Fuzzy Band Structure of Quantum Dots by Bloch Orbital Expansion: Unconventional Insights into Geometric-Electronic Structure Relations

The extension of ab initio methods like density functional theory (DFT) to quantum dot (QD) geometries has enabled researchers to explore relationships between QD surface termination and electronic structure. However, fully utilizing the data from DFT requires novel classification methods for QD orbitals. Here, we identify relationships between QD geometry and electronic structure by transforming real-space QD orbitals into momentum-space using Bloch orbital expansion (BOE), yielding a fuzzy QD band structure. Comparing with bulk band structures, we show that truncated, unpassivated facets in III-V and II-VI QDs produce midgap orbitals derived from bulk surface orbitals, an identification challenging in real space. QDs with reconstructed facets, however, feature delocalized orbitals formed by superposition of bulk Bloch orbitals. Moreover, we demonstrate that atomistic core/shell QD models of relevant sizes with realistic surface termination exhibit fuzzy bands, allowing us to identify the core/shell band alignment, an analysis that is not possible in real space. These findings emphasize BOE as a vital tool for connecting computational and experimental insights in nanocrystal research.