TY - JOUR
T1 - Spin-orbit-free topological insulators
AU - Alexandradinata, A.
AU - Bernevig, B. Andrei
N1 - Funding Information:
Chen Fang and Matthew Gilbert played an essential role in formulating the theory of Cnv insulators, whose short review we have presented here. AA and BAB were supported by Packard Foundation, 339-4063-Keck Foundation, NSF CAREER DMR-095242, ONR-N00014-11-1-0635 and NSF-MRSEC DMR-0819860 at Princeton University. This work was also supported by DARPA under SPAWAR Grant No.: N66001-11-1-4110.
Publisher Copyright:
© 2015 The Royal Swedish Academy of Sciences.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We review a class of translational-invariant insulators without spin-orbit coupling, as may be realized in intrinsically spinless systems, e.g., photonic crystals and ultra-cold atoms. Some of these insulators have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. To describe these phases, we introduce the notions of (a) a halved-mirror chirality: an integer invariant which characterizes half-mirror planes in the 3D Brillouin zone, and (b) a bent Chern number: the traditional Thouless-Kohmoto-Nightingale-Nijs invariant generalized to bent 2D manifolds. Like other well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes - they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Finally, we describe the Weyl semimetallic phase that intermediates two distinct, gapped phases.
AB - We review a class of translational-invariant insulators without spin-orbit coupling, as may be realized in intrinsically spinless systems, e.g., photonic crystals and ultra-cold atoms. Some of these insulators have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. To describe these phases, we introduce the notions of (a) a halved-mirror chirality: an integer invariant which characterizes half-mirror planes in the 3D Brillouin zone, and (b) a bent Chern number: the traditional Thouless-Kohmoto-Nightingale-Nijs invariant generalized to bent 2D manifolds. Like other well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes - they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Finally, we describe the Weyl semimetallic phase that intermediates two distinct, gapped phases.
KW - cold atom
KW - photonic crystal
KW - topological insulator
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U2 - 10.1088/0031-8949/2015/T164/014013
DO - 10.1088/0031-8949/2015/T164/014013
M3 - Conference article
AN - SCOPUS:84974527984
SN - 0281-1847
VL - 2015
JO - Physica Scripta
JF - Physica Scripta
IS - T164
M1 - 014013
T2 - 156th Nobel Symposium on New Forms of Matter: Topological Insulators and Superconductors
Y2 - 12 June 2014 through 15 June 2014
ER -