Superconductivity induced by flexural modes in non $\sigma_{\rm h}$-symmetric Dirac-like two-dimensional materials: A theoretical study for silicene and germanene

TL;DR

This theoretical study suggests that in non-$\sigma_h$-symmetric 2D materials like silicene and germanene, strong coupling between electrons and flexural phonons can induce superconductivity with potentially high critical temperatures.

Contribution

The paper introduces a theoretical framework showing how flexural modes can mediate superconductivity in Dirac-like 2D materials lacking horizontal mirror symmetry.

Findings

Flexural phonons can mediate electron pairing in certain 2D materials.

Superconductivity with T_c up to tens of Kelvin is possible in silicene and germanene.

Electron-flexural mode coupling should be considered in superconductivity studies of non-$\sigma_h$-symmetric 2D crystals.

Abstract

In two-dimensional crystals that lack symmetry under reflections on the horizontal plane of the lattice (non-$\sigma_{\rm h}$-symmetric), electrons can couple to flexural modes (ZA phonons) at first order. We show that in materials of this type that also exhibit a Dirac-like electron dispersion, the strong coupling can result in electron pairing mediated by these phonons, as long as the flexural modes are not damped or suppressed by additional interactions with a supporting substrate or gate insulator. We consider several models: The weak-coupling limit, which is applicable only in the case of gapped and parabolic materials, like stanene and HfSe$_{2}$, thanks to the weak coupling; the full gap-equation, solved using the constant-gap approximation and considering statically screened interactions; its extensions to energy-dependent gap and to dynamic screening. We argue that in the case of silicene and germanene superconductivity mediated by this process can exhibit a critical temperature of a few degrees K, or even a few tens of degrees K when accounting for the effect of a high-dielectric-constant environment. We conclude that the electron/flexural-modes coupling should be included in studies of possible superconductivity in non-$\sigma_{\rm h}$-symmetric two-dimensional crystals, even if alternative forms of coupling are considered.