Abstract
We investigate excitation modes in multi-gap superconductors. Multi-gap superconductors have multiple excitation modes. In particular, the Nambu-Goldstone mode , Leggett mode and Higgs modes are important and play an important role in multi-gap superconductors. The multiple-phase invariance in a multi-gap system is partially or totally spontaneously broken in a superconductor. We evaluate the dispersion relation and the mass formulas of these modes by using the functional-integral method. The broken multiple-phase invariance leads to a new quantum phase such as the time-reversal symmetry breaking , the emergence of massless modes and fractionally quantized-flux vortices. There is a possibility that half-flux vortices exist in a two-component superconductor in magnetic field .
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References
V.A. Moskalenko, Fiz. Metal Metallored 8, 2518 (1959)
H. Suhl, B.T. Mattis, L.W. Walker, Phys. Rev. Lett. 3, 552 (1959)
J. Peretti, Phys. Lett. 2, 275 (1962)
J. Kondo, Prog. Theor. Phys. 29, 1 (1963)
J. Bardeen, L. Cooper, R. Schrieffer, Phys. Rev. 106, 162 (1957)
G. Binning, A. Baratoff, H.E. Hoenig, J.G. Bednorz, Phys. Rev. Lett. 45, 1352 (1980)
L. P. Gorkov, arXiv:1508.00529
S.V. Shulga et al., Phys. Rev. Lett. 80, 1730 (1998)
J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature 410, 63 (2001)
Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Ame. Chem. Soc. 130, 3296 (2008)
K.H. Bennemann, J.B. Ketterson (eds.), The Physics of Superconductors (Springer-Verlag, Berlin, 2004)
A. Bianconi, Nat. Phys. 9, 536 (2013)
A. Bianconi, A.C. Castellano, M. De, Santis, P. Delogu, A. Garano and R. Giorgi. Solid State Commun. 63, 1135 (1987)
The Physics of superconductors, vols. I and II, ed. by K.H. Bennemann, J.B. Ketterson (Springer, Berlin, 2003)
V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987)
J.E. Hirsch, D. Loh, D.J. Scalapino, S. Tang, Phys. Rev. B 39, 243 (1989)
K. Yamaji et al., Physica C 304, 225 (1998)
T. Yanagisawa, S. Koike, K. Yamaji, Phys. Rev. B 64, 184509 (2001)
T. Yanagisawa, S. Koike, K. Yamaji, Phys. Rev. B 67, 132408 (2003)
C. Weber, A. Lauchi, G.A. Sawatzky, Phys. Rev. Lett. 102, 017005 (2009)
T. Yanagisawa, J. Phys. Soc. Jpn. 85, 114707 (2016)
S. Koike et al., J. Phys. Soc. Jpn. 68, 1657 (1999)
K. Yamaji et al., Physica C 235, 2221 (1994)
T. Yanagisawa, Y. Shimoi, K. Yamaji, Phys. Rev. B 52, R3860 (1995)
A. Bussmann-Holder, H. Keller, R. Khasanov, A. Simon, A. Bianconi, A.R. Bishop, New J. Phys. 13, 093009 (2011)
H.Y. Choi et al., Phys. Rev. B 80, 052505 (2009)
P.M. Shirage, K. Kihou, K. Miyazawa, C.-H. Lee, H. Kito, H. Eisaki, T. Yanagisawa, Y. Tanaka, A. Iyo. Phys. Rev. Lett. 103, 257003 (2009)
T. Yanagisawa, K. Odagiri, I. Hase, K. Yamaji, P.M. Shirage, Y. Tanaka, A. Iyo, H. Eisaki, J. Phys. Soc. Jpn. 78, 094718 (2009)
A.D. Hillier, J. Quintanilla, R. Cywinskii, Phys. Rev. Lett. 102, 117007 (2009)
I. Hase, T. Yanagisawa, J. Phys. Soc. Jpn. 78, 084724 (2009)
A.D. Hillier, J. Quintanilla, B. Mazidian, J.F. Annett, R. Cywinskii, Phys. Rev. Lett. 109, 097001 (2012)
I. Hase, T. Yanagisawa, J. Phys. Soc. Jpn. 81, 103704 (2012)
D.J. Singh, Phys. Rev. B 86, 174507 (2012)
V.K. Pecharsky, L.L. Miller, K.A. Gschneider, Phys. Rev. B 58, 497 (1998)
