Isotope effect on the superconducting critical temperature of cuprates in the presence of charge order

Abstract

Using the large-N limit of the t-J model and also allowing for phonons and the electron-phonon interaction, we study the isotope effect α for coupling constants appropriate for YB 2 C 3 O y . We find that α has a minimum at optimal doping and increases strongly (slightly) towards the underdoped (overdoped) region. Using values for the electron-phonon interaction from the local density approximation we get good agreement for α as a function of T c and doping δ with recent experimental data in YB 2 C 3 O y . Our results strongly suggest that the large increase of α in the underdoped region is (a) caused by the shift of electronic spectral density from low to high energies associated with a competing phase (in our case a charge density wave) and the formation of a gap, and (b) compatible with the small electron-phonon coupling constants obtained from the local density approximation. We propose a similar explanation for the anomalous behavior of α in Sr-doped La 2 CuO 4 near the doping 1/8.

Unconventional superconductivity

“…Greco and Zeyher [371] calculate in a t-J model that the large measured  values in the underdoped YBCO-and Bi-based cuprates come from a shift of the electronic density of states from low to higher energies. This shift is caused by a ground state (e. g. a charge density wave state) that competes with (rather than enhancing) the superconductivity, with the competing state also the source of the pseudogap.…”

Dual parquet scheme for the two-dimensional Hubbard model: Modeling low-energy physics of high- Tc cuprates with high momentum resolution

“…While this feature is virtually common to all hole-doped cuprate compounds, the nature of the superconducting phase is, however, still highly debated. The absence of an isotope effect 15,16 of the form T c ∼ 1/ √ M suggests that the pairing glue for the electrons is not (exclusively) due to phonons. Instead, collective excitations of the electrons themselves, such as the above mentioned antiferromagnetic spin fluctuations, may generate 17,18 an effective attractive interaction.…”

“…Therefore, the planar single-band Hubbard model 24 on a square lattice, which incorporates correlation effects via a purely local on-site Coulomb repulsion U , is commonly used for the theoretical description of these compounds. One should mention, that this model neglects several possibly important degrees of freedom in realistic cuprate crystals: The tunnel coupling between different CuO 2 planes, phonon degrees of freedom which may be responsible for the experimentally observed charge density waves 16,25,26 , or oxygen p-orbitals which can give rise to a metal-to-insulator transition of charge-transfer type. 27,28 Nevertheless, the Hubbard model is usually considered as a minimal model which incorporates the important correlations effects in the Cu d x 2 −y 2 orbitals.…”