DOI: 10.1063/10.0029644. Josephson effect in superconductive bridges: microscopic theory

Josephson effect in superconductive bridges: microscopic theory

10.1063/10.0029644

Crossref journal-article

AIP Publishing

Soviet Journal of Low Temperature Physics (317)

Abstract

A theory is developed for the stationary Josephson effect in superconductive constrictions (microbridges).The theory is based on the microscopic Eilenberger equations and is valid for arbitrary temperatures 0&lt;T&lt;Tc. The current-phase relationships I(Q) and critical current Ic(T) obtained differ from the corresponding expressions for a tunnel junction. The difference is greatest at low temperatures and for limitingly pure bridges. In the pure limit l≫a (where l is the free path length; a is the orifice radius) the current is expressed by the formula I(φ)=πΔ0(T)eRNsin(φ/2) th Δn(T)cos(φ/2)2T. The critical current of a pure microbridge at t = 0 is twice the critical current of a tunnel junction with the same normal resistance RN, and the phase-current relationship at the points Q = ±π is discontinuous. The properties of microbridges in the pure (l≫a) and dirty (l≪a) limits are compared.

Bibliography

Kulik, I. O., & Omelâyanchuk, A. N. (1978). Josephson effect in superconductive bridges: microscopic theory. Soviet Journal of Low Temperature Physics, 4(3), 142â149.

