Abstract
We give a review of the role of the Van Hove singularities in superconductivity. Van Hove singularities (VHs) are a general feature of low-dimensional systems. They appear as divergences of the electronic density of states (DOS). Jacques Friedel and Jacques Labbé were the first to propose this scenario for the A15 compounds. In NbTi, for example, Nb chains give a quasi-1D electronic structure for the d-band, leading to a VHs. They developed this model and explained the high T C and the many structural transformations occurring in these compounds. This model was later applied by Jacques Labbé and Julien Bok to the cuprates and developed by Jacqueline Bouvier and Julien Bok. The high T C superconductors cuprates are quasi-bidimensional (2D) and thus lead to the existence of Van Hove singularities in the band structure. The presence of VHs near the Fermi level in the cuprates is now well established. In this context we show that many physical properties of these materials can be explained, in particular the high critical temperature T C, the anomalous isotope effect, the superconducting gap and its anisotropy, and the marginal Fermi liquid properties, they studied these properties in the optimum and overdoped regime. These compounds present a topological transition for a critical hole doping p≈0.21 hole per CuO2 plane.
Similar content being viewed by others
References
Labbé, J., Barišić, S., Friedel, J.: Phys. Rev. Lett. 19, 233 (1962)
Labbé, J., Friedel, J.: J. Phys. Radium 27, 153 (1966)
Labbé, J., Friedel, J.: J. Phys. (Paris) 27, 153 (1966)
Labbé, J., Friedel, J.: J. Phys. (Paris) 27, 303 (1966)
Labbé, J., Friedel, J.: J. Phys. (Paris) 27, 708 (1966)
Labbé, J., Barišić, S., Friedel, J.: Phys. Rev. Lett. 19, 1039 (1967)
Barišić, S., Labbé, J.: J. Phys. Chem. Solids 28, 2477 (1967)
Labbé, J.: Phys. Rev. Lett. 158, 647 (1967)
Labbé, J.: Phys. Rev. 158, 655 (1967)
Labbé, J.: Phys. Rev. Lett. 172, 451 (1968)
Friedel, J.: Transition metals. In: Ziman, J.M. (ed.) Physics of Metals I. Electrons. Cambridge University Press, Cambridge (1969)
Barišić, S., Labbé, J., Cyrot-Lackmann, F.: J. Phys. (Paris) 30, 955 (1969)
Labbé, J., van Reuth, E.C.: Phys. Rev. Lett. 24, 1232 (1970)
Barišić, S., Labbé, J., Friedel, J.: Phys. Rev. Lett. 25, 919 (1970)
Barišić, S.: Phys. Rev. B 5, 932 (1972)
Testardi, L.R., Bateman, T.B., Reed, W.A., Chirba, V.G.: Phys. Rev. Lett. 15, 250 (1965)
Testardi, L.R., Bateman, T.B.: Phys. Rev. 154, 402 (1967)
Bednorz, J.G., Müller, K.A.: Z. Angew. Phys. B 64, 189 (1986)
Barišić, S., Batistic, I., Friedel, J.: Europhys. Lett. 3, 1231 (1987)
Van Hove, L.: Phys. Rev. 89, 1189 (1953)
Labbé, J., Bok, J.: Europhys. Lett. 3, 1225 (1987)
Bok, J., Bouvier, J.: Van Hove scenario for high T C superconductors. In: Bussmann-Holder, A., Keller, H. (eds.) High T C Superconductors and Related Transition Metal Oxides, pp. 35–41. Springer, Berlin (2007)
Bouvier, J., Bok, J.: Electron–phonon Interaction in the high-T C cuprates in the framework of the Van Hove scenario. Adv. Condens. Matter Phys. 2010, 472636 (2010). doi:10.1155/2010/472636
Ino, A., Kim, C., Nakamura, M., Yoshida, Y., Mizokawa, T., Fujimori, A., Shen, Z.X., Takeshita, T., Eisaki, H., Uchida, S.: Phys. Rev. B 65, 094504 (2002)
Lee, P.A., Nagaosa, N., Wen, X.-G.: Rev. Mod. Phys. 78, 17 (2006)
Bouvier, J., Bok, J.: Physica C 249, 117 (1995)
Bouvier, J., Bok, J.: Physica C 288, 217 (1997)
Koike, Y., Iwabuchi, Y., Hosoya, S., Kobayashi, N., Fukase, T.: Physica C 159, 105 (1989)
Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)
Morel, P., Anderson, P.W.: Phys. Rev. 125, 1263 (1962)
Cohen, M.L., Anderson, P.W.: In: Douglass, D.H. (ed.) Superconductivity in d and f Band Metals. AIP, New York (1972)
Ginzburg, V.: Contemp. Phys. 33, 15 (1992)
