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. 
David G. Gonz\'alez, Fernando Sols, Francisco Guinea, and Ivar Zapata
cond-mat.mes-hall cond-mat.supr-con