Y. Iwamoto, Y. Iwasaki, K. Ueda, T. Kohara, Phys. Lett. A 250, 439 (1998)
H.H. Sung, S.Y. Chou, K.J. Syu, W.H. Lee, J. Phys. COndens. Matter 20, 165207 (2008)
S. Katano et al., Phys. Rev. B 90, 220508 (2014)
V. Stanev, Z. Tesanovic, Phys. Rev. B 81, 134522 (2010)
Y. Tanaka, T. Yanagisawa, J. Phys. Soc. Jpn. 79, 114706 (2010)
Y. Tanaka, T. Yanagisawa, Solid State Commun. 150, 1980 (2010)
R.G. Dias, A.M. Marques, Supercond. Sci. Technol. 24, 085009 (2011)
T. Yanagisawa, Y. Tanaka, I. Hase, K. Yamaji, J. Phys. Soc. Jpn. 81, 024712 (2012)
X. Hu, Z. Wang, Phys. Rev. B 85, 064516 (2012)
V. Stanev, Phys. Rev. B 85, 174520 (2012)
C. Platt, R. Thomale, C. Homerkamp, S.C. Zhang, Phys. Rev. B 85, 180502 (2012)
S. Maiti, A.V. Chubukov, Phys. Rev. B 87, 144511 (2013)
B.J. Wilson, M.P. Das, J. Phys. Condens. Matter 25, 425702 (2013)
Y. Takahashi, Z. Huang, X. Hu, J. Phys. Soc. Jpn. 83, 034701 (2014)
R. Ganesh, G. Baskaran, J. van den Brink, D.V. Efremov, Phys. Rev. Lett. 113, 177001 (2014)
Y. S. Yerin, A. N. Omelyanchouk and E. ll’chev, arXiv:1503.04653 (2015)
T. Yanagisawa, I. Hase, J. Phys. Soc. Jpn. 82, 124704 (2013)
S.Z. Lin, X. Hu, New J. Phys. 14, 063021 (2012)
K. Kobayashi, M. Machida, Y. Ota, F. Nori, Phys. Rev. B 88, 224516 (2013)
T. Koyama, J. Phys. Soc. Jpn. 83, 074715 (2014)
T. Yanagisawa, Y. Tanaka, New J. Phys. 16, 123014 (2014)
Y. Tanaka et al., Physica C 516, 10 (2015)
S.-Z. Lin, X. Hu, Phys. Rev. Lett. 108, 177005 (2012)
YuA Izyumov, V.M. Laptev, Phase Transitions 20, 95 (1990)
G.E. Volovik, The Universe in a Helium Droplet (Oxford University Press, Oxford, 2009)
Y. Tanaka, Phys. Rev. Lett. 88, 017002 (2002)
E. Babaev, Phys. Rev. Lett. 89, 067001 (2002)
S.V. Kuplevakhsky, A.N. Omelyanchouk, Y.S. Yerin, J. Low Temp. Phys. 37, 667 (2011)
A.J. Leggett, Prog. Theor. Phys. 36, 901 (1966)
Y. Tanaka et al., Physica C 471, 747 (2011)
V. Moshchalkov et al., Phys. Rev. Lett. 102, 117001 (2009)
M. Silaev, E. Babaev, Phys. Rev. B 84, 094515 (2011)
Y. Nambu, Phys. Rev. 117, 648 (1960)
Y. Nambu, in Physics in the 21st Century edited by K, ed. by H. Kunitomo, H. Otsubo (World Scientific, Singapore, Kikkawa, 1997)
T. Yanagisawa, Novel Supercon. Materials 1, (2015)
B. T. Geilikman, R. O. Zaitsev and V. Z. Kresin, Sov. Phys.: Solid State 9642, (1967)
D.R. Tilley, Proc. Phys. Soc. 84, 573 (1964)
I.P. Ivanov, Phys. Rev. E 79, 021116 (2009)
N.V. Orlova, A.A. Shanenko, M.V. Milosevic, F.M. Peeters, A. V. Vagov ad V. M. Axt. Phys. Rev. B 87, 134510 (2013)
Z. Huang, X. Hu, Appl. Phys. Lett. 104, 162602 (2014)
Y.S. Yerin, A.N. Omelyanchouk, Low Temp. Phys. 40, 943 (2014)
Y. Tanaka, Super. Sci. Tech. 28, 034002 (2015)
J.G. Storey, J.W. Loram, J.R. Cooper, Z. Bukowski, J. Karpinski, Phys. Rev. B 88, 144502 (2013)
R.G. Cai, L. Li, L.F. Li, Y.Q. Wang, JHEP 9, 074 (2013)
W.-Y. Wen, M.-S. Wu, S.-Y. Wu, Phys. Rev. D 89, 066005 (2014)
M. Nishida, JHEP 08, 136 (2015)
R. Rajaraman, Solitons and Instantons (North-Holland, Elsevier, Amsterdam, 1987)
Y. Tanaka, J. Phys. Soc. Jpn. 70, 2844 (2001)
E. Babaev, L.D. Faddeev, A.J. Niemi, Phys. Rev. B 65, 100512 (2002)
Y.M. Cho, P. Zhang, Phys. Rev. B 73, 180506 (2006)
M. Eto, Y. Hirono, M. Nitta and S. Yasui, Prog. Theor. Exp. Phys. 012D01 (2014)
