Second Order Perturbation Theory for a Superconducting Double Quantum Dot

JPS Conf. Proc. 30, 011002 (2020) [8 pages]

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)

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Vladislav Pokorný¹, Martin Žonda², Georgios Loukeris², and Tomáš Novotný³^,*

¹Institute of Physics, Czech Academy of Sciences, Na Slovance 2, Praha 8 CZ-182 21, Czech Republic

²Institute of Physics, Albert Ludwig University of Freiburg, Hermann-Herder-Strasse 3, Freiburg DE-791 04, Germany

³Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Praha 2 CZ-121 16, Czech Republic

Received September 2, 2019

We extend our approach based on the second order perturbation theory in the Coulomb interaction recently developed for quantum dots coupled to superconducting leads to the superconducting double quantum dot setups. Using our perturbative method we evaluate several single-particle quantities such as on-dot induced gap and generalized occupations together with the Andreev in-gap spectra and compare them with numerically exact results from the Numerical Renormalization Group and Quantum Monte Carlo finding a very good correspondence for not too strongly correlated regimes. Thus we can offer in a wide parameter range this method as an efficient and reliable alternative to the heavy numerical tools exclusively used so far for the description of such experimentally relevant systems.

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https://doi.org/10.7566/JPSCP.30.011002

References

1) S.De Franceschi, L.Kouwenhoven, C.Schönenberger, and W.Wernsdorfer, Nat. Nanotechnol. 5, 703 (2010). 10.1038/nnano.2010.173 Google Scholar
2) J. P.Cleuziou, W.Wernsdorfer, V.Bouchiat, T.Ondarcuhu, and M.Monthioux, Nat. Nanotechnol. 1, 53 (2006). 10.1038/nnano.2006.54 Google Scholar
3) V.Bouchiat, Supercond. Sci. Technol. 22, 064002 (2009). 10.1088/0953-2048/22/6/064002 Google Scholar
4) J. D.Pillet, P.Joyez, R.Žitko, and M. F.Goffman, Phys. Rev. B 88, 045101 (2013). 10.1103/PhysRevB.88.045101 Google Scholar
5) D.Sherman, J. S.Yodh, S. M.Albrecht, J.Nygård, P.Krogstrup, and C. M.Marcus, Nat. Nanotechnol. 12, 212 (2017). 10.1038/nnano.2016.227 Google Scholar
6) J. C.Estrada Saldaña, A.Vekris, G.Steffensen, R.Žitko, P.Krogstrup, J.Paaske, K.Grove-Rasmussen, and J.Nygård, Phys. Rev. Lett. 121, 257701 (2018). 10.1103/PhysRevLett.121.257701 Google Scholar
7) K.Grove-Rasmussen, G.Steffensen, A.Jellinggaard, M. H.Madsen, R.Žitko, J.Paaske, and J.Nygård, Nat. Commun. 9, 2376 (2018). 10.1038/s41467-018-04683-x Google Scholar
8) J. C.Estrada Saldaña, A.Vekris, R.Žitko, G.Steffensen, P.Krogstrup, J.Paaske, K.Grove-Rasmussen, and J.Nygård, arXiv:1812.09303.Google Scholar
9) Z.Su, A. B.Tacla, M.Hocevar, D.Car, S. R.Plissard, E. P. A. M.Bakkers, A. J.Daley, D.Pekker, and S. M.Frolov, Nat. Commun. 8, 585 (2017). 10.1038/s41467-017-00665-7 Google Scholar
10) M.Ruby, B. W.Heinrich, Y.Peng, F.von Oppen, and K. J.Franke, Phys. Rev. Lett. 120, 156803 (2018). 10.1103/PhysRevLett.120.156803 Google Scholar
11) D.-J.Choi, C. G.Fernández, E.Herrera, C.Rubio-Verdú, M. M.Ugeda, I.Guillamón, H.Suderow, J. I.Pascual, and N.Lorente, Phys. Rev. Lett. 120, 167001 (2018). 10.1103/PhysRevLett.120.167001 Google Scholar
12) S.Kezilebieke, R.Žitko, M.Dvorak, T.Ojanen, and P.Liljeroth, Nano Lett. 19, 4614 (2019). 10.1021/acs.nanolett.9b01583 Google Scholar
13) S.Droste, S.Andergassen, and J.Splettstoesser, J. Phys.: Condens. Matter 24, 415301 (2012). 10.1088/0953-8984/24/41/415301 Google Scholar
14) S.Pfaller, A.Donarini, and M.Grifoni, Phys. Rev. B 87, 155439 (2013). 10.1103/PhysRevB.87.155439 Google Scholar
15) R.Žitko, Phys. Rev. B 91, 165116 (2015). 10.1103/PhysRevB.91.165116 Google Scholar
16) M.Žonda, V.Pokorný, V.Janiš, and T.Novotný, Sci. Rep. 5, 8821 (2015). 10.1038/srep08821 Google Scholar
17) M.Žonda, V.Pokorný, V.Janiš, and T.Novotný, Phys. Rev. B 93, 024523 (2016). 10.1103/PhysRevB.93.024523 Google Scholar
18) A.Kadlecová, M.Žonda, and T.Novotný, Phys. Rev. B 95, 195114 (2017). 10.1103/PhysRevB.95.195114 Google Scholar
19) J.Bauer, A.Oguri, and A. C.Hewson, J. Phys.: Condens. Matter 19, 486211 (2007). 10.1088/0953-8984/19/48/486211 Google Scholar
20) O.Parcollet, M.Ferrero, T.Ayral, H.Hafermann, I.Krivenko, L.Messio, and P.Seth, Comput. Phys. Commun. 196, 398 (2015). 10.1016/j.cpc.2015.04.023 Google Scholar
21) H. J.Vidberg and J. W.Serene, J. Low Temp. Phys. 29, 179 (1977). 10.1007/BF00655090 Google Scholar
22) R.Bulla, T. A.Costi, and T.Pruschke, Rev. Mod. Phys. 80, 395 (2008). 10.1103/RevModPhys.80.395 Google Scholar
23) T.Hecht, A.Weichselbaum, J.von Delft, and R.Bulla, J. Phys.: Condens. Matter 20, 275213 (2008). 10.1088/0953-8984/20/27/275213 Google Scholar
24) R.Žitko and T.Pruschke, Phys. Rev. B 79, 085106 (2009). 10.1103/PhysRevB.79.085106 Google Scholar
25) R. Žitko, NRG Ljubljana - Open Source Numerical Renormalization Group Code, nrgljubljana.ijs.si.Google Scholar
26) P.Seth, I.Krivenko, M.Ferrero, and O.Parcollet, Comput. Phys. Commun. 200, 274 (2016). 10.1016/j.cpc.2015.10.023 Google Scholar
27) V.Pokorný and M.Žonda, Physica B 536, 488 (2018). 10.1016/j.physb.2017.08.059 Google Scholar
28) A.Kadlecová, M.Žonda, V.Pokorný, and T.Novotný, Phys. Rev. Appl. 11, 044094 (2019). 10.1103/PhysRevApplied.11.044094 Google Scholar

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