We consider a semi-periodic two-dimensional Schrödinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the incommensurable case, there are no gaps: the gaps of the bulk operator are filled with edge spectrum.
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Gontier, David 1
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@article{CRMATH_2021__359_8_949_0,
author = {Gontier, David},
title = {Spectral properties of periodic systems cut at an angle},
journal = {Comptes Rendus. Math\'ematique},
pages = {949--958},
year = {2021},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {8},
doi = {10.5802/crmath.251},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.251/}
}
TY - JOUR AU - Gontier, David TI - Spectral properties of periodic systems cut at an angle JO - Comptes Rendus. Mathématique PY - 2021 SP - 949 EP - 958 VL - 359 IS - 8 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.251/ DO - 10.5802/crmath.251 LA - en ID - CRMATH_2021__359_8_949_0 ER -
%0 Journal Article %A Gontier, David %T Spectral properties of periodic systems cut at an angle %J Comptes Rendus. Mathématique %D 2021 %P 949-958 %V 359 %N 8 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.251/ %R 10.5802/crmath.251 %G en %F CRMATH_2021__359_8_949_0
Gontier, David. Spectral properties of periodic systems cut at an angle. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 949-958. doi: 10.5802/crmath.251
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