Intertwining between electron and phonon driven order: A functional renormalization group approach

The competition and cooperation of different degrees of freedom is crucial for the understanding of the instabilities of a Fermi liquid. The functional renormalization group (fRG) allows for an unbiased treatment of all electron-electron and electron-hole fluctuations and is a powerful technique for mapping the phase diagram in the weak- and intermediate coupling limit. An extension of the established all-electronic fRG to include phonon induced retarded interactions allows an embedding of phonon-driven order in this picture. The consequences of the intertwining of electrons and phonons for the ordering and critical temperatures are revealed for different kinds of electron-phonon couplings and electronic interactions and band structures.