Authors 2

I. O. Kulik (first)
A. N. Omel’yanchuk (additional)

References 29 Referenced 82

{'key': '2024112518110292800_c1', 'volume-title': 'Quantum Field Theory Methods in Statistical Physics [in Russian]', 'year': '1962'} / Quantum Field Theory Methods in Statistical Physics [in Russian] (1962)
{'key': '2024112518110292800_c2', 'volume-title': 'The Josephson Effect in Superconductive Tunnel Structures [in Russian]', 'year': '1970'} / The Josephson Effect in Superconductive Tunnel Structures [in Russian] (1970)
{'key': '2024112518110292800_c3', 'first-page': '945', 'volume': '3', 'year': '1977', 'journal-title': 'Fiz. Nizk. Temp.'} / Fiz. Nizk. Temp. (1977)
{'key': '2024112518110292800_c4', 'first-page': '216', 'volume': '21', 'year': '1975', 'journal-title': 'Pis’ma Zh. Eksp. Teor. Fiz.'} / Pis’ma Zh. Eksp. Teor. Fiz. (1975)
10.1103/PhysRevLett.10.486 / Phys. Rev. Lett.
10.1103/PhysRevLett.11.104 / Phys. Rev. Lett. by Ambegaokar (1963)
{'key': '2024112518110292800_c6', 'volume-title': 'Inst. Fiz. Mat., Sib. Otd. Akad. Nauk SSSR', 'year': '1973'} / Inst. Fiz. Mat., Sib. Otd. Akad. Nauk SSSR (1973)
{'key': '2024112518110292800_c7', 'first-page': '906', 'volume': '1', 'year': '1975', 'journal-title': 'Fiz. Nizk. Temp.'} / Fiz. Nizk. Temp. (1975)
{'key': '2024112518110292800_c8', 'first-page': '150', 'volume': '9', 'year': '1969', 'journal-title': 'Pis’ma Zh. Eksp. Teor. Fiz.'} / Pis’ma Zh. Eksp. Teor. Fiz. (1969)
10.1007/BF00628738 / J. Low Temp. Phys. (1971)
{'key': '2024112518110292800_c10', 'first-page': '2139', 'volume': '68', 'year': '1975', 'journal-title': 'Zh. Eksp. Teor. Fiz.'} / Zh. Eksp. Teor. Fiz. (1975)
{'key': '2024112518110292800_c11', 'first-page': '1503', 'volume': '45', 'year': '1975', 'journal-title': 'Zh. Eksp.Teor. Fiz.'} / Zh. Eksp.Teor. Fiz. (1975)
{'key': '2024112518110292800_c12', 'volume-title': 'Electrical Contacts [Russian translation]', 'year': '1961'} / Electrical Contacts [Russian translation] (1961)
{'key': '2024112518110292800_c13', 'first-page': '984', 'volume': '48', 'year': '1965', 'journal-title': 'Zh. Eksp. Teor. Fiz.'} / Zh. Eksp. Teor. Fiz. (1965)
{'key': '2024112518110292800_c14', 'first-page': '465', 'volume': '25', 'year': '1977', 'journal-title': 'Pis’ma Zh. Eksp. Teor. Fiz.'} / Pis’ma Zh. Eksp. Teor. Fiz. (1977)
10.1007/BF01379803 / Z. Phys. (1968)
{'key': '2024112518110292800_c16', 'volume-title': 'Superconductivity of Metals and Alloys [Russian translation]', 'year': '1968'} / Superconductivity of Metals and Alloys [Russian translation] (1968)
{'key': '2024112518110292800_c17', 'first-page': '547', 'volume': '216', 'year': '1953', 'journal-title': 'Proc. Roy. Soc. A'} / Proc. Roy. Soc. A (1953)
{'key': '2024112518110292800_c18', 'first-page': '1364', 'volume': '15', 'year': '1973', 'journal-title': 'Fiz. Tverd. Tela (Leningrad)'} / Fiz. Tverd. Tela (Leningrad) (1973)
10.1007/BF00654918 / J. Low Temp. Phys. (1973)
10.1103/PhysRevLett.25.507 / Phys. Rev. Lett. (1970)
{'key': '2024112518110292800_c21', 'volume-title': 'The Mathematical Apparatus of Physics [in Russian]', 'year': '1961'} / The Mathematical Apparatus of Physics [in Russian] (1961)
10.1016/0038-1098(77)91333-3 / Solid State Commun. (1977)
10.1103/RevModPhys.36.312 / Rev. Mod. Phys. by Discussion 49 (1964)
10.1002/pssa.2210170104 / Phys. Status Solidi (a) (1973)
{'key': '2024112518110292800_c25', 'volume-title': 'Ph. D. Dissertation', 'year': '1976'} / Ph. D. Dissertation (1976)
{'key': '2024112518110292800_c26', 'first-page': '544', 'volume-title': 'Proc. Appl. Superconductivity Conference', 'year': '1972'} / Proc. Appl. Superconductivity Conference (1972)
{'key': '2024112518110292800_c27', 'first-page': '141', 'volume': '1', 'year': '1975', 'journal-title': 'Fiz. Nizk. Temp.'} / Fiz. Nizk. Temp. (1975)
{'key': '2024112518110292800_c28', 'first-page': '1522', 'volume': '2', 'year': '1976', 'journal-title': 'Fiz. Nizk. Temp.'} / Fiz. Nizk. Temp. (1976)

Dates

Type	When
Created	9 months, 1 week ago (Nov. 25, 2024, 1:11 p.m.)
Deposited	9 months, 1 week ago (Nov. 25, 2024, 1:11 p.m.)
Indexed	2 months ago (July 5, 2025, 1:22 a.m.)
Issued	47 years, 6 months ago (March 1, 1978)
Published	47 years, 6 months ago (March 1, 1978)
Published Print	47 years, 6 months ago (March 1, 1978)

