Abstract
The behavior of the 1D Holstein polaron is described, with emphasis on lattice coarsening effects, by distinguishing between adiabatic and nonadiabatic contributions to the local correlations and dispersion properties. The original and unifying systematization of the crossovers between the different polaron behaviors, usually considered in the literature, is obtained in terms of quantum to classical, weak coupling to strong coupling, adiabatic to nonadiabatic, itinerant to self-trapped polarons and large to small polarons. It is argued that the relationship between various aspects of polaron states can be specified by five regimes: the weak-coupling regime, the regime of large adiabatic polarons, the regime of small adiabatic polarons, the regime of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of small pinned polarons for which the adiabatic and nonadiabatic contributions are inextricably mixed in the polaron dispersion properties. The crossovers between these five regimes are positioned in the parameter space of the Holstein Hamiltonian.
Similar content being viewed by others
References
G.-M. Zhao, K. Conder, H. Keller, K.A. Müller, Nature (London) 381, 676 (1996)
G.-M. Zhao, D.J. Kang, W. Prellier, M. Rajeswari, H. Keller, T. Venkatesanl, R.L. Greene, Phys. Rev. B 63, 060402(R) (2001)
R.P. Sharma, Guo-meng Zhao, D.J. Kang, M. Robson, M. Rajeswari, H. Keller, H.D. Drew, T. Venkatesan, Phys. Rev. B 66, 214411 (2002)
R. Khasanov, D.G. Eshchenko, H. Luetkens, E. Morenzoni, T. Prokscha, A. Suter, N. Garifianov, M. Mali, J. Roos, K. Conder, H. Keller, Phys. Rev. Lett. 92, 057602 (2004); A. Bussmann-Holder, H. Keller, A.R. Bishop, A. Simon, R. Micnas, K.A. Müller, Europhys. Lett. 72, 423 (2005)
G.-H. Gweon, S.Y. Zhou, M.C. Watson, T. Sasagawa, H. Takagi, A. Lanzara, Phys. Rev. Lett. 97, 227001 (2006)
X.J. Zhou, T. Cuk, T. Devereaux, N. Nagaosa, Z.-X. Shen, e-print arXiv:cond-mat/0604284 in Hightemperature Superconductivity (A Treatise on Theory And Applications), edited by J.R. Schrieffer (Springer-Verlag, Berlin, 2006)
A.J. Millis, P.B. Littlewood, B.I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995); A.J. Millis, B.I. Shraiman, R. Müller, Phys. Rev. Lett. 77, 175 (1996); A.S. Alexandrov, A.M. Bratkovsky, Phys. Rev. Lett. 82, 141 (1999); D.M. Edwards, Adv. Phys. 51, 1259 (2002)
A.S. Alexandrov, N. Mott, Polarons and Bipolarons (World Scientific Publishing Co. Pte. Ltd., Singapore, 1995)
A.R. Bishop, D. Mihailovic, J. Mustre de Leone, J. Phys.: Condens. Matter 15, L169 (2003)
J.T. Devreese, J. Phys.: Condens. Matter 19, 255201 (2007), references therein
J. Loos, M. Hohenadler, A. Alvermann, H. Fehske, J. Phys.: Condens. Matter 19, 236233 (2007)
Ch. Hartinger, F. Mayr, A. Loidl, T. Kopp, Phys. Rev. B 73, 024408 (2006)
J.L. M. van Mechelen, D. van der Marel, C. Grimaldi, A.B. Kuzmenko, N.P. Armitage, N. Reyren, H. Hagemann, I.I. Mazin, Phys. Rev. Lett. 100, 226403 (2008)
D.M. Eagles, R.P. S.M. Lobo, F. Gervais, Phys. Rev. B 52, 6440 (1995)
S. Lupi, P. Maselli, M. Capizzi, P. Calvani, P. Giura, P. Roy, Phys. Rev. Lett. 83, 4852 (1999)
