Anomalous isotope Effect in d-wave superconductors on the square lattice

Abstract

Isotope effect with a large coefficient $\alpha =-\partial \ln T_c/\partial \ln M$ is usually taken as an evidence of phonon mediated superconductors in the Bardeen-Cooper-Schrieffer (BCS) theory. However, in cuprates which are now widely believed to be strong correlation induced d-wave superconductors, $\alpha$ is experimentally observed to be quite small at optimal doping, but keeps growing up with decreasing $T_c$ upon doping, even after exceeding the BCS value $1/2$. Such an anomalous isotope effect seems to challenge the non-phonon picture and still leave room for the phonon-dominated mechanism. In this work, we show that the anomalous dependence of $\alpha$ on $T_c$ can actually be obtained in spin fluctuation induced d-wave superconductors, by studying the Hubbard model on square lattices with functional renormalization group. We have considered two types of electron-phonon couplings (EPCs). The first type couples to electron densities, including the Holstein, breathing and buckling phonons, called Holstein-like. For all these EPCs, $\alpha$ is negative and drops down towards $-\infty$ with decreasing $T_c$ upon doping. On the opposite, for the other type of Peierls-like EPC coupling to electron hoppings on the nearest bonds, also called Su-Schrieffer-Heeger phonon, $\alpha$ is positive, grows up with decreasing $T_c$ and tends to diverge as $T_c\to 0$, in qualitative agreement with the experiments. The difference between these two types of EPCs can be understood by their isotope effects on spin fluctuations. From this study, we conclude that the SSH phonon can explain the anomalous isotope effect in cuprates, although it is not the leading pairing mechanism.

References in corpus (13)

• A Systematic Study of Electron-Phonon Coupling to Oxygen Modes Across the Cuprates
• Anomalously Strong Near-Neighbor Attraction in Doped 1D Cuprate Chains
• Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates
• Bipolaronic high-temperature superconductivity
• Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
• Antiferromagnetism induced by electron-phonon-coupling
• Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
• Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model
• A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model
• The isotope effect in the Hubbard model with local phonons
• Electronic orders on the kagome lattice at the lower Van Hove filling
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Absence of the 1/8 -anomaly in oxygen isotope effect on YBa${}_2$Cu${}_3$O${}_y$

Cited by in corpus (2)

• Cooperation between electron-phonon coupling and electronic interaction in bilayer nickelates La${}_3$Ni${}_2$O${}_7$
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization