Band Unfolding in Finite Nanostructures: Visualizing Dirac, Spin-Valley, and Rashba Features.

Nanomaterials possess unique electronic properties distinct from bulk systems, and spatially resolved techniques such as nano-ARPES now allow for local band structure measurements at the nanoscale. However, theoretical tools for interpreting band dispersion in finite, aperiodic systems remain limited. Here, we propose a "giant molecule band unfolding" (GMBU) procedure that enables the extraction of band dispersion from molecular orbital levels of finite systems without assuming periodic boundary conditions. Using first-principles calculations for graphene, tungsten disulfide, and bismuth/silver surface alloy nanoflakes, we successfully reproduced the characteristic band structures of Dirac cones, spin-valley locking, and Rashba spin splitting, respectively. Our spin-resolved formulation visualizes spin textures and provides an efficient framework for analyzing spintronic and valleytronic properties. GMBU enabled visualization of band dispersion, even when nanoflakes were bent. The method bridges discrete and continuous electronic descriptions and is applicable across dimensionalities and symmetry classes, offering new possibilities for understanding and designing functional nanoscale materials.