Doping dependent isotope effects of the quasi-1D electron-phonon system: comparison with the high-temperature superconductors

TL;DR

This study investigates how doping affects isotope effects and superconducting properties in quasi-1D electron-phonon systems, revealing non-monotonic doping dependence and similarities with high-temperature superconductors.

Contribution

It provides a detailed analysis of doping-dependent isotope effects and spin gaps in 1D models, connecting these findings to high-temperature superconductor behavior.

Findings

Spin gap decreases monotonically with doping.

Superconducting susceptibility peaks at an optimal doping.

Isotope effect on T_c is strongest near half-filling.

Abstract

The weak-coupling quantum phase diagrams of the one-dimensional (1D) Holstein-Hubbard and Peierls-Hubbard models are computed near half-filling, using a multi-step renormalization group technique. If strong enough, the electron-phonon interaction induces a spin gap. The spin gap, which determines the superconducting pairing energy, depends strongly on the band filling and decreases monotonically as the system is doped away from half-filling. However, the superconducting susceptibility exhibits a different doping dependence; it can vary non-monotonically with doping and exhibit a maximum at an "optimal" value of the doping. For a quasi-1D array of weakly coupled, fluctuating 1D chains, the superconducting transition temperature T_c exhibits a similar non-monotonic doping dependence. The effect of changing the ion mass (isotope effect) on T_c is found to be largest near half-filling and to decrease rapidly upon doping away from half-filling. The isotope effect on the spin gap is the opposite sign as the isotope effect on T_c. We discuss qualitative similarities between these results and properties of the high-temperature superconductors.