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 YB2C3Oy. 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 Tc and doping δ with recent experimental data in YB2C3Oy. 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 La2CuO4 near the doping 1/8.
Highlights
The isotope effect on the superconducting transition temperature Tc is one of the hallmarks of phonon-induced superconductivity in conventional superconductors [1]
Superconductivityinduced shifts of zone center phonons are in good agreement with calculated local density approximation (LDA) values [29, 30] and with such small EP coupling constants
Our calculations of the isotope coefficient α were based on a mean-field, like treatment of the t–J model, where optimal doping coincides with the onset of a charge-density wave (CDW), which competes with superconductivity in the underdoped regime and suppresses Tc there
Summary
The isotope effect on the superconducting transition temperature Tc is one of the hallmarks of phonon-induced superconductivity in conventional superconductors [1]. Many experiments showed that the measured isotope coefficient α in these systems is near the theoretical value of 1/2, confirming the important role played by phonons [2]. On the other hand the experiments show that very large values of α occur in high-Tc oxides if a competing phase with a gap or pseudogap is present [4]. Theories of this kind [12, 13] may explain α without assuming a strong EP coupling. A convincing explanation of α could contribute to the presently controversial discussed question of the role played by phonons in high-Tc oxides.
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