Semiclassical theory of quasiparticles in giant vortices
Methods for investigating Andreev bound states in superconducting vortices continue to be of experimental and theoretical interest [Phys. Rev. Lett. 90 (2003) 177002]. We have recently developed a semiclassical theory of quasiparticles in the superconducting state [Ann. Phy. (NY) 298 (2002) 273]. It...
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| Published in: | Physica. C, Superconductivity Vol. 404; no. 1; pp. 153 - 157 |
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01-05-2004
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| Abstract | Methods for investigating Andreev bound states in superconducting vortices continue to be of experimental and theoretical interest [Phys. Rev. Lett. 90 (2003) 177002]. We have recently developed a semiclassical theory of quasiparticles in the superconducting state [Ann. Phy. (NY) 298 (2002) 273]. It is based upon the study of classical orbits, the Bogoliubov–de Gennes equation being replaced by Hamiltonian systems describing an effective (fictious) classical mechanics. The orbits are quantised using a generalisation of the Bohr–Sommerfeld or EBK quantisation rule which includes both a Maslov index and an additional topological integer arising from the lines of phase singularity running along the vortex cores. We deploy this theory to the spectra of a single giant vortex. |
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| AbstractList | Methods for investigating Andreev bound states in superconducting vortices continue to be of experimental and theoretical interest [Phys. Rev. Lett. 90 (2003) 177002]. We have recently developed a semiclassical theory of quasiparticles in the superconducting state [Ann. Phy. (NY) 298 (2002) 273]. It is based upon the study of classical orbits, the Bogoliubov–de Gennes equation being replaced by Hamiltonian systems describing an effective (fictious) classical mechanics. The orbits are quantised using a generalisation of the Bohr–Sommerfeld or EBK quantisation rule which includes both a Maslov index and an additional topological integer arising from the lines of phase singularity running along the vortex cores. We deploy this theory to the spectra of a single giant vortex. |
| Author | Györffy, Balazs L. Duncan, Kevin P. |
| Author_xml | – sequence: 1 givenname: Kevin P. surname: Duncan fullname: Duncan, Kevin P. email: k.duncan@open.ac.uk organization: Department of Applied Mathematics, The Open University, Milton Keynes MK7 6AA, UK – sequence: 2 givenname: Balazs L. surname: Györffy fullname: Györffy, Balazs L. organization: H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK |
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| CitedBy_id | crossref_primary_10_1103_PhysRevA_77_063617 crossref_primary_10_1103_PhysRevA_75_011603 |
| Cites_doi | 10.1103/PhysRevLett.90.177002 10.1103/PhysRevLett.85.1528 10.1038/36797 10.1073/pnas.082096799 10.1016/0031-9163(64)90375-0 10.1103/PhysRev.187.556 10.1088/0953-8984/15/2/323 10.1006/aphy.2002.6240 |
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| Keywords | Magnetic flux Quasiparticles Singularity Andreev reflection Superconductors Hamiltonians Vortices Theoretical study Semiclassical theory Quantum theory |
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| MeetingName | Third European Conference on Vortex Matter in Superconductors at Extreme Scales and Conditions, Crete, Greece, September 20-28, 2003 (VORTEX-ESF) |
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| References | K.P. Duncan, B.L. Györffy, Physica C (2004), these Proceedings Giem, Giem (BIB3) 2000; 85 Koshelev, Golubov (BIB1) 2003; 90 Bardeen, Kümmel, Jacobs, Tewordt (BIB8) 1969; 187 Tanaka, Robel, Jankó (BIB4) 2002; 99 Maslov, Fedoriuk (BIB13) 1981 de Gennes (BIB6) 1989 Gutzwiller (BIB10) 1990 Volovik (BIB15) 2003 Andreev, Andreev (BIB7) 1964; 19 Caroli, de Gennes, Matricon (BIB14) 1964; 9 Ozorio de Almeida (BIB11) 1988 Volovik (BIB5) 1993; 57 Azbel (BIB9) 1971; 32 Duncan, Györffy (BIB2) 2002; 298 Duncan, Györffy (BIB16) 2003; 15 Brack, Bhaduri (BIB12) 1997 Caroli (10.1016/j.physc.2003.10.035_BIB14) 1964; 9 Giem (10.1016/j.physc.2003.10.035_BIB3_1) 2000; 85 Azbel (10.1016/j.physc.2003.10.035_BIB9) 1971; 32 10.1016/j.physc.2003.10.035_BIB17 Koshelev (10.1016/j.physc.2003.10.035_BIB1) 2003; 90 Ozorio de Almeida (10.1016/j.physc.2003.10.035_BIB11) 1988 Andreev (10.1016/j.physc.2003.10.035_BIB7_2) 1966; 22 Maslov (10.1016/j.physc.2003.10.035_BIB13) 1981 Volovik (10.1016/j.physc.2003.10.035_BIB5) 1993; 57 Andreev (10.1016/j.physc.2003.10.035_BIB7_1) 1964; 19 Tanaka (10.1016/j.physc.2003.10.035_BIB4) 2002; 99 de Gennes (10.1016/j.physc.2003.10.035_BIB6) 1989 Gutzwiller (10.1016/j.physc.2003.10.035_BIB10) 1990 Giem (10.1016/j.physc.2003.10.035_BIB3_2) 1997; 390 Duncan (10.1016/j.physc.2003.10.035_BIB16) 2003; 15 Bardeen (10.1016/j.physc.2003.10.035_BIB8) 1969; 187 Brack (10.1016/j.physc.2003.10.035_BIB12) 1997 Duncan (10.1016/j.physc.2003.10.035_BIB2) 2002; 298 Volovik (10.1016/j.physc.2003.10.035_BIB15) 2003 |
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| SubjectTerms | Condensed matter: electronic structure, electrical, magnetic, and optical properties Critical currents Exact sciences and technology Physics Properties of type I and type II superconductors Proximity effects, weak links, tunneling phenomena, and josephson effects, adreev effect, sn and sns junctions Superconductivity |
| Title | Semiclassical theory of quasiparticles in giant vortices |
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