Abstract
Using dynamical mean-field theory we explore the electronic properties of the bilayer Hubbard model. For realistic model parameters we find a large reduction of the bonding-antibonding splitting of pure and hole doped Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8 +\delta }\) bilayer superconductor due to sizable dynamical correlations. Our results reveal a remarkable layer-selective renormalization of the Cu-3d bands caused by the interplay of intralayer Coulomb interaction and layer polarization with emergent Landau–Fermi liquid electronic excitations. At finite repulsive interlayer Coulomb interaction we predict a continuous layer decoupling phenomenon with coexisting Landau–Fermi liquid and Mott localized electrons. The emergence of layer-selectivity is important for the ongoing debate of correlated two-fluid superconductivity.
Graphical abstract
Similar content being viewed by others
Data availability statement
This manuscript has no associated data or the data will not be deposited. [Author’s comment: This is a purely computational work, and all the data related to this work is provided in the form of figures within this article.]
References
S. Chakravarty, A. Sudbo, P.W. Anderson, S. Strong, Science 261, 337 (1993)
A. Fuhrmann, D. Heilmann, H. Monien, Phys. Rev. B 73, 245118 (2006)
M. Golor, T. Reckling, L. Classen, M.M. Scherer, S. Wessel, Phys. Rev. B 90, 195131 (2014)
K. Bouadim, G.G. Batrouni, F. Hébert, R.T. Scalettar, Phys. Rev. B 77, 144527 (2008)
H. Lee, Y.-Z. Zhang, H.O. Jeschke, R. Valentí, Phys. Rev. B 89, 035139 (2014)
T.I. Vanhala, J.E. Baarsma, M.O.J. Heikkinen, M. Troyer, A. Harju, P. Törmä, Phys. Rev. B 91, 144510 (2015)
X.-X. Huang, M. Claassen, E.W. Huang, B. Moritz, T.P. Devereaux, Phys. Rev. Lett. 124, 077601 (2020)
M. Gall, N. Wurz, J. Samland, C.F. Chan, M. Köhl, Nature 589, 40 (2021)
T.A. Maier, D.J. Scalapino, Phys. Rev. B 84, 180513(R) (2011)
S. Capponi, C. Wu, S.-C. Zhang, Phys. Rev. B 70, 220505 (2004)
H. Zhai, F. Wang, D.-H. Lee, Phys. Rev. B 80, 064517 (2009)
See also, L. Craco, Phys. Rev. B 104, 064509 (2021) and references therein
S.S. Kancharla, S. Okamoto, Phys. Rev. B 75, 193103 (2007)
A.I. Liechtenstein, O. Gunnarsson, O.K. Andersen, R.M. Martin, Phys. Rev. B 54, 12505 (1996)
L. Rademaker, S. Johnston, J. Zaanen, J. van den Brink, Phys. Rev. B 88, 235115 (2013)
S. Karakuzu, S. Johnston, and T. A. Maier, arXiv:2107.13996 (unpublished)
A.M. Fulterer, E. Arrigoni, J. Supercond. Nov. Magn. 25, 1769 (2012)
L. Zou, T. Senthil, Phys. Rev. B 94, 115113 (2016)
M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
M. Neumann, J. Nyéki, B. Cowan, J. Saunders, Science 317, 1356 (2007)
Y. Sato, Y. Kawasugi, M. Suda, H.M. Yamamoto, R. Kato, Nano Lett. 17, 708 (2017)
T. Senthil, Phys. Rev. B 78, 045109 (2008)
R. V. Mishmash, I. González, R. G. Melko, O. I. Motrunich, and M. P. A. Fisher, Phys. Rev. B 91, 235140 (2015)
S. Sen, N.S. Vidhyadhiraja, Phys. Rev. B 93, 155136 (2016)
P. Haldar, M.S. Laad, S.R. Hassan, Phys. Rev. B 94, 081115(R) (2016)
R.T. Scalettar, J.W. Cannon, D.J. Scalapino, R.L. Sugar, Phys. Rev. B 50, 13419 (1994)
K. Jiang, C. Le, Y. Li, S. Qin, Z. Wang, F. Zhang, J. Hu, Phys. Rev. B 103, 045108 (2021)
Q. Gao, H. Yan, J. Liu, P. Ai, Y. Cai, C. Li, X. Luo, C. Hu, C. Song, J. Huang, H. Rong, Y. Huang, Q. Wang, G. Liu, G. Gu, F. Zhang, F. Yang, S. Zhang, Q. Peng, Z. Xu, L. Zhao, T. Xiang, X.J. Zhou, Phys. Rev. B 101, 014513 (2020)
As a side note we shall mentention that an intrinsic feature of the bilayer superconductor Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+\delta }\) (Bi2212) is that there are two CuO\(_2\) planes in one structural unit separated by calcium. The interaction between the copper-oxide planes gives rise to bilayer splitting, i.e., two bonding-antibonding Fermi surface sheets, with different doping levels [26]
A.A. Kordyuk, S.V. Borisenko, M. Knupfer, J. Fink, Phys. Rev. B 67, 064504 (2003)
