Abstract
We analyze the spatial and energy dependence of the local density of states in a SNS junction. We model our system as a one-dimensional tight-binding chain which we solve exactly by numerical diagonalization. We calculate the dependence of the Andreev bound states on position, phase difference, gate voltage, and coupling with the superconducting leads. Our results confirm the physics predicted by certain analytical approximations, but reveal a much richer set of phenomena beyond the grasp of these approximations, such as the metamorphosis of the discrete states of the normal link (the normal bound states) into Andreev bound states as the leads become superconducting.
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References
B.D. Josephson, Rev. Mod. Phys. 46, 251 (1974)
P.-G. de Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966)
A. Griffin, J. Demers, Phys. Rev. B 4, 2202 (1971)
E. Blonder, M. Tinkham, T.M. Klapwijk, Phys. Rev. B 25, 4515 (1982)
I. Kulik, Sov. Phys. JETP-USSR 30, 944 (1970)
C.W.J. Beenakker, Transport Phenomena in Mesoscopic Systems, edited by H. Fukuyama, T. Ando (Springer, Berlin, 1992), Vol. 109, p. 235, Springer Series in Solid-State Science, arXiv:cond-mat/0406127
C.W.J. Beenakker, Transport Phenomena in Mesoscopic Systems, edited by H. Fukuyama, T. Ando (Springer, Berlin, 1992)
A.F. Andreev, Sov. Phys. JETP 19, 1228 (1964)
C.W.J. Beenakker, Phys. Rev. Lett. 67, 3836 (1991)
M.L. Della Rocca et al., Phys. Rev. Lett. 99, 127005 (2007)
R.S. Deacon et al., Phys. Rev. Lett. 104, 076805 (2010)
J.-D. Pillet et al., Nat. Phys. 11, (2010)
T. Dirks et al., Nat. Phys. 7, 386 (2011)
A. Furusaki, M. Tsukada, Phys. Rev. B 43, 10164 (1991)
M. Hurd, G. Wendin, Phys. Rev. B 49, 15258 (1994)
A. Richter, P. Baars, U. Merkt, Physica E 12, 911 (2002)
I. Affleck, J.S. Caux, A.M. Zagoskin, Phys. Rev B 62, 1433 (2000)
T. Meng, S. Florens, P. Simon, Phys. Rev. B 79, 224521 (2009)
J. Caux, H. Saleur, F. Siano, Phys. Rev. Lett. 88, 106402 (2002)
R. Fazio, F. Hekking, A. Odintsov, Phys. Rev. Lett. 74, 1843 (1995)
E. Perfetto, G. Stefanucci, M. Cini, Phys. Rev. B 80, 205408 (2009)
J. Bauer, A. Oguri, A.C. Hewson, J. Phys.: Condens. Matter 19, 486211 (2007)
A. Martin-Rodero, F.J. Garcia-Vidal, A. Levy Yeyati, Phys. Rev. B 72, 554 (1994)
A. Levy Yeyati, A. Martin-Rodero, F.J. Garcia-Vidal, Phys. Rev. B 51, 3743 (1995)
J.C. Cuevas, A. Martin-Rodero, A. Levy Yeyati, Phys. Rev. B 54, 7366 (1996)
A. Nakayama, J. Appl. Phys. 91, 7119 (2002)
A. Siber, Am. J. Phys. 74, 692 (2006)
A.M. Black-Schaffer, S. Doniach, Phys. Rev. B 78, 024504 (2008)
E. Vecino, A. Martin-Rodero, A. Levy Yeyati, Phys. Rev. B 68, 035105 (2003)
Y. Zhu, Q.-F. Sun, T.-H. Lin, J. Phys.: Condens. Matter 13, 8783 (2001)
I. Schneider, S. Eggert, Phys. Rev. Lett. 104, 036402 (2010)
P. Kakashvili, H. Johannesson, S. Eggert, Phys. Rev. B 74, 085114 (2006)
G. Buchs, D. Bercioux, P. Ruffieux, P. Groning, H. Grabert, O. Groning, Phys. Rev. Lett. 102, 245505 (2009)
I. Schneider, A. Struck, M. Bortz, S. Eggert, Phys. Rev. Lett. 101, 206401 (2008)
S.G. Lemay et al., Nature 412, 617 (2001)
K. Grove-Rasmussen, H.I. Jorgensen, P.E. Lindelof, Physica E 40, 92 (2008)
J.M. Byers, M.E. Flatte, D.J. Scalapino, Phys. Rev. Lett. 71, 3363 (1993)
M.I. Salkola, A.V. Balatsky, D.J. Scalapino, Phys. Rev. Lett. 77, 1841 (1996)
W. Ziegler et al., Phys. Rev. B 53, 8704 (1996)
X.-L. Song, Z.-Y. Zhao, Y. Wang, Y.-M. Shi, J. of Shanghai Univ. 7, 361 (2003)
W.G. van der Wiel et al., Rev. Mod. Phys. 75, 1 (2003)
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Bena, C. Metamorphosis and taxonomy of Andreev bound states. Eur. Phys. J. B 85, 196 (2012). https://doi.org/10.1140/epjb/e2012-30133-0
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DOI: https://doi.org/10.1140/epjb/e2012-30133-0