S. Barišić, Int. Journ. Mod. Phys. B 5, 2439 (1991), references therein
A.S. Mishchenko, N. Nagaosa, Phys. Rev. Lett. 93, 036402 (2004); V. Cataudella, G. De Filippis, A.S. Mishchenko, N. Nagaosa, Phys. Rev. Lett. 99, 226402 (2007)
O. Gunnarsson, O. Rösch, J. Phys.: Condens. Matter 20, 043201 (2008)
A. Damascelli, Z. Hussain, Z.X. Shen, Rev. Mod. Phys. 75, 473 (2003), references therein
K.M. Shen, F. Ronning, W. Meevasana, D.H. Lu, N.J.C. Ingle, F. Baumberger, W.S. Lee, L.L. Miller, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, Z.X. Shen, Phys. Rev. B 75, 075115 (2007)
L. Perfetti, H. Berger, A. Reginelli, L. Degiorgi, H. Höchst, J. Voit, G. Margaritondo, M. Grioni, Phys. Rev. Lett. 87, 216404 (2001)
S. Mitrovic, L. Perfetti, C. Søndergaard, G. Margaritondo, M. Grioni, N. Barišić, L. Forró, L. Degiorgi, Phys. Rev. B 69, 035102 (2004)
L. Vasiliu-Doloc, S. Rosenkranz, R. Osborn, S.K. Sinha, J.W. Lynn, J. Mesot, O.H. Seeck, G. Preosti, A.J. Fedro, J.F. Mitchell, Phys. Rev. Lett. 83, 4393 (1999)
Pengcheng Dai, J.A. Fernandez-Baca, N. Wakabayashi, E.W. Plummer, Y. Tomioka, Y. Tokura, Phys. Rev. Lett. 85, 2553 (2000)
J.C. Hicks, G.A. Blaisdell, Phys. Rev. B 31, 919 (1985)
A.J. Heeger, S. Kivelson, J.R. Schrieffer, W.-P. Su, Rev. Mod. Phys. 60, 781 (1988), references therein
P. Gaal, W. Kuehn, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, Nature 450, 1210 (2007)
P.E. Kornilovitch, Phys. Rev. B 60, 3237 (1999)
O.S. Barišić, Phys. Rev. B 65, 144301 (2002)
L.-C. Ku, S.A. Trugman, J. Bonča, Phys. Rev. B 65, 174306 (2002)
M. Hohenadler, M. Aichhorn, W. von der Linden, Phys. Rev. B 68, 184304 (2003)
M. Hohenadler, H.G. Evertz, W. von der Linden, Phys. Rev. B 69, 024301 (2004)
V. Cataudella, G. De Filippis, F. Martone, C.A. Perroni, Phys. Rev. B 70, 193105 (2004)
P.E. Spencer, J.H. Samson, P.E. Kornilovitch, A.S. Alexandrov, Phys. Rev. B 71, 184310 (2005)
J. Loos, M. Hohenadler, A. Alvermann, H. Fehske, J. Phys.: Condens. Matter. 18, 7299 (2006)
C. Slezak, A. Macridin, G.A. Sawatzky, M. Jarrell, T.A. Maier, Phys. Rev. B 73, 205122 (2006)
L.-C. Ku, S.A. Trugman, Phys. Rev. B 75, 014307 (2007)
M.I. Salkola, A.R. Bishop, V.M. Kenkre, S. Raghavan, Phys. Rev. B 52, R3824 (1995)
O.S. Barišić, Phys. Rev. B 73, 214304 (2007)
D. Feinberg, S. Ciuchi, F. de Pasquale, Int. J. Mod. Phys. B 4, 1395 (1990)
A.S. Alexandrov, V.V. Kabanov, D.K. Ray, Phys. Rev. B 49, 9915 (1994); A.S. Alexandrov, P.E. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999)
G. Wellein, H. Fehske, Phys. Rev. B 58, 6208 (1998)
H. Fehske, J. Loos, G. Wellein, Phys. Rev. B 61, 8016 (2000)
J.P. Hague, P.E. Kornilovitch, A.S. Alexandrov, J.H. Samson, Phys. Rev. B 73, 054303 (2006)
A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Rev. B 59, 13728 (1999)
V. Cataudella, G. De Filippis, G. Iadonisi, Phys. Rev. B 62, 1496 (2000)
O.S. Barišić, S. Barišić, Eur. Phys. J. B 54, 1 (2006)
M. Berciu, Phys. Rev. Lett. 97, 036402 (2006)
S. Ciuchi, F. de Pasquale, S. Fratini, D. Feinberg, Phys. Rev. B 56, 4494 (1997)
