) Kondo Effect and Spin-Active Scattering in Ferromagnet-Superconductor Junctions. Physical Review B, 85, Article ID: 174512.

[21]   Pérez-Willard, F., Cuevas, J.C., Sürgers, C., Pfundstein, P., Kopu, J., Eschrig, M. and Löhneysen, H.V. (2004) Determining the Current Polarization in Al/Co Nanostructured Point Contacts. Physical Review B, 69, Article ID: 140502.

[22]   Soller, H. (2013) Fcs of Superconducting Tunnel Junctions in Nonequilibrium. International Journal of Modern Physics B, 27, Article ID: 1350072.

[23]   Soller, H. and Komnik, A. (2011) Hamiltonian Approach to the Charge Transfer Statistics of Kondo Quantum Dots Contacted by a Normal Metal and a Superconductor. Physica E: Low-Dimensional Systems and Nanostructures, 44, 425-429.

[24]   Cuevas, J.C., Martín-Rodero, A. and Yeyati, A.L. (1999) Shot Noise and Coherent Multiple Charge Transfer in Superconducting Quantum Point Contacts. Physical Review Letters, 82, 4086-4089.

[25]   Soller, H. and Komnik, A. (2011) Charge Transfer Statistics and Entanglement in Normal-Quantum Dot-Superconductor Hybrid Structures. The European Physical Journal D, 63, 3-8.

[26]   Soller, H. and Komnik, A. (2012) P-Wave Cooper Pair Splitting. Beilstein Journal of Nanotechnology, 3, 493-500.

[27]   Machon, P., Eschrig, M. and Belzig, W. (2013) Nonlocal Thermoelectric Effects and Nonlocal Onsager Relations in a Three-Terminal Proximity-Coupled Superconductor-Ferromagnet Device. Physical Review Letters, 110, Article ID: 047002.

[28]   Belzig, W., Wilhelm, F.K., Bruder, C., Schön, G. and Zaikin, A.D. (1999) Quasiclassical Green’s Function Approach to Mesoscopic Superconductivity. Superlattices and Microstructures, 25, 1251-1288.

[29]   Hofstetter, L., Csonka, S., Baumgartner, A., Fülöp, G., d’Hollosy, S., Nygård, J. and Schönenberger, C. (2011) Finite-Bias Cooper Pair Splitting. Physical Review Letters, 107, Article ID: 136801.

[30]   Schindele, J., Baumgartner, A. and Schönenberger, C. (2012) Near-Unity Cooper Pair Splitting Efficiency. Physical Review Letters, 109, Article ID: 157002.

[31]   Soller, H. (2014) Generic Model for Cooper Pair Splitting. International Journal of Modern Physics B, 28, Article ID: 1450137.

[32]   Soller, H. (2013) Non-Linear Transport Properties of Hybrid Nanoelectronic Devices. Logos Verlag, Berlin.

[33]   Goldhaber-Gordon, D., Shtrikman, H., Mahalu, D., Abusch-Magder, D., Meirav, U. and Kastner, M.A. (1998) Kondo Effect in a Single-Electron Transistor. Nature, 391, 156-159.

[34]   Jehl, X., Sanquer, M., Calemczuk, R. and Mailly, D. (2000) Detection of Doubled Shot Noise in Short Normal-Metal/Superconductor Junctions. Nature, 405, 50-53.

[35]   Soller, H. and Komnik, A. (2014) Full Counting Statistics of Interacting Quantum Dots Contacted by a Normal Metal and a Superconductor. Europhysics Letters, 106, 37009.

[36]   Schmidt, T.L., Komnik, A. and Gogolin, A.O. (2007) Hanbury Brown-Twiss Correlations and Noise in the Charge Transfer Statistics through a Multiterminal Kondo Dot. Physical Review Letters, 98, Article ID: 056603.

[37]   Fazio, R. and Raimondi, R. (1998) Resonant Andreev Tunneling in Strongly Interacting Quantum Dots. Physical Review Letters, 80, 2913-2916.

