非$σ_{\rm h}$对称类Dirac二维材料中弯曲模诱导的超导电性：硅烯和锗烯的理论研究
Superconductivity induced by flexural modes in non $σ_{\rm h}$-symmetric Dirac-like two-dimensional materials: A theoretical study for silicene and germanene
摘要：
在晶格的水平面上的反射下缺乏对称性（非$σ_{\rm h}$对称）的二维晶体中，电子可以耦合到一阶弯曲模（ZA声子）。我们表明，在这种类型的材料，也表现出一个Dirac-like电子色散，强耦合可以导致电子配对介导的这些声子，只要弯曲模式不阻尼或抑制额外的相互作用与支持衬底或栅极绝缘体。我们考虑几种模型：弱耦合极限，由于弱耦合，仅适用于带隙和抛物线材料，如锡烯和HfSe $_{2}$;完整的带隙方程，使用恒定带隙近似并考虑静态屏蔽相互作用求解;其扩展到能量相关带隙和动态屏蔽。我们认为，在硅烯和锗烯的情况下，由这个过程介导的超导性可以表现出几个K度的临界温度，甚至几十度K时占高介电常数环境的影响。我们的结论是，电子/弯曲模耦合应包括在非$σ_{\rm h}$对称的二维晶体中的可能的超导性的研究，即使考虑替代形式的耦合。
英文摘要：
In two-dimensional crystals that lack symmetry under reflections on the horizontal plane of the lattice (non-$σ_{\rm h}$-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-$σ_{\rm h}$-symmetric two-dimensional crystals, even if alternative forms of coupling are considered.
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