{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:04:08Z","timestamp":1790762648114,"version":"4.1.0"},"reference-count":52,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T00:00:00Z","timestamp":1721865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Education in Guangdong Province","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Department of Education in Guangdong Province","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Department of Education in Guangdong Province","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Department of Education in Guangdong Province","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Department of Education in Guangdong Province","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Department of Education in Guangdong Province","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Department of Education in Guangdong Province","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Department of Education in Guangdong Province","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Department of Education in Guangdong Province","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Guangdong Province of China","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Guangdong Province of China","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Guangdong Province of China","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Guangdong Province of China","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Guangdong Province of China","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Guangdong Province of China","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Guangdong Province of China","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Guangdong Province of China","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Guangdong Province of China","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Private University Scientific Research Project of Guangdong Private Education Association of China","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Guangdong University Teaching Management Institute of China","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Zhongshan Institute of University of Electronic Science and Technology of China","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Engineering Technology Center of Regular Universities in Guangdong Province","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["2023GXJK542"],"award-info":[{"award-number":["2023GXJK542"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["SJD202302"],"award-info":[{"award-number":["SJD202302"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["4YYJS04"],"award-info":[{"award-number":["4YYJS04"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["GMG2024041"],"award-info":[{"award-number":["GMG2024041"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["GDZLGL2325"],"award-info":[{"award-number":["GDZLGL2325"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["SFTD2022"],"award-info":[{"award-number":["SFTD2022"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["232023XYWLSZ10"],"award-info":[{"award-number":["232023XYWLSZ10"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["2021GCZX005"],"award-info":[{"award-number":["2021GCZX005"]}]},{"name":"Key Laboratory of Regular Universities in Guangdong Province","award":["2023KSYS011"],"award-info":[{"award-number":["2023KSYS011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin\u2013orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.<\/jats:p>","DOI":"10.3390\/nano14151251","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T14:31:07Z","timestamp":1721917867000},"page":"1251","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires"],"prefix":"10.3390","volume":"14","author":[{"given":"Yu-Mei","family":"Gao","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hu","family":"Xiao","sequence":"additional","affiliation":[{"name":"Zhongshan Zhuoman Microelectronics Co., Ltd., Zhongshan 528400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9298-2449","authenticated-orcid":false,"given":"Mou-Hua","family":"Jiang","sequence":"additional","affiliation":[{"name":"South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Chi","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7670-7916","authenticated-orcid":false,"given":"Zi-Chuan","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li-Ming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, UEST of China, Zhongshan Institute, Zhongshan 528400, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"067004","DOI":"10.1103\/PhysRevLett.99.067004","article-title":"Proposed Design of a Josephson Diode","volume":"99","author":"Hu","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1038\/s41586-020-2590-4","article-title":"Observation of superconducting diode effect","volume":"584","author":"Ando","year":"2020","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1038\/d41586-020-02380-8","article-title":"One-way supercurrent achieved in an electrically polar film","volume":"584","author":"Ideue","year":"2020","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1038\/s41567-022-01701-0","article-title":"Superconducting diode effects","volume":"18","author":"Jiang","year":"2022","journal-title":"Nat. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1038\/s41567-022-01699-5","article-title":"Josephson diode effect from Cooper pair momentum in a topological semimetal","volume":"18","author":"Pal","year":"2022","journal-title":"Nat. