Variational Scarring in Graphene Quantum Dots (2410.13157v2)

Abstract: A quantum eigenstate of a classically chaotic system is referred as scarred by an unstable periodic orbit if its probability density is concentrated in the vicinity of that orbit. Recently, a new class of scarring - variational scarring - was discovered in numerical studies of disordered quantum dots, arising from near-degeneracies in the quantum spectrum associated with classical resonances of the unperturbed system. Despite the increasing body of theoretical evidence on variational scarring, its experimental observation has remained out of reach. Motivated by this dearth, we argue and demonstrate that variational scarring can occur in an elliptical quantum dot fabricated on monolayer graphene, and locally perturbed by a nanotip. Then, we further show that the fingerprint of these variational scars can potentially be detected via scanning tunneling microscopy, thus offering an attractive experimental pathway for the first validation of this puzzling quantum-chaotic phenomenon.