Local density of states and level width for Wannier-Stark ladders

Journal Article · Thu Jul 15 04:00:00 EDT 1993 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.48.2215· OSTI ID:6327419

Chang, M C; Niu, Q ^[1]

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1. Department of Physics, University of Texas, Austin, Texas 78712 (United States)

The local density of states [rho]([ital x],[ital E]) is calculated for a Bloch electron in an electric field. Depending on the system size, we can see one or more sequences of Wannier-Stark ladders in [rho]([ital x],[ital E]), with Lorentz-type level widths and apparent spatial localization of the states. Our model is a chain of [delta]-function potential barriers plus a steplike electric potential, with open boundary conditions at both ends of the system. Using a wave-tunneling picture, we find that the level widths shrink to zero as an inverse power of the system size as the system size approaches infinity, confirming an earlier result. The level width will not approach zero if the [delta]-function barriers are replaced by the Kronig-Penney potential or smoother ones, as is commonly believed.

• OSTI ID: 6327419
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 48:4; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

665400* -- Quantum Physics Aspects of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BLOCH THEORY
ELECTRIC FIELDS
ENERGY-LEVEL DENSITY
LEVEL WIDTHS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
TUNNEL EFFECT