TY - JOUR

T1 - Recovering hidden Bloch character

T2 - Unfolding electrons, phonons, and slabs

AU - Allen, P. B.

AU - Berlijn, T.

AU - Casavant, D. A.

AU - Soler, J. M.

PY - 2013/2/27

Y1 - 2013/2/27

N2 - 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 k z of the wave vector are not explicitly defined, but may be hidden in the state (and eigenvector). 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.

AB - 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 k z of the wave vector are not explicitly defined, but may be hidden in the state (and eigenvector). 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.

UR - http://www.scopus.com/inward/record.url?scp=84874522615&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.87.085322

DO - 10.1103/PhysRevB.87.085322

M3 - Article

AN - SCOPUS:84874522615

SN - 1098-0121

VL - 87

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 8

M1 - 085322

ER -