Abstract
A review is made on the developments in the last two decades in the field of the Jahn–Teller effect on itinerant electrons in Jahn–Teller crystals. Special attention is paid to the current status of the researches on the fullerene superconductors and the manganite perovskites exhibiting the colossal magnetoresistance. Present knowledge about the polarons and bipolarons in the typical Jahn–Teller model systems is also summarized, together with some original results of our own.
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References
H.A. Jahn, E. Teller, Proc. R. Soc. Lond. A161, 220 (1937)
R. Engleman, The Jahn–Teller Effect in Molecules and Crystals (Wiley, New York, 1972)
I.B. Bersuker, The Jahn–Teller Effect (Cambridge University Press, Cambridge, 2006)
M.D. Kaplan, B.G. Vekhter, Cooperative Phenomena in Jahn–Teller Crystals (Plenum, New York, 1995)
J.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986)
A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez, A.R. Kortan, Nature 350, 600 (1991)
S. Jin, T.H. Tiefel, M. McCormack, R.A. Fastnacht, R. Ramesh, J.H. Chen, Science 264, 413 (1994)
Y. Tokura, Y. Tomioka, H. Kuwabara, A. Asamitsu, Y. Moritomo, M. Kasai, J. Appl. Phys. 79 5288 (1996)
C. Zener, Phys. Rev. 82 403 (1951)
P.W. Anderson, H. Hasegawa, Phys. Rev. 100, 675 (1955)
P.-G. de Gennes, Phys. Rev. 118 141 (1960)
A.J. Millis, P.B. Littlewood, B.I. Shariman, Phys. Rev. Lett. 74 5144 (1995)
N. Mannella, A. Rosenhahn, C.H. Booth, S. Marchesini, B.S. Mun, S.-H. Yang, K. Ibrahim, Y. Tomioka, C.S. Fadley, Phys. Rev. Lett. 92 166401 (2004)
Z. Popovic, S. Satpathy, Phys. Rev. Lett. 84 1603 (2000)
C. Ederer, C. Lin, A.J. Millis, Phys. Rev. B 76 155105 (2007)
A.P. Ramirez, J. Phys. : Condens. Matter 9, 8171 (1997)
A. Mareo, S. Yunoki, E. Dagotto, Science 283 2034 (1999)
Y. Tokura, in Colossal Magnetoresistive Oxides, ed. by Y. Tokura (Gordon & Breach, Amsterdam, 2000)
Y. Tokura, N. Nagaosa, Science 288 462 (2000)
E. Dagotto, T. Hotta, A. Moreo, Phys. Rep. 344 1 (2001)
M.B. Salamon, M. Jaime, Rev. Mod. Phys. 73 583 (2001)
Y. Takada, T. Hotta, Int. J. Mod. Phys. B 15 4267 (2001)
J. van den Brink, D. Khomskii, Phys. Rev. B 63 140416(R) (2001)
T. Hotta, Y. Takada, H. Koizumi, Int. J. Mod. Phys. B 12 3437 (1998)
T. Hotta, Y. Takada, H. Koizumi, E. Dagotto, Phys. Rev. Lett. 84 2477 (2000)
Y. Takada, T. Hotta, H. Koizumi, Int. J. Mod. Phys. B 13 3778 (1999)
T. Holstein, Ann. Phys. 8 325 (1959)
C.M. Varma, J. Zaanen, K. Raghavachari, Science 254 989 (1991)
M. Schluter, M. Lannoo, M. Needels, G.A. Baraff, D. Tomanek, Phys. Rev. Lett. 68 526 (1992)
I.I. Mazin, S.N. Rashkeev, V.P. Antropov, O. Jepsen, A.I. Liechtenstein, O.K. Andersen, Phys. Rev. B. 45 5114 (1992)
S. Suzuki, K. Nakao, Phys. Rev. B. 52 14206 (1995)
A.P. Ramirez, Superconduct. Rev. 1 1 (1994)
M.P. Gelfand, Superconductivity Review 1 103 (1994)
O. Gunnarsson, Rev. Mod. Phys. 69 575 (1997)
L. Degiorgi, Adv. Phys. 47 207 (1998)
Y. Takada, T. Hotta, Int. J. Mod. Phys. B 12 3042 (1998)
B. Sundqvist, Adv. Phys. 48 1 (1999)
S. Suzuki, S. Okada, K. Nakao, J. Phys. Soc. Jpn. 69 2615 (2000)
O. Gunnarsson, Alkali-Doped Fullerides (World Scientific, Singapore, 2004)
T.W. Ebbesen, J.S. Tsai, K. Tanigaki, J. Tabuchi, Y. Shimakawa, Y. Kubo, I. Hirosawa, J. Mizuki, Nature 355 620 (1992)
A.P. Ramirez, A.R. Kortan, M.J. Rosseinsky, S.J. Duclos, A.M. Mujsce, R.C. Haddon, D.W. Murphy, A.V. Makhija, S.M. Zahurak, K.B. Lyons, Phys. Rev. Lett. 68 1058 (1992)