[38]   Braggio, A., Governale, M., Pala, M.G. and König, J. (2011) Superconducting Proximity Effect in Interacting Quantum Dots Revealed by Shot Noise. Solid State Communications, 151, 155-158.

[39]   Albrecht, K.F., Soller, H., Mühlbacher, L. and Komnik, A. (2013) Transient Dynamics and Steady State Behavior of the Anderson-Holstein Model with a Superconducting Lead. Physica E: Low-Dimensional Systems and Nanostructures, 54, 15-23.

[40]   Zazunov, A., Egger, R., Mora, C. and Martin, T. (2006) Superconducting Transport through a Vibrating Molecule. Physical Review B, 73, Article ID: 214501.

[41]   Bai, L., Zhang, Z.Z. and Jiang, L. (2011) Andreev Reflection Current through a Molecule Quantum Dot in the Presence of the Electron-Phonon Interaction and the Spin-Flip Scattering. Physics Letters A, 375, 661-665.

[42]   Zazunov, A. and Egger, R. (2010) Adiabatic Polaron Dynamics and Josephson Effect in a Superconducting Molecular Quantum Dot. Physical Review B, 81, Article ID: 104508.

[43]   Recher, P., Sukhorukov, E.V. and Loss, D. (2001) Andreev Tunneling, Coulomb Blockade, and Resonant Transport of Non-local Spin-Entangled Electrons. Physical Review B, 63, Article ID: 165314.

[44]   Chevallier, D., Rech, J., Jonckheere, T. and Martin, T. (2011) Current and Noise Correlations in a Double-Dot Cooper-Pair Beam Splitter. Physical Review B, 83, Article ID: 125421.

[45]   Burset, P., Herrera, W.J. and Yeyati, A.L. (2011) Microscopic Theory of Cooper Pair Beam Splitters Based on Carbon Nanotubes. Physical Review B, 84, Article ID: 115448.

[46]   Di Lorenzo, A. and Nazarov, Y.V. (2005) Full Counting Statistics with Spin-Sensitive Detectors Reveals Spin Singlets. Physical Review Letters, 94, Article ID: 210601.

[47]   Akhmerov, A.R., et al. (2011) Quantized Conductance at the Majorana Phase Transition in a Disordered Superconducting Wire. Physical Review Letters, 106, Article ID: 057001.

[48]   Liu, J., Potter, A.C., Law, K.T. and Lee, P.A. (2012) Zero-Bias Peaks in the Tunneling Conductance of Spin-Orbit-Coupled Superconducting Wires with and without Majorana End-States. Physical Review Letters, 109, Article ID: 267002.

[49]   Oreg, Y., Refael, G. and von Oppen, F. (2010) Helical Liquids and Majorana Bound States in Quantum Wires. Physical Review Letters, 105, Article ID: 177002.

[50]   Gangadharaiah, S., Braunecker, B., Simon, P. and Loss, D. (2011) Majorana Edge States in Interacting One-Dimensional Systems. Physical Review Letters, 107, Article ID: 036801.

[51]   Soller, H. and Breyel, D. (2013) Signatures in the Conductance for Phase Transitions in Excitonic Systems. Modern Physics Letters B, 27, Article ID: 1350185.

[52]   Soller, H. and Komnik, A. (2014) Charge Transfer Statistics of Transport through Majorana Bound States. Physica E: Low-Dimensional Systems and Nanostructures, 63, 99-104.

[53]   Beenakker, C.W.J. (2013) Search for Majorana Fermions in Superconductors. Annual Review of Condensed Matter Physics, 4, 113-136.

[54]   Soller, H. (2016) Dissipative Quantum Computing with Majorana Fermions. Journal of Applied Mathematics and Physics, 4, 227-232.

[55]   Soller, H., Dolcini, F. and Komnik, A. (2012) Nanotransformation and Current Fluctuations in Exciton Condensate Junctions. Physical Review Letters, 108, Article ID: 156401.

[56]   Soller, H. (2015) Exciton Condensates and Superconductors-Technical Differences and Physical Similarities. Journal of Applied Mathematics and Physics, 3, 1218-1225.