@article{Schindler:2021:10.1103/physrevb.104.l201114,
author = {Schindler, F and Bernevig, BA},
doi = {10.1103/physrevb.104.l201114},
journal = {Physical Review B},
pages = {1--5},
title = {Noncompact atomic insulators},
url = {http://dx.doi.org/10.1103/physrevb.104.l201114},
volume = {104},
year = {2021}
}

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TY  - JOUR
AB  - We study the conditions for Bloch bands to be spanned by symmetric and strictly compact Wannier states that have zero overlap with all lattice sites beyond a certain range. Similar to the characterization of topological insulators in terms of an algebraic (rather than exponential) localization of Wannier states, we find that there may be impediments to the compact localization even of topologically “trivial” obstructed atomic insulators. These insulators admit exponentially localized Wannier states centered at unoccupied orbitals of the crystalline lattice. First, we establish a sufficient condition for an insulator to have a compact representative. Second, for C2 rotational symmetry, we prove that the complement of fragile topological bands cannot be compact, even if it is an atomic insulator. Third, for C4 symmetry, our findings imply that there exist fragile bands with zero correlation length. Fourth, for a C3-symmetric atomic insulator, we explicitly derive that there are no compact Wannier states overlapping with less than 18 lattice sites. We conjecture that this obstruction generalizes to all finite Wannier sizes. Our results can be regarded as the stepping stone to a generalized theory of Wannier states beyond dipole or quadrupole polarization.
AU  - Schindler,F
AU  - Bernevig,BA
DO  - 10.1103/physrevb.104.l201114
EP  - 5
PY  - 2021///
SN  - 2469-9950
SP  - 1
TI  - Noncompact atomic insulators
T2  - Physical Review B
UR  - http://dx.doi.org/10.1103/physrevb.104.l201114
UR  - http://hdl.handle.net/10044/1/105870
VL  - 104
ER  - 

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