A.A. Zakhidov, K. Imaeda, D.M. Petty, K. Yakushi, H. Inokuchi, K. Kikuchi, I. Ikemoto, S. Suzuki, Y. Achiba, Phys. Lett. A 164 355 (1992)
C.-C. Chen, C.M. Lieber, J. Am. Chem. Soc. 114, 3141 (1992)
W.L. McMillan, Phys. Rev. 167 331 (1968)
P.B. Allen, R.C. Dynes, Phys. Rev. B 12 905 (1975)
T. Yildirim, J.E. Fischer, R. Dinnebier, P.W. Stephens, C.L. Lin, Solid State Commun. 93 269 (1995)
G.M. Eliashberg, Sov. Phys. JETP 11 696 (1960)
A.B. Migdal, Sov. Phys. JETP 7 996 (1958)
Y. Takada, J. Phys. Chem. Solids 54 1779 (1993)
O. Gunnarsson, G. Zwicknagl, Phys. Rev. Lett. 69 957 (1992)
N. Manini, E. Tosatti, A. Auerbach, Phys. Rev. B 49 13008 (1994)
L.F. Chibotaru, A. Ceulemans, Phys. Rev. B 53 15522 (1996)
C.C. Chancey, M.C.M. OfBrien, The Jahn–Teller Effect in C 60 and Other Icosahedral Complexes (Princeton University Press, Princeton, 1997)
S. Wehrli, M. Sigrist, Phys. Rev. B 76 125419 (2007)
Y. Wang, R. Yamachika, A. Wachowiak, M. Grobis, M.F. Crommie, Nat. Mater. 7 194 (2008)
D.M. Deaven, D.S. Rokhsar, Phys. Rev. B 48 4114 (1993)
C.-C. Chen, C.M. Lieber, Science 259 655 (1993)
M. Riccò, F. Gianferrari, D. Pontiroli, M. Belli, C. Bucci, T. Shiroka, Europhys. Lett. 81 57002 (2008)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68 13 (1996)
J.E. Han, O. Gunnarsson, V.H. Crespi, Phys. Rev. Lett. 90 167006 (2003)
T. Yildirim, L. Barbedette, J.E. Fischer, C.L. Lin, J. Robert, P. Petit, T.T.M. Plastra, Phys. Rev. Lett. 77 167 (1996)
E. Cappelluti, P. Paci, C. Grimaldi, L. Pietronero1, Phys. Rev. B 72, 054521 (2005)
Y. Takada, Physica C 364-365 71 (2001)
J.E. Han, E. Koch, O. Gunnarsson, Phys. Rev. Lett. 84 1276 (2000)
J.E. Han, O. Gunnarsson, Phys. B 292 196 (2000)
Y. Iwasa, H. Shimoda, T.T.M. Palstra, Y. Maniwa, O. Zhou, T. Mitani, Phys. Rev. B 53 R8836 (1996)
M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Science 296 2364 (2002)
M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Phys. Rev. Lett. 93 047001 (2004)
K. Tanigaki, I. Hirosawa, T.W. Ebbesen, J. Mizuki, J.S. Tsai, J. Phys. Chem. Solids 54 1645 (1993)
Y. Takada, Int. J. Mod. Phys. B 21 3138 (2007)
Y. Takada, J. Phys. Soc. Jpn. 65 3134 (1996)
Y. Takada, J. Phys. Soc. Jpn. 65 1544 (1996)
M.R. Schafroth, S.T. Butler, J.M. Blatt, Helv. Phys. Acta 30 93 (1957)
J.M. Blatt Theory of Superconductivity (Academic, New York, 1964)
A.S. Alexandrov, J. Ranninger, Phys. Rev. B 23 1796 (1981)
A.S. Alexandrov, J. Ranninger, Phys. Rev. B 24 1164 (1981)
Y. Takada, Phys. Rev. B 26 1223 (1982)
A.S. Alexandrov, N.F. Mott, Polarons and Bipolarons (World Scientific, Singapore, 1995)
D.R. Pooler, J. Phys. A: Math. Gen. 11 1045 (1978)
I.G. Lang, Yu. A . Firsov, Sov. Phys. JETP 16 1301 (1963)
T.D. Lee, F.E. Low, D. Pines, Phys. Rev. 90 297 (1953)
H. Fröhlich, Phys. Rev. 79 845 (1950)
P.E. Kornilovitch, Phys. Rev. Lett. 81 5382 (1998)
E. Jeckelmann, S.R. White, Phys. Rev. B 57 6376 (1998)
J. Bonča, S.A. Trugman, I. Batistič, Phys. Rev. B 60 1633 (1999)
J. Bonča, T. Katrašnik, S.A. Trugman, Phys. Rev. Lett. 84 3153 (2000)
S. Ciuchi, F. de Pasquale, S. Fratini, D. Feinberg, Phys. Rev. B 56, 4494 (1997)
A.S. Mishchenko, N.V. Prokof’ev, A. Sakamoto, B.V. Svistunov, Phys. Rev. B. 62 6317 (2000)
A.S. Alexandrov (Ed.), Polarons in Advanced Materials: Springer series in materials science 103 (Canopus Publishing and Springer Gmbh, Bath, UK, 2007).
