A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov–Milne–Pinney equation. Killing isometries include spatial translations and rotations, Newton–Hooke boosts and translation in the null direction. Geodesic motion in Ermakov–Milne–Pinney cosmoi is analyzed. The derivation of the Ermakov–Lewis invariant, the Friedmann equations and the Dmitriev–Zel'dovich equations within the Eisenhart–Duval framework is presented.
The influence of graphene and retinoic acid (RA) – a π-conjugated organic semiconductor – interface on their hybrid system is investigated. The physical properties of the interface are assessed via scanning probe microscopy, optical spectroscopy (photoluminescence and Raman) and ab initio calculations. The graphene/RA interaction induces the formation of a well-organized π-conjugated self-assembled monolayer (SAM) at the interface. Such structural organization leads to the high optical emission efficiency of the RA SAM, even at room temperature. Additionally, photo-assisted electrical force microscopy, photo-assisted scanning Kelvin probe microscopy and Raman spectroscopy indicate a RA-induced graphene doping and photo-charge generation. Finally, the optical excitation of the RA monolayer generates surface potential changes on the hybrid system. In summary, interface-induced organized structures atop 2D materials may have an important impact on both design and operation of π-conjugated nanomaterial-based hybrid systems.