M.C.N. Fiolhais, J.L. Birman, Phys. Lett. A 378, 2632 (2014)
E. Babaev, M. Speight, Phys. Rev. B 72, 180502 (2005)
V.G. Kogan, J. Schmalian, Phys. Rev. B 83, 054515 (2011)
E. Babaev, M. Silaev, Phys. Rev. B 86, 016501 (2012)
V.G. Kogan, J. Schmalian, Phys. Rev. B 86, 016502 (2012)
M. Marciani, L. Fanfarillo, C. Castellani, L. Benfatto, Phys. Rev. B 88, 214508 (2013)
T. Yanagisawa, EPL 113, 41001 (2016)
R. Kleiner, F. Steinmeyer, G. Kunkel, P. Muller, Phys. Rev. Lett. 68, 2349 (1992)
G. Ohya, N. Aoyama, A. Irie, S. Kishida, H. Tokutaka, Jpn. J. Appl. Phys. 31, L829 (1992)
K. Tamasaku, Y. Nakamura, S. Uchida, Phys. Rev. Lett. 69, 1455 (1992)
Y. Matsuda, M.B. Gaifullin, K. Kumagai, K. Kadowaki, T. Mochiku, Phys. Rev. Lett. 75, 4512 (1995)
T. Koyama, M. Tachiki, Phys. Rev. B 54, 16183 (1996)
S.G. Sharapov, V.P. Gusynin, H. Beck, Eur. Phys. J. B 39, 062001 (2002)
H.J. Choi, D. Roundy, H. Sun, M.L. Cohen, S.G. Louie, Nature 418, 758 (2002)
G. Blumberg et al., Phys. Rev. Lett. 99, 014507 (2007)
Y. Ota, M. Machida, T. Koyama, H. Aoki, Phys. Rev. B 83, 060507 (2011)
R. Matsunaga, Y.I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, R. Shimano, Phys. Rev. Lett. 111, 057002 (2013)
M.A. Measson, Y. Gallais, M. Cazayous, B. Clair, P. Rodiere, L. Cario, A. Sacuto, Phys. Rev. B 89, 060503 (2014)
Y. Barlas, C.M. Varma, Phys. Rev. B 87, 054503 (2013)
T. Koyama, Phys. Rev. B 90, 064514 (2014)
N. Tsuji, H. Aoki, Phys. Rev. B 92, 064508 (2015)
Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)
Y. Nambu, G. Jona-Lasinio, Phys. Rev. 124, 246 (1961)
Y. Nambu, Physica D 15, 147 (1985)
T. Koyama, J. Phys. Soc. Jpn. 88, 064715 (2016)
U. Welp et al., Phys. Rev. B 78, 140510 (R) (2008)
A. Gurevich, V. Vinokur, Phys. Rev. Lett. 90, 047004 (2003)
H.-Y. Kee, Y.B. Kim, K. Maki, Phys. Rev. B 62, R9275 (2000)
J. Jang et al., Science 331, 186 (2011)
M. Nitta, M. Eto, T. Fujimori, T. Ohashi, J. Phys. Soc. Jpn. 81, 084711 (2012)
K.G. Wilson, J.B. Kogut, Phys. Rep. 12C, 75 (1974)
J.B. Kogut, Rev. Mod. Phys. 51, 659 (1979)
C. Chakravarty, B.I. Halperin, D.R. Nelson, Phys. Rev. B 39, 2344 (1989)
T. Yanagisawa, Phys. Rev. B 46, 13896 (1992)
J.M. Kosterlitz, D. Thouless, J. Phys. C 6, 1181 (1973)
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1989)
D.J. Amit, Y.Y. Goldschmidt, S. Grinstein, J. Phys. A: Math. Gen. 13, 585 (1980)
T.A. Bojesen, E. Babaev, A. Sudbo, Phys. Rev. B 88, 220511 (2013)
Y. Tanaka et al., J. Phys. Soc. Jpn. 83, 074705 (2014)
S. Miyashita, H. Shiba, J. Phys. Soc. Jpn. 53, 1145 (1984)
D.J. Gross, E. Witten, Phys. Rev. D 21, 446 (1980)
E. Brezin, D.J. Gross, Phys. Lett. B 97, 120 (1980)
R.C. Brower, M. Nauenberg, Nucl. Phys. B 180, 221 (1981)
E. Brezin, S. Hikami, JHEP 7, 67 (2010)
M. Nitta, Nucl. Phys. B 895, 288 (1995)
Acknowledgements
The author expresses his sincere thanks to J. Kondo, K. Yamaji, I. Hase and Y. Tanaka for helpful discussions.
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Yanagisawa, T. (2017). Fluctuation Modes in Multi-gap Superconductors . In: Crisan, A. (eds) Vortices and Nanostructured Superconductors. Springer Series in Materials Science, vol 261. Springer, Cham. https://doi.org/10.1007/978-3-319-59355-5_8
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