L. Craco, Phys. Rev. B 77, 125122 (2008)
M.S. Laad, L. Craco, E. Müller-Hartmann, Phys. Rev. Lett. 91, 156402 (2003)
L. Craco, M.S. Laad, E. Müller-Hartmann, Phys. Rev. Lett. 90, 237203 (2003)
A. Koitzsch, S.V. Borisenko, A.A. Kordyuk, T.K. Kim, M. Knupfer, J. Fink, H. Berger, R. Follath, Phys. Rev. B 69, 140507(R) (2004)
S.V. Borisenko, A.A. Kordyuk, T.K. Kim, S. Legner, K.A. Nenkov, M. Knupfer, M.S. Golden, J. Fink, H. Berger, and R. Follath Phys. Rev. B 66, 140509(R) (2002)
The computations of the retarded Green’s functions and self-energies were performed using \(\eta =0.005\) eV with a \(k\)-point grid of \(900 \times 900\). Moreover, 500 frequency points were considered for the energy window from \(-5\) to 5 eV around \(E_F\) to ensure that all relevant electronic excitations are included
R. Žitko, J. Bonča, T. Pruschke, Phys. Rev. B 80, 245112 (2009)
D.L. Feng, N.P. Armitage, D.H. Lu, A. Damascelli, J.P. Hu, P. Bogdanov, A. Lanzara, F. Ronning, K.M. Shen, H. Eisaki, C. Kim, Z.-X. Shen, J.-I. Shimoyama, K. Kishio, Phys. Rev. Lett. 86, 5550 (2001)
D. Fournier, G. Levy, Y. Pennec, J.L. McChesney, A. Bostwick, E. Rotenberg, R. Liang, W.N. Hardy, D.A. Bonn, I.S. Elfimov, A. Damascelli, Nature Phys. 6, 905 (2010)
T.J. Reber, X. Zhou, N.C. Plumb, S. Parham, J.A. Waugh, Y. Cao, Z. Sun, H. Li, Q. Wang, J.S. Wen, Z.J. Xu, G. Gu, Y. Yoshida, H. Eisaki, G.B. Arnold, D.S. Dessau, Nat. Commun. 10, 5737 (2019)
R.S. Markiewicz, J. Phys. and Chem. of Solids 58, 1179 (1997)
D.J. Singh, Phys. Rev. B 52, 1358 (1995)
A. Liebsch, A. Lichtenstein, Phys. Rev. Lett. 84, 1591 (2000)
K.M. Shen, N. Kikugawa, C. Bergemann, L. Balicas, F. Baumberger, W. Meevasana, N.J.C. Ingle, Y. Maeno, Z.-X. Shen, A.P. Mackenzie, Phys. Rev. Lett. 99, 187001 (2007)
For the particular case of graphene, see L. Craco, Phys. Rev. B 103, 075135 (2021) and references therein
J. Bok, J. Bouvier, J. Supercond. Nov. Magn. 25, 657 (2012)
R. S. Markiewicz, Tanmoy Das, and A. Bansil, Phys. Rev. B 86, 024511 (2012)
L. Craco, S. Leoni, Phys. Rev. B 100, 115156 (2019)
N. Trivedi, Nature Physics 4, 163 (2008)
B. J. Ramshaw1, S. E. Sebastian, R. D. McDonald, J. Day, B. S. Tan, Z. Zhu, J. B. Betts, R. Liang, D. A. Bonn, W. N. Hardy, N. Harrison, Science 348, 317 (2015)
Z.-Y. Song, X.-C. Jiang, Y.-Z. Zhang, Phys. Rev. B 102, 245124 (2020)
See, M. Vandelli, J. Kaufmann, V. Harkov, A. I. Lichtenstein, K. Held, E. A. Stepanov, arXiv:2204.02116 (unpublished) and references therein
M. J. Han, Xin Wang, C. A. Marianetti, and A. J. Millis, Phys. Rev. Lett. 107, 206804 (2011)
A.I. Poteryaev, M. Ferrero, A. Georges, O. Parcollet, Phys. Rev. B 78, 045115 (2008)
L. Craco, M.S. Laad, S. Leoni, Scientific Reports 7, 2632 (2017)
Y. Ni, Y.-M. Quan, J. Liu, Y. Song, L.-J. Zou, Phys. Rev. B 103, 214510 (2021)
P. Werner, A.J. Millis, Phys. Rev. Lett. 99, 126405 (2007)
L. de’ Medici, Phys. Rev. B 83, 205112 (2011)
L. de’Medici, J. Mravlje, A. Georges, Phys. Rev. Lett. 107, 256401 (2011)
L. de’Medici, Phys. Rev. Lett. 118, 167003 (2017)
M. Capone, Nat. Mater. 17, 855 (2018)
F.B. Kugler, S.-S.B. Lee, A. Weichselbaum, G. Kotliar, J. von Delft, Phys. Rev. B 100, 115159 (2019)
A. Mezio, R.H. McKenzie, Phys. Rev. B 100, 205134 (2019)
C.-Y. Moon, npj Comput. Mater. 6, 147 (2020)
L. Fanfarillo, G. Giovannetti, M. Capone, E. Bascones, Phys. Rev. B 95, 144511 (2017)
L. Fanfarillo, E. Bascones, Phys. Rev. B 92, 075136 (2015)
J. Bardeen, Phys. Rev. Lett. 1, 399 (1958)
Acknowledgements
I would like to thank Jörg Fink for interesting discussions as well as the Leibniz Institute for Solid State and Materials Research Dresden for hospitality in the early stages of this work. Acknowledgement is also made to CNPq and CAPES.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Craco, L. Electronic properties of normal and extended Hubbard model for bilayer cuprates. Eur. Phys. J. B 95, 125 (2022). https://doi.org/10.1140/epjb/s10051-022-00393-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-022-00393-y