# Modification of the effective action approach for the Leggett mode

## TL;DR

This paper presents a modified effective action approach for the Leggett mode, emphasizing the phase of electrons and the Hubbard-Stratonovich field as a pair wavefunction, applicable to strong interband coupling, with implications for Raman spectroscopy observations.

## Contribution

It introduces a new method for deriving the effective action that remains valid for strong interband coupling, unlike previous approaches.

## Key findings

- The spectral peak for the Leggett mode differs significantly between the earlier and modified theories.
- The modified theory provides a more accurate description of the Leggett mode in strong coupling regimes.
- The approach clarifies the role of electron phase in effective action formulation.

## Abstract

The modified procedure to get the effective action is discussed. Careful observation of phase of electrons leads to the conclusion that Hubbard-Stratonovich field should be pair wavefunction, instead of gap. The modified theory is valid for arbitrary strong interband coupling while the earlier approach only deals with weak interband coupling. This paper also discusses experimental observation of the Leggett mode: Raman spectroscopy. The spectral peak which corresponds to the Leggett mode is calculated in earlier the earlier and the modified theory, which shows that they are much different.