Breakdown of Adiabatic Superconductivity in Ca-Doped h-BN Monolayer

Abstract

In the present paper, we report the breakdown of the adiabatic picture of superconductivity in a calcium-doped hexagonal boron nitride (Ca-h-BN) monolayer and discuss its implications for the selected properties of this phase. In particular, it is shown that the shallow conduction band of the Ca-h-BN superconductor potentially cause a violation of the adiabatic Migdal’s theorem. As a result, the pivotal parameters that describe the superconducting state in Ca-h-BN are found to be notably influenced by the non-adiabatic effects. This finding is described here within the vertex-corrected Eliashberg formalism that predicts a strong reduction of the order parameter, superconducting transition temperature and superconducting gap in comparison to the estimates obtained in the framework of the adiabatic theory. The observed trends are in agreement with the recent results on superconductivity in hexagonal monolayers and confirm that the non-adiabatic effects have to be taken into account during the design of such future low-dimensional superconductors.