TY - JOUR
T1 - Gapless Criterion for Crystals from Effective Axion Field
AU - Yu, Jiabin
AU - Song, Zhi Da
AU - Liu, Chao Xing
N1 - Funding Information:
J. Y. thanks Biao Lian, Hoi Chun Po, and Xiao-Qi Sun for helpful discussions. Z. D. S. is supported by the U.S. Department of Energy (Grant No. DE-SC0016239), the National Science Foundation (EAGER Grant No. DMR 1643312), Simons Investigator Awards (Grant No. 404513), ONR (Grant No. N00014-14-1-0330), NSF-MRSEC (Grant No. DMR-142051), the Packard Foundation, the Schmidt Fund for Innovative Research, and the Guggenheim Fellowship. J. Y. and C. X. L. acknowledge the support of the Office of Naval Research (Grant No. N00014-18-1-2793), the U.S. Department of Energy (Grant No. DESC0019064), and Kaufman New Initiative research Grant No. KA2018-98553 of the Pittsburgh Foundation.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/7/17
Y1 - 2020/7/17
N2 - Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry-representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.
AB - Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry-representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.
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U2 - 10.1103/PhysRevLett.125.036401
DO - 10.1103/PhysRevLett.125.036401
M3 - Article
C2 - 32745391
AN - SCOPUS:85089046939
SN - 0031-9007
VL - 125
JO - Physical review letters
JF - Physical review letters
IS - 3
M1 - 036401
ER -