H. Fehske, R. Schneider, A. Weiße (Eds.), Computational Many-Particle Physics (Springer, Heidelberg, 2008)
K. -H. Höck, H. Nickisch, H. Thomas, Helv. Phys. Acta 56 237 (1983)
K. Ziegler, Phys. Rev. B 72 075120 (2005)
Y. Takada, Phys. Rev. B 61 8631 (2000)
P.E. Kornilovitch, Phys. Rev. Lett. 84 1551 (2000)
H. Barentzen, Eur. Phys. J. B 24 197 (2001)
S. El Shawish, J. Bonča, L.-C. Ku, S.A. Trugman, Phys. Rev. B 67, 014301 (2003).
S.A. Trugman, L.-C. Ku, J. Bonča, J. Supercond. 17, 193 (2004)
R. Ramakumar, S. Yarlagadda, Phys. Rev. B 69 104519 (2004)
H. Barentzen, J. Phys.: Condes. Matter 17 4713 (2005)
Y. Takada, M. Masaki, J. Mol. Struct. 838 207 (2007)
Y. Takada, M. Masaki, J. Supercond. Nov. Magn. 20 629 (2007)
H.C. Longuet-Higgins, U. ÖPik, M.H.L. Pryce, R.A. Sack, Proc. R. Soc. Lond. A244 1 (1958)
W. Moffitt, W. Thorson, Phys. Rev. 108 1251 (1957)
M.C.M. O’Brien, J. Phys. A: Math. Gen. 22 1779 (1989)
Y.M. Liu, C.A. Bates, J.L. Dunn, V.Z. Polinger, J. Phys.: Condens. Matter 8 L523 (1996)
T. Okuda, A. Asamitsu, Y. Tomioka, T. Kimura, Y. Taguchi, Y. Tokura, Phys. Rev. Lett. 81 3203 (1998)
A. Macridin, G.A. Sawatzky, M. Jarrell, Phys. Rev. B 69, 245111 (2004)
J.E. Han, O. Gunnarsson, Phys. B 292 196 (2000)
M. Fabrizio, E. Tosatti, Phys. Rev. B 55 13465 (1997)
J.E. Han, Phys. Rev. B 70 054513 (2004)
R. Micnas, J. Ranninger, S. Robaszkiewicz, Rev. Mod. Phys. 62 113 (1990)
M. Schiró, M. Capone, M. Fabrizio, C. Castellani, Phys. Rev. B 77 104522 (2008)
J.E. Hirsch, E. Fradkin, Phys. Rev. B 27, 4302 (1983)
J.K. Freericks, Phys. Rev. B 48 3881 (1993)
M. Takahashi, Thermodynamics of One-dimensional Solvable Models (Cambridge University Press, Cambridge, 1999)
D.C. Cabra, P. Pujol, in Quantum Magnetism, ed. by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop. Lect. Notes Phys. 645 (Springer, Heidelberg, 2004), p. 253
A.J. Leggett, Phys. Fenn. 8 125 (1973)
F. Hébert, G.G. Batrouni, R.T. Scalettar, G. Schmid, M. Troyer, A. Dorneich, Phys. Rev. B, 65, 014513 (2001)
G. Schmid, S. Todo, M. Troyer, A. Dorneih, Phys. Rev. Lett. 88, 167208 (2002).
G.-H. Liu, H.-L. Wang, G.-S. Tian, Phys. Rev. B 77, 214418 (2008) and references therein
Acknowledgements
This work was partially supported by Global COE Program “the Physical Sciences Frontier”, the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan as well as by a Grant-in-Aid for Scientific Research in Priority Areas “Development of New Quantum Simulators and Quantum Design” (No.17064004) of MEXT, Japan. We would like to thank M. Kaplan, H. Koizumi, T. Hotta, and H. Maebashi for useful discussions for years.
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Hori, C., Takada, Y. (2009). Polarons and Bipolarons in Jahn–Teller Crystals. In: Köppel, H., Yarkony, D., Barentzen, H. (eds) The Jahn-Teller Effect. Springer Series in Chemical Physics, vol 97. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03432-9_26
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