Speaker
Description
Two-dimensional (2D) materials of atomic thickness exhibit rich physics and strong potential for advanced technologies. Following the discovery of graphene, extensive research has explored fundamental properties of 2D materials and inspired analogous developments in photonics, cold atoms, and engineered metamaterials. Progress in electronics, optoelectronics, quantum technologies, catalysis, and energy applications highlights the critical role of edge effects. In this context, edge states have emerged as a key factor in understanding and controlling wave propagation in low-dimensional systems. We present theoretical and computational studies, often supported by experiments, on the structural and electronic properties of 2D nanostructures, emphasizing cases where simplified models successfully capture the essential physics. For the well-studied graphene nanoribbons using a tight-binding model with nearest-neighbor interactions, extended to the discrete nonlinear Schrödinger equation to incorporate interaction-induced nonlinearity, we reveal novel spatially localized states. By analyzing the time evolution of initially localized wave packets, we identify distinct dynamical regimes, ranging from linear spreading to nonlinear self-trapping, or governed by edge geometry and initial conditions. For semiconducting armchair nanoribbons, we demonstrate analytically and numerically the existence of flat band states that remain strictly localized across the ribbon width without spreading along the periodic direction. In zigzag nanoribbons, we construct localized states from partially flat band edge states at the Fermi level, leading to confinement in both transverse and longitudinal directions. The inclusion of strong disorder via random on-site energies results in Anderson localization in all cases. Extensions to related 2D lattices reveal the emergence of robust topological states. These results show that geometry, nonlinearity, disorder, and topology provide multiple localization mechanisms, offering new strategies for controlling transfer of excitations in 2D systems.
Support by S.A.R.F. of the University of Crete, KA11568.