14 Topology in Magnetism
403
157. Y. Su, X.R. Wang, Chiral anomaly of Weyl magnons in stacked honeycomb ferromagnets.
Phys Rev B 96, 104437 (2017)
158. G. Jackeli, G. Khaliullin, Mott insulators in the strong spin-orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009)
159. M. Sato, K. Hasebe, K. Esaki, M. Kohmoto, Time-reversal symmetry in non-hermitian systems. Progress Theor. Phys. 127(6), 937–974 (2012)
160. R.M. White, M. Sparks, I. Ortenburger, Diagonalization of the antiferromagnetic magnonphonon interaction. Phys. Rev. 139, A450–A454 (1965)
161. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic
properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
162. J.E. Avron, R. Seiler, B. Simon, Homotopy and quantization in condensed matter physics.
Phys. Rev. Lett. 51, 51–53 (1983)
163. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The Geometric Phase in
Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and
Condensed Matter Physics (Theoretical and Mathematical Physics. Springer, Berlin Heidelberg, 2013)
164. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Topological semimetal and Fermi-arc
surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)
165. A.A. Burkov, L. Balents, Weyl semimetal in a topological insulator multilayer. Phys. Rev.
Lett. 107, 127205 (2011)
166. S-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z.
Yuan, C-C. Lee, S-M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B. Wang, A. Bansil, F. Chou,
P.P. Shibayev, H. Lin, S. Jia, M. Zahid Hasan, Discovery of a Weyl fermion semimetal and
topological Fermi arcs. Science 349(6248), 613–617 (2015)
167. B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao,
G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, Experimental discovery of Weyl Semimetal
TaAs. Phys. Rev. X 5, 031013 (2015)
168. L. Ling, Z. Wang, D. Ye, L. Ran, F. Liang, J.D. Joannopoulos, M. Soljaˇ ci´ c, Experimental
observation of Weyl points. Science 349(6248), 622–624 (2015)
169. F-Y. Li, Y-D. Li, Y. Baek Kim, L. Balents, Y. Yu, G. Chen, Weyl magnons in breathing
pyrochlore antiferromagnets. Nat. Commun. 7(1), 12691 (2016)
170. A. Mook, J. Henk, I. Mertig, Tunable magnon Weyl points in ferromagnetic pyrochlores.
Phys. Rev. Lett. 117, 157204 (2016)
171. A. Alexey, Soluyanov, Dominik Gresch, Zhijun Wang, QuanSheng Wu, Matthias Troyer, Xi
Dai, and B. Andrei Bernevig. Type-II Weyl semimetals. Nature 527(7579), 495–498 (2015)
172. F. Meier, D. Loss, Magnetization transport and quantized spin conductance. Phys. Rev. Lett.
90, 167204 (2003)
173. J. Sugiyama, K. Mukai, H. Nozaki, M. Harada, M. Månsson, K. Kamazawa, D. Andreica, A.
Amato, A.D. Hillier, Antiferromagnetic spin structure and lithium ion diffusion in Li 2 MnO 3
probed by μ + SR. Phys. Rev. B 87, 024409 (2013)
174. T. Takayama, A. Kato, R. Dinnebier, J. Nuss, H. Kono, L.S.I. Veiga, G. Fabbris, D. Haskel, H.
Takagi, Hyperhoneycomb iridate β-Li 2 IrO 3 as a platform for Kitaev magnetism. Phys. Rev.
Lett. 114, 077202 (2015)
175. X.-L. Sheng, B.K. Nikoli´ c, Monolayer of the 5d transition metal trichloride OsCl 3 : A playground for two-dimensional magnetism, room-temperature quantum anomalous hall effect,
and topological phase transitions. Phys. Rev. B 95, 201402 (2017)
176. J. He, X. Li, P. Lyu, P. Nachtigall, Near-room-temperature Chern insulator and Dirac spingapless semiconductor: nickel chloride monolayer. Nanoscale 9, 2246–2252 (2017)
177. M-H. Pan, H. Liu, Z. Wang, J-F. Jia, Q-K. Xue, J-L. Li, S. Qin, U.M. Mirsaidov, X.-R. Wang,
J.T. Markert, Z. Zhang, C.-K. Shih, Quantum growth of magnetic nanoplatelets of Co on Si
with high blocking temperature. Nano Lett. 5(1), 87–90 (2005) PMID: 15792418
178. This work is supported by the NSFC Grants (No. 11974296, 11774296 and 11804045) and
Hong Kong RGC Grants (No. 16301518 and 16301619)
403
157. Y. Su, X.R. Wang, Chiral anomaly of Weyl magnons in stacked honeycomb ferromagnets.
Phys Rev B 96, 104437 (2017)
158. G. Jackeli, G. Khaliullin, Mott insulators in the strong spin-orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009)
159. M. Sato, K. Hasebe, K. Esaki, M. Kohmoto, Time-reversal symmetry in non-hermitian systems. Progress Theor. Phys. 127(6), 937–974 (2012)
160. R.M. White, M. Sparks, I. Ortenburger, Diagonalization of the antiferromagnetic magnonphonon interaction. Phys. Rev. 139, A450–A454 (1965)
161. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic
properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
162. J.E. Avron, R. Seiler, B. Simon, Homotopy and quantization in condensed matter physics.
Phys. Rev. Lett. 51, 51–53 (1983)
163. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The Geometric Phase in
Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and
Condensed Matter Physics (Theoretical and Mathematical Physics. Springer, Berlin Heidelberg, 2013)
164. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Topological semimetal and Fermi-arc
surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)
165. A.A. Burkov, L. Balents, Weyl semimetal in a topological insulator multilayer. Phys. Rev.
Lett. 107, 127205 (2011)
166. S-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z.
Yuan, C-C. Lee, S-M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B. Wang, A. Bansil, F. Chou,
P.P. Shibayev, H. Lin, S. Jia, M. Zahid Hasan, Discovery of a Weyl fermion semimetal and
topological Fermi arcs. Science 349(6248), 613–617 (2015)
167. B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao,
G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, Experimental discovery of Weyl Semimetal
TaAs. Phys. Rev. X 5, 031013 (2015)
168. L. Ling, Z. Wang, D. Ye, L. Ran, F. Liang, J.D. Joannopoulos, M. Soljaˇ ci´ c, Experimental
observation of Weyl points. Science 349(6248), 622–624 (2015)
169. F-Y. Li, Y-D. Li, Y. Baek Kim, L. Balents, Y. Yu, G. Chen, Weyl magnons in breathing
pyrochlore antiferromagnets. Nat. Commun. 7(1), 12691 (2016)
170. A. Mook, J. Henk, I. Mertig, Tunable magnon Weyl points in ferromagnetic pyrochlores.
Phys. Rev. Lett. 117, 157204 (2016)
171. A. Alexey, Soluyanov, Dominik Gresch, Zhijun Wang, QuanSheng Wu, Matthias Troyer, Xi
Dai, and B. Andrei Bernevig. Type-II Weyl semimetals. Nature 527(7579), 