# Cross-band versus intra-band pairing in superconductors: signatures and consequences of the interplay

## TL;DR

This paper investigates the competition between intra-band and cross-band pairing in two-band superconductors, revealing experimental signatures and consequences of their interplay, with implications for materials like MgB2 and iron-based superconductors.

## Contribution

It introduces a phase-sensitive framework for analyzing intra- and cross-band pairing competition and describes the crossover regimes, including a gapless state, in two-band superconductors.

## Key findings

- Identification of gap-splitting as a signature of crosspairing
- Observation of non-BCS temperature dependence of gaps
- Changes in pairing symmetry with temperature

## Abstract

We analyze the paradigmatic competition between intra-band and cross-band Cooper-pair formation in two-band superconductors, neglected in most works to date. We derive the phase-sensitive gap equations and describe the crossover between the intraband-dominated and the crossband-dominated regimes, delimited by a ``gapless'' state. Experimental signatures of crosspairing comprise notable gap-splitting in the excitation spectrum, non-BCS behavior of gaps versus temperature, as well as changes in the pairing symmetry as a function of temperature. The consequences of these findings are illustrated on the examples of MgB$_2$ and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$.