Spectroscopic signatures of tetralayer graphene polytypes

Tetralayer graphene has recently become a new addition to the family of few-layer graphene with versatile electronic properties. This material can be realised in three distinctive stacking configurations, for which we determine spectroscopic signatures in angle-resolved photoemission spectroscopy (ARPES), dynamical optical conductivity, and Raman spectra of inter-band excitations. The reported library of spectral features of tetralayer graphenes can be used for the non-invasive identification of the stacking order realised in a particular film.