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Title: Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field

Abstract

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.

Authors:
;
Publication Date:
Sponsoring Org.:
(US)
OSTI Identifier:
40203609
Resource Type:
Journal Article
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 63; Journal Issue: 23; Other Information: DOI: 10.1103/PhysRevB.63.235410; Othernumber: PRBMDO000063000023235410000001; 050123PRB; PBD: 15 Jun 2001; Journal ID: ISSN 0163-1829
Publisher:
The American Physical Society
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; DIELECTRIC MATERIALS; ELECTRIC FIELDS; ELECTROSTATICS; OSCILLATIONS; QUANTIZATION; SUPERLATTICES; THICKNESS; TUNNELING

Citation Formats

Onipko, Alexander, and Malysheva, Lyuba. Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field. United States: N. p., 2001. Web. doi:10.1103/PhysRevB.63.235410.
Onipko, Alexander, & Malysheva, Lyuba. Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field. United States. doi:10.1103/PhysRevB.63.235410.
Onipko, Alexander, and Malysheva, Lyuba. Fri . "Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field". United States. doi:10.1103/PhysRevB.63.235410.
@article{osti_40203609,
title = {Noncanonical Wannier-Stark ladders and surface state quantization in finite crystals subjected to a homogeneous electric field},
author = {Onipko, Alexander and Malysheva, Lyuba},
abstractNote = {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.},
doi = {10.1103/PhysRevB.63.235410},
journal = {Physical Review B},
issn = {0163-1829},
number = 23,
volume = 63,
place = {United States},
year = {2001},
month = {6}
}