2012/12/22 by Philip B. Allen, P. B. Allen, Tom Berlijn +4 · 110 citations
Engineering · Physics and Astronomy · #Character (mathematics) #Condensed matter physics #Electron #Force Microscopy Techniques and Applications #Geometry #Materials science #Phonon #Physics #Quantum and electron transport phenomena #Quantum mechanics #Semiconductor materials and devices #Strongly correlated material #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.87.085322
published in Physical Review B 87(8) (American Physical Society) · 11 pages, 7 figures
arxiv created 2012/12/22 · openalex publication_date 2013/02/27 · arxiv updated 2013/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a quantum state, or classical harmonic normal mode, of a system of spatial periodicity ``R,'' Bloch character is encoded in a wave vector ``K.'' One can ask whether this state has partial Bloch character ``k'' corresponding to a finer scale of periodicity ``r.'' Answering this is called ``unfolding.'' A theorem is proven that yields a mathematically clear prescription for unfolding, by examining translational properties of the state, requiring no ``reference states'' or basis functions with the finer periodicity (r,k). A question then arises: How should one assign partial Bloch character to a state of a finite system? A slab, finite in one direction, is used as the example. Perpendicular components kz of the wave vector are not explicitly defined, but may be hidden in the state (and eigenvector |i\ensuremath⟩). A prescription for extracting kz is offered and tested. An idealized silicon (111) surface is used as the example. Slab unfolding reveals surface-localized states and resonances which were not evident from dispersion curves alone.