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1038\/s42254-023-00632-w","article-title":"The superconducting diode effect","volume":"5","author":"Nadeem","year":"2023","journal-title":"Nat. Rev. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1038\/nphys3242","article-title":"Superconducting spintronics","volume":"11","author":"Linder","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10948-018-4884-4","article-title":"Superconductor electronics: Status and outlook","volume":"32","author":"Braginski","year":"2019","journal-title":"J. Supercond. Nov. Magn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e2119548119","DOI":"10.1073\/pnas.2119548119","article-title":"Supercurrent diode effect and finite-momentum superconductors","volume":"119","author":"Yuan","year":"2022","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104501","DOI":"10.1103\/PhysRevB.106.104501","article-title":"Superconducting diode effect due to magnetochiral anisotropy in topological insulators and Rashba nanowires","volume":"106","author":"Legg","year":"2022","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1038\/s42005-024-01618-5","article-title":"Superconducting diode effect sign change in epitaxial Al-InAs Josephson junctions","volume":"7","author":"Lotfizadeh","year":"2024","journal-title":"Commun. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"174516","DOI":"10.1103\/PhysRevB.108.174516","article-title":"Josephson transistor from the superconducting diode effect in domain wall and skyrmion magnetic racetracks","volume":"108","author":"Hess","year":"2023","journal-title":"Phys. Rev. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1103\/PhysRevLett.25.794","article-title":"Current-Phase Relations in Superconducting Bridges","volume":"25","author":"Fulton","year":"1970","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1103\/PhysRevB.6.855","article-title":"Quantum Interference Properties of Double Josephson Junctions","volume":"6","author":"Fulton","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1063\/1.5024540","article-title":"Spatial characterization of the edge barrier in wide superconducting films","volume":"44","author":"Sivakov","year":"2018","journal-title":"Low. Temp. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4573","DOI":"10.1063\/1.321397","article-title":"Dc analysis of parallel arrays of two and three Josephson junctions","volume":"46","author":"Tsang","year":"1975","journal-title":"J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7138","DOI":"10.1021\/acs.nanolett.9b02686","article-title":"Nonlocal Josephson effect in Andreev molecules","volume":"19","author":"Pillet","year":"2019","journal-title":"Nano Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"245415","DOI":"10.1103\/PhysRevB.107.245415","article-title":"Nonsinusoidal current-phase relations in semiconductor-superconductor-ferromagnetic insulator devices","volume":"107","author":"Maiani","year":"2023","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"177001","DOI":"10.1103\/PhysRevLett.128.177001","article-title":"Theory of the supercurrent diode effect in rashba superconductors with arbitrary disorder","volume":"128","author":"Ilic","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3078","DOI":"10.1038\/s41467-023-38856-0","article-title":"Gate-tunable superconducting diode effect in a three-terminal Josephson device","volume":"14","author":"Gupta","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9221","DOI":"10.1021\/acsnano.4c01642","article-title":"Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction","volume":"18","author":"Coraiola","year":"2024","journal-title":"ACS Nano"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1038\/s41578-018-0003-1","article-title":"Majorana zero modes in superconductor-semiconductor heterostructures","volume":"3","author":"Lutchyn","year":"2018","journal-title":"Nat. Rev. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1038\/s41578-021-00336-6","article-title":"Engineered platforms for topological superconductivity and Majorana zero modes","volume":"6","author":"Flensberg","year":"2021","journal-title":"Nat. Rev. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF02961314","article-title":"Teoria simmetrica dellelettrone e del positrone","volume":"14","author":"Majorana","year":"1937","journal-title":"Nuovo Cim"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"085418","DOI":"10.1103\/PhysRevB.96.085418","article-title":"Measuring Majorana nonlocality and spin structure with a quantum dot","volume":"96","author":"Prada","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1103\/RevModPhys.83.1057","article-title":"Topological insulators and superconductors","volume":"83","author":"Qi","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1038\/nphys1915","article-title":"Non-abelian statistics and topological quantum information processing in 1d wire networks","volume":"7","author":"Alicea","year":"2011","journal-title":"Nat. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10938","DOI":"10.1073\/pnas.1810003115","article-title":"Topological quantum computation based on chiral Majorana fermions","volume":"115","author":"Lian","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"205418","DOI":"10.1103\/PhysRevB.89.205418","article-title":"Thermoelectrical detection of majorana states","volume":"89","author":"Lopez","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1186\/s11671-020-03307-y","article-title":"Thermoelectric effect in a quantum dot side-coupled to majorana bound states","volume":"15","author":"Chi","year":"2020","journal-title":"Nanoscale Res. