Reply to "Comment on 'Isotope effect in multi-band and multi-channel attractive systems and inverse isotope effect in iron-based superconductors'"

TL;DR

This paper defends a BCS-type multi-channel model for superconductivity against a comment, clarifying assumptions about energy ranges and interaction cutoffs, and providing detailed methodological explanations.

Contribution

It clarifies the assumptions and methodology of a multi-channel BCS model for superconductivity, countering misinterpretations in a comment.

Findings

The model assumes specific energy cutoffs for interactions.

The interaction is non-zero only within defined energy ranges.

The paper provides detailed solution methods for the gap equation.

Abstract

The Comment insists on the following: in our model it is assumed that the effective interactions have specific energy ranges within the single band with a cutoff at \omega_1 for the phononic part and a range from \omega_1 to \omega_2 in the AF channel. Our reply is that we assume that V_i(k,k')\neq 0 if |\xi_k|<\omega_i and |\xi_{k'}|<\omega_i, and otherwise V_i(k,k')= 0 (i=1,2), as stated in our paper. This is the model of BCS type with two attractive interactions, and this assumption is the characteristic of the BCS approximation. The claim "the integration limits have been modified such that the AF channel mediated pairing sets in where the ph-channel pairing terminates and is limited at an energy given by \omega_j=\omega_{AF}" in the Comment is wrong. We describe the model and the method to solve the gap equation in more detail.