Electron-phonon vertex and its influence on the superconductivity of two-dimensional metals on a piezoelectric substrate

We investigate the interaction between the electrons of a two-dimensional metal and the acoustic phonons of an underlying piezoelectric substrate. Fundamental inequalities can be obtained from general energy arguments. As a result, phonon mediated attraction can be proven to never overcome electron Coulomb repulsion, at least for long phonon wavelengths. We study the influence of these phonons on the possible pairing instabilities of a two-dimensional electron gas such as graphene.

Figure 1

A flat piezoelectric substrate with an interface to air or vacuum, with $\mathbf{b}=\left[cos\left(\theta \right),sin\left(\theta \right)\right]$ the propagation direction of the piezoelectric SAW.

Figure 2

Critical temperature and variation from the “bare” one in Ref. [19] for graphene on a piezoelectric substrate, as a function of the conduction band density. Three pairs of plots are given for three different values of $K_R$ and the two values of the constant $C=3.5$ and 5 in Eq. (5.1) for $\lambda$ in Ref. [19].