Fig. 1: Realization of a quantum-phase (Q-phase) material.
From: An image interaction approach to quantum-phase engineering of two-dimensional materials

a Sketch of the non-contact interaction between a two-dimensional (2D) material and a neighboring neutral structure. The image potential experienced by conduction electrons in the material imprints a Q-phase on their wave functions ψj(r) that in turn changes the optical, electrical, and thermal transport properties. b Possible realization of a Q-phase material. In the absence of an additional structure, there is no image interaction (A), so conduction electrons exhibit a characteristic parabolic dispersion (B), leading to a collective response function like that of a 2DEG (C). An image potential landscape (D) is produced by introducing a neighboring neutral structure (a periodic array of conducting ribbons of period a, width b, and separation d). The electron wave functions then acquire a Q-phase that reshapes the band structure, opening gaps (E) and enabling additional electronic transitions that translate into modifications of the material properties (F), including its collective excitations.