Funders 0

None

BibTeX

@article{Kulik_1978, title={Josephson effect in superconductive bridges: microscopic theory}, volume={4}, ISSN={0360-0335}, url={http://dx.doi.org/10.1063/10.0029644}, DOI={10.1063/10.0029644}, number={3}, journal={Soviet Journal of Low Temperature Physics}, publisher={AIP Publishing}, author={Kulik, I. O. and Omel’yanchuk, A. N.}, year={1978}, month=mar, pages={142–149} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        5
      ]
    ],
    "date-time": "2025-07-05T05:22:21Z",
    "timestamp": 1751692941935,
    "version": "3.28.0"
  },
  "reference-count": 29,
  "publisher": "AIP Publishing",
  "issue": "3",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1978,
        3,
        1
      ]
    ]
  },
  "abstract": "<jats:p>A theory is developed for the stationary Josephson effect in superconductive constrictions (microbridges).The theory is based on the microscopic Eilenberger equations and is valid for arbitrary temperatures 0&amp;lt;T&amp;lt;Tc. The current-phase relationships I(Q) and critical current Ic(T) obtained differ from the corresponding expressions for a tunnel junction. The difference is greatest at low temperatures and for limitingly pure bridges. In the pure limit l\u226ba (where l is the free path length; a is the orifice radius) the current is expressed by the formula I(\u03c6)=\u03c0\u03940(T)eRNsin(\u03c6/2)\u00a0th\u00a0\u0394n(T)cos(\u03c6/2)2T. The critical current of a pure microbridge at t = 0 is twice the critical current of a tunnel junction with the same normal resistance RN, and the phase-current relationship at the points Q = \u00b1\u03c0 is discontinuous. The properties of microbridges in the pure (l\u226ba) and dirty (l\u226aa) limits are compared.</jats:p>",
  "DOI": "10.1063/10.0029644",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2024,
        11,
        25
      ]
    ],
    "date-time": "2024-11-25T18:11:09Z",
    "timestamp": 1732558269000
  },
  "page": "142-149",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 82,
  "title": "Josephson effect in superconductive bridges: microscopic theory",
  "prefix": "10.1063",
  "volume": "4",
  "author": [
    {
      "given": "I. O.",
      "family": "Kulik",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR"
        }
      ]
    },
    {
      "given": "A. N.",
      "family": "Omel\u2019yanchuk",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024112518110292800_c1",
      "volume-title": "Quantum Field Theory Methods in Statistical Physics [in Russian]",
      "year": "1962"
    },
    {
      "key": "2024112518110292800_c2",
      "volume-title": "The Josephson Effect in Superconductive Tunnel Structures [in Russian]",
      "year": "1970"
    },
    {
      "key": "2024112518110292800_c3",
      "first-page": "945",
      "volume": "3",
      "year": "1977",
      "journal-title": "Fiz. Nizk. Temp."
    },
    {
      "key": "2024112518110292800_c4",
      "first-page": "216",
      "volume": "21",
      "year": "1975",
      "journal-title": "Pis\u2019ma Zh. Eksp. Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c5a",
      "doi-asserted-by": "publisher",
      "first-page": "486",
      "DOI": "10.1103/PhysRevLett.10.486",
      "volume": "10",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024112518110292800_c5b",
      "doi-asserted-by": "publisher",
      "first-page": "104",
      "DOI": "10.1103/PhysRevLett.11.104",
      "volume": "11",
      "author": "Ambegaokar",
      "year": "1963",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024112518110292800_c6",
      "volume-title": "Inst. Fiz. Mat., Sib. Otd. Akad. Nauk SSSR",
      "year": "1973"
    },
    {
      "key": "2024112518110292800_c7",
      "first-page": "906",
      "volume": "1",
      "year": "1975",
      "journal-title": "Fiz. Nizk. Temp."
    },
    {
      "key": "2024112518110292800_c8",
      "first-page": "150",
      "volume": "9",
      "year": "1969",
      "journal-title": "Pis\u2019ma Zh. Eksp. Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c9",
      "doi-asserted-by": "publisher",
      "first-page": "349",
      "DOI": "10.1007/BF00628738",
      "volume": "4",
      "year": "1971",
      "journal-title": "J. Low Temp. Phys."
    },
    {
      "key": "2024112518110292800_c10",
      "first-page": "2139",
      "volume": "68",
      "year": "1975",