G.L. Goodvin, M. Berciu, G.A. Sawatzky, Phys. Rev. B 74, 245104 (2006); O.S. Barišić, Phys. Rev. Lett. 98, 209701 (2007); M. Berciu, Phys. Rev. Lett. 98, 209702 (2007)
O.S. Barišić, Phys. Rev. B 76, 193106 (2007)
O.S. Barišić, Europhys. Lett. 77, 57004 (2007)
T. Holstein, Ann. Phys. (N.Y.) 8, 325 (1959)
S. Engelsberg, J.R. Schrieffer, Phys. Rev. 131, 993 (1963)
O.S. Barišić, Phys. Rev. B 69, 064302 (2004)
G.D. Mahan, Many-Particle Physics (Plenum Press, New York, USA, 1990)
A. Klamt, J. Phys. C 21, 1953 (1988)
A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Lett. A 254, 287 (1999)
F. Marsiglio, Physica C 244, 21 (1995); W. Stephan, Phys. Rev. B 54, 8981 (1996)
M. Born, J.R. Oppenheimer, Ann. Phys. (Leipzig) 87, 457 (1927)
A.S. Davydov, Quantum Mechanics (Pergamon Press, New York, 1976)
R. Rajaraman, Phys. Rep. C 21, 227 (1975); R. Rajaraman, Solitons, Instantons: An Introduction to Solitons, Instantons in Quantum Field Theory (North-Holland, Amsterdam, 1982)
W.H. Miller, N.C. Handy, J.E. Adams, J. Chem. Phys. 72, 99 (1980)
M. Page, J.W. McIver, J. Chem. Phys. 88, 922 (1988); C. Gonzalev, H.B. Schlegel, J. Chem. Phys. 90, 2154 (1989)
P.B. Shaw, E.W. Young, Phys. Rev. B 24, 714 (1981)
H.B. Schüttler, T. Holstein, Ann. Phys. (N.Y.) 166, 93 (1986)
T.D. Holstein, L.A. Turkevich, Phys. Rev. B 38, 1901 (1988); T.D. Holstein, L.A. Turkevich, Phys. Rev. B 38, 1923 (1988)
A.H. Castro Neto, A.O. Caldeira, Phys. Rev. B 46, 8858 (1992)
G. Kalosakas, S. Aubry, G.P. Tsironis, Phys. Rev. B 58, 3094 (1998)
Y.S. Kivshar, D.K. Campbell, Phys. Rev. E 48, 3077 (1993); D. Cai, A.R. Bishop, N. Grønbech-Jensen, Phys. Rev. E 53, 4131 (1996)
L. Brizhik, A. Eremko, L. Cruzeiro-Hansson, Y. Olkhovska, Phys. Rev. B 61, 1129 (2000)
E.I. Rashba, Opt. Spectrosk. 2, 664 (1957)
D. Emin, Phys. Rev. B 48, 13691 (1993)
V.I. Mel’nikov, Sov. Phys. JETP 45, 1233 (1977); P.B. Shaw, G. Whitfield, Phys. Rev. B 17, 1495 (1978)
M. Wagner, Z. Physik B 32, 225 (1979)
M. Sonnek, T. Frank, M. Wagner, Phys. Rev. B 49, 15637 (1994)
Yu.A. Firsov, E.K. Kudinov, Fiz. Tverd. Tela (St. Petersburg) 39, 2159 (1997)
Yu. A. Firsov, E.K. Kudinov, Phys. Solid State 43, 447 (2001)
D. Emin, T. Holstein, Ann. Phys. 53, 439 (1969)
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (GITTL, Moscow, 1948; Pergamon, Oxford, 1977)
T. Holstein, Ann. Phys. (N.Y.) 8, 343 (1959)
M. Büttiker, R. Landauer, Phys. Rev. Lett. 49, 1739 (1982); J.P. Sethna, Phys. Rev. B 24, 698 (1981); A.B. Krebs, S.G. Rubin, Phys. Rev. 49, 11808 (1994)
A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Rev. B 60, 14080 (1999)
D. Emin, T. Holstein, Phys. Rev. Lett. 36, 323 (1976)
V.V. Kabanov, O.Yu. Mashtakov, Phys. Rev. B 47, 6060 (1993)
S. Fratini, S. Ciuchi, Phys. Rev. Lett. 91, 256403 (2003)
S. Fratini, S. Ciuchi, Phys. Rev. B 74, 075101 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barišić, O.S., Barišić, S. Phase diagram of the Holstein polaron in one dimension. Eur. Phys. J. B 64, 1–18 (2008). https://doi.org/10.1140/epjb/e2008-00280-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00280-0