Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field
In the one-particle single band approximation, which is the basis of the original Wannier result, commonly referred to as the Wannier-Stark ladder (WSL), we have extended the concept by predicting the existence of noncanonical WSLs which are a set of evenly spaced levels (in the middle of the tilted band) with noncanonical level spacing equal to the Plank constant times (1{minus}2m{sup {prime}}/m){sup {minus}1} times Bloch oscillation frequency. To observe a particular WSL, the certain voltage must be applied. The latter is related to the numbers m=3,4,{hor_ellipsis} and m{sup {prime}}=1,2,{hor_ellipsis}{lt}m/2. We also show that, if the electrostatic energy due to applied voltage is larger than the zero-field band width, the quantization of surface localized states smoothly changes from the Airy type (at the spectrum edges) to the Wannier-Stark type with a pronounced energy interval in between, where the level spacing doubles that of canonical WSL. Analytical results are derived within the exactly solvable model of finite tilted tight-binding band. Their experimental implications and further-to-go directions are addressed to dielectric crystalline layers and superlattices, whose thickness (length) admits the direct tunneling.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40203609
- Journal Information:
- Physical Review B, Vol. 63, Issue 23; Other Information: DOI: 10.1103/PhysRevB.63.235410; Othernumber: PRBMDO000063000023235410000001; 050123PRB; PBD: 15 Jun 2001; ISSN 0163-1829
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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