      "journal-title": "Zh. Eksp. Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c11",
      "first-page": "1503",
      "volume": "45",
      "year": "1975",
      "journal-title": "Zh. Eksp.Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c12",
      "volume-title": "Electrical Contacts [Russian translation]",
      "year": "1961"
    },
    {
      "key": "2024112518110292800_c13",
      "first-page": "984",
      "volume": "48",
      "year": "1965",
      "journal-title": "Zh. Eksp. Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c14",
      "first-page": "465",
      "volume": "25",
      "year": "1977",
      "journal-title": "Pis\u2019ma Zh. Eksp. Teor. Fiz."
    },
    {
      "key": "2024112518110292800_c15",
      "doi-asserted-by": "publisher",
      "first-page": "195",
      "DOI": "10.1007/BF01379803",
      "volume": "214",
      "year": "1968",
      "journal-title": "Z. Phys."
    },
    {
      "key": "2024112518110292800_c16",
      "volume-title": "Superconductivity of Metals and Alloys [Russian translation]",
      "year": "1968"
    },
    {
      "key": "2024112518110292800_c17",
      "first-page": "547",
      "volume": "216",
      "year": "1953",
      "journal-title": "Proc. Roy. Soc. A"
    },
    {
      "key": "2024112518110292800_c18",
      "first-page": "1364",
      "volume": "15",
      "year": "1973",
      "journal-title": "Fiz. Tverd. Tela (Leningrad)"
    },
    {
      "key": "2024112518110292800_c19",
      "doi-asserted-by": "publisher",
      "first-page": "407",
      "DOI": "10.1007/BF00654918",
      "volume": "10",
      "year": "1973",
      "journal-title": "J. Low Temp. Phys."
    },
    {
      "key": "2024112518110292800_c20",
      "doi-asserted-by": "publisher",
      "first-page": "507",
      "DOI": "10.1103/PhysRevLett.25.507",
      "volume": "25",
      "year": "1970",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024112518110292800_c21",
      "volume-title": "The Mathematical Apparatus of Physics [in Russian]",
      "year": "1961"
    },
    {
      "key": "2024112518110292800_c22",
      "doi-asserted-by": "publisher",
      "first-page": "301",
      "DOI": "10.1016/0038-1098(77)91333-3",
      "volume": "23",
      "year": "1977",
      "journal-title": "Solid State Commun."
    },
    {
      "key": "2024112518110292800_c23",
      "doi-asserted-by": "publisher",
      "first-page": "312",
      "DOI": "10.1103/RevModPhys.36.312",
      "volume": "36",
      "author": "Discussion 49",
      "year": "1964",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024112518110292800_c24",
      "doi-asserted-by": "publisher",
      "first-page": "59",
      "DOI": "10.1002/pssa.2210170104",
      "volume": "17",
      "year": "1973",
      "journal-title": "Phys. Status Solidi (a)"
    },
    {
      "key": "2024112518110292800_c25",
      "volume-title": "Ph. D. Dissertation",
      "year": "1976"
    },
    {
      "key": "2024112518110292800_c26",
      "first-page": "544",
      "volume-title": "Proc. Appl. Superconductivity Conference",
      "year": "1972"
    },
    {
      "key": "2024112518110292800_c27",
      "first-page": "141",
      "volume": "1",
      "year": "1975",
      "journal-title": "Fiz. Nizk. Temp."
    },
    {
      "key": "2024112518110292800_c28",
      "first-page": "1522",
      "volume": "2",
      "year": "1976",
      "journal-title": "Fiz. Nizk. Temp."
    }
  ],
  "container-title": "Soviet Journal of Low Temperature Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/ltp/article-pdf/4/3/142/20264395/142_1_10.0029644.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/ltp/article-pdf/4/3/142/20264395/142_1_10.0029644.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        11,
        25
      ]
    ],
    "date-time": "2024-11-25T18:11:13Z",
    "timestamp": 1732558273000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/ltp/article/4/3/142/3321783/Josephson-effect-in-superconductive-bridges"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1978,
        3,
        1
      ]
    ]
  },
  "references-count": 29,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1978,
          3,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/10.0029644",
  "relation": {},
  "ISSN": [
    "0360-0335"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1978,
        3
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1978,
        3,
        1
      ]
    ]
  }
}