Force, L., Bok, J.: Solid State Commun. 85, 975 (1993)
Batlogg, B., Kourouklis, G., Weber, W., Cava, R.J., Jayaraman, A., White, A.E., Short, K.T., Rupp, L.W., Rietman, E.A.: Phys. Rev. Lett. 59, 912 (1987)
Crawford, M.K., Kunchur, M.N., Farneth, W.E., McCarron, E.M. III, Poon, S.J.: Phys. Rev. B 41, 282 (1990)
Keller, H.: In: Müller, K., Bussmann-Holder, A. (eds.) Structure and Bonding, vol. 114, p. 143. Springer, Heidelberg (2005)
Tsuei, C.C., Newns, D.M., Chi, C.C., Pattnaik, P.C.: Phys. Rev. Lett. 65, 2724 (1990)
Pattnaik, P.C., Kane, C.L., Newns, D.M., Tsuei, C.C.: Phys. Rev. B 45, 5714 (1992)
Newns, D.M., Tsuei, C.C., Pattnaik, P.C., Lane, C.L.: Comments Condens. Matter Phys. 15, 273 (1992)
Hlubina, R., Rice, T.M.: Phys. Rev. B 51, 9253 (1995)
Olson, C.G., Liu, R., Lynch, D.W., List, R.S., Arko, A.J., Veal, B.W., Chang, Y.C., Jiang, P.Z., Paulikas, A.P.: Phys. Rev. B 42, 381 (1990)
Schlesinger, Z., et al.: Phys. Rev. Lett. 67, 2741 (1991)
Kubo, Y., Shimakawa, Y., Manako, T., Igarashi, H.: Phys. Rev. B 43, 7875 (1991)
Matthey, D., Gariglio, S., Giovannini, B., Triscone, J.-M.: Phys. Rev. B 64, 024513 (2001)
Balakirev, F.F., Betts, J.B., Migliori, A., Ono, S., Ando, Y., Boebinger, G.S.: Nature 424, 912 (2003)
Bok, J., Bouvier, J.: Physica C, Supercond. 403, 263 (2004)
Ong, N.P.: Phys. Rev. B 43, 193 (1991)
Williams, G.V.M., Tallon, J.L., Haines, E.M., Michalak, R., Dupree, R.: Phys. Rev. Lett. 78, 721 (1997)
Cooper, J.R., Loram, J.W.: J. Phys. I Fr. 6, 2237 (1996)
Abrikosov, A.A.: Physica C 244, 243 (1995)
Tsuei, C.C., Kirtley, J.R., Hammerl, G., Mannhart, J., Raffy, H., Li, Z.Z.: Phys. Rev. Lett. 93, 187004 (2004)
Bouvier, J., Bok, J.: J. Supercond. 10, 673 (1997)
Kyomen, T., Oguni, M., Itoh, M., Yu, J.D.: Phys. Rev. B 60, 6821 (1999)
Egami, T.: Essential role of the lattice in the mechanism of high temperature superconductivity. In: Bussmann-Holder, A., Keller, H. (eds.) High T C Superconductors and Related Transition Metal Oxides, pp. 103–129. Springer, Berlin (2007)
Toby, B.H., Egami, T., Jorgensen, J.D., Subrmanian, M.A.: Phys. Rev. Lett. 64, 2414 (1990)
Oyanagi, H.: Lattice effects in high temperature superconducting cuprates revealed by X-ray absorption spectroscopy. In: Bussmann-Holder, A., Keller, H. (eds.) High T C Superconductors and Related Transition Metal Oxides, pp. 253–258. Springer, Berlin (2007)
Lee, J., Fujita, K., McElroy, K., Slezak, J.A., Wang, M., Aiura, Y., Bando, H., Ishikado, M., Masui, T., Zhu, J.-X., Balatsky, A.V., Eisaki, H., Uchida, S., Davis, J.C.: Nature 442, 546 (2006)
Graf, J., d’Astuto, M., Jozwiak, C., Garcia, D.R., Saini, N.L., Krisch, M., Ikeuchi, K., Baron, A.Q.R., Eisaki, H., Lanzaral, A.: Phys. Rev. Lett. 100, 227002 (2008)
Deutscher, G., de Gennes, P.G.: C. R. Phys. 8, 937 (2007)
Acknowledgements
Jacqueline Bouvier personally met Professor Friedel for the first time the day of her thesis defense. He came, invited by one of my researcher friends, and he stayed during the cocktail. She adds: I was very impressed by his long and slim figure and his glittering eyes with strength emerging from him. After this first meeting, we met sometimes in his home to discuss our respective work. He was always very interested and always took into account my own words and capacities. I was very touched by his gentleman behavior regarding me. Until now, we are corresponding to exchange the ideas submitted in our papers. I want to deeply thank him for his intellectual interest in our work and express how I am admiring his lifelong work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bok, J., Bouvier, J. Superconductivity and the Van Hove Scenario. J Supercond Nov Magn 25, 657–667 (2012). https://doi.org/10.1007/s10948-012-1434-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10948-012-1434-3