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"124302","DOI":"10.1063\/1.5125971","article-title":"Large enhancement of thermoelectric effect by majorana bound states coupled to a quantum dot","volume":"127","author":"Hong","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"014511","DOI":"10.1103\/PhysRevB.94.014511","article-title":"Majorana spintronics","volume":"94","author":"Liu","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"195301","DOI":"10.1088\/1361-648X\/aa6661","article-title":"Majorana dc Josephson current mediated by a quantum dot","volume":"29","author":"Xu","year":"2017","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"185301","DOI":"10.1088\/1361-648X\/ab052a","article-title":"Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot","volume":"31","author":"Stefanski","year":"2019","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chi, F., Jia, Q.S., Liu, J., Gao, Q.G., Yi, Z.C., and Liu, L.M. (2023). Enhancement of the Josephson Current in a Quantum Dot Connected to Majorana Nanowires. Nanomaterials, 13.","DOI":"10.3390\/nano13091482"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zhang, H.R., Sun, L.L., and Liu, J. (2023). Josephson dc Current through T-Shaped Double-Quantum-Dots Hybridized to Majorana Nanowires. Coatings, 13.","DOI":"10.3390\/coatings13030523"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Gao, Y., and Zhang, X. (2023). Tunable Josephson Current through a Semiconductor Quantum Dot Hybridized to Majorana Trijunction. Coatings, 13.","DOI":"10.3390\/coatings13091627"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"13126","DOI":"10.1103\/PhysRevB.59.13126","article-title":"Photon-assisted andreev tunneling through a mesoscopic hybrid system","volume":"59","author":"Sun","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1103\/PhysRevB.62.648","article-title":"Control of the supercurrent in a mesoscopic four-terminal Josephson junction","volume":"62","author":"Sun","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"8783","DOI":"10.1088\/0953-8984\/13\/39\/307","article-title":"Andreev bound states and the \u03c0-junction transition in a superconductor\/quantum-dot\/superconductor system","volume":"13","author":"Zhu","year":"2001","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"235312","DOI":"10.1103\/PhysRevB.74.235312","article-title":"Control of the supercurrent through a parallel-coupled double quantum dot system","volume":"74","author":"Pan","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"505202","DOI":"10.1088\/0953-8984\/20\/50\/505202","article-title":"Josephson current transport through T-shaped double quantum dots","volume":"20","author":"Cheng","year":"2008","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1038\/nature08432","article-title":"Cooper pair splitter realized in a two-quantum-dot Y-junction","volume":"461","author":"Hofstetter","year":"2009","journal-title":"Nature"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"7446","DOI":"10.1038\/ncomms8446","article-title":"Cooper pair splitting in parallel quantum dot Josephson junctions","volume":"6","author":"Deacon","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"L180507","DOI":"10.1103\/PhysRevB.106.L180507","article-title":"Josephson Current via Spin and Orbital States of a Tunable Double Quantum Dot","volume":"106","author":"Debbarma","year":"2022","journal-title":"Phys. Rev. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"214519","DOI":"10.1103\/PhysRevB.108.214519","article-title":"Design of Josephson diode based on magnetic impurity","volume":"108","author":"Sun","year":"2023","journal-title":"Phys. Rev. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1038\/nature11702","article-title":"The Josephson heat interferometer","volume":"492","author":"Giazotto","year":"2012","journal-title":"Nature"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"267702","DOI":"10.1103\/PhysRevLett.129.267702","article-title":"Josephson Diode Effect in Supercurrent Interferometers","volume":"129","author":"Souto","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1038\/s41586-022-05585-1","article-title":"Realization of a minimal Kitaev chain in coupled quantum dots","volume":"614","author":"Dvir","year":"2023","journal-title":"Nature"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"256001","DOI":"10.1103\/PhysRevLett.131.256001","article-title":"Josephson Junction \u03c0-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot","volume":"131","author":"Debbarma","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"180516","DOI":"10.1103\/PhysRevB.82.180516","article-title":"Tunneling characteristics of a chain of Majorana bound states","volume":"82","author":"Flensberg","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"201308R","DOI":"10.1103\/PhysRevB.84.201308","article-title":"Detecting a majorana-fermion zero mode using a quantum dot","volume":"84","author":"Liu","year":"2011","journal-title":"Phys. Rev. B"}],"container-title":["Nanomaterials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-4991\/14\/15\/1251\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:23:30Z","timestamp":1760109810000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-4991\/14\/15\/1251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,25]]},"references-count":52,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["nano14151251"],"URL":"https:\/\/doi.org\/10.3390\/nano14151251","relation":{},"ISSN":["2079-4991"],"issn-type":[{"value":"2079-4991","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,25]]}}}