Isotope effect on $m^*$ in high-T_c materials due to the breakdown of Migdal's theorem

TL;DR

This paper demonstrates that considering effects beyond Migdal's theorem in electron-phonon interactions can cause an isotope effect on the effective mass of charge carriers, offering an alternative explanation to polaronic models for recent experimental observations.

Contribution

It introduces a nonadiabatic approach to electron-phonon interactions that predicts isotope effects on effective mass before polaron formation, challenging traditional interpretations.

Findings

Isotope effect on $m^*$ can occur without polaron formation.

Nonadiabatic effects explain recent isotope effect observations.

Provides a different scenario from polaronic models.

Abstract

We show that the inclusion of effects beyond Migdal's limit in the electron-phonon interaction naturally leads to an isotope effect for the effective mass $m^{*}$ of the charge carriers even much before reaching the polaron limit. This is the situation already considered in our approach to nonadiabatic superconductivity. Such a result provides a scenario different from the polaronic one for the interpretation of the recently observed isotope effect on $m^{*}$ in YBa$_{2}$Cu$_{3}$O$_{6+x}$ and La$_{2-x}$Sr$_{x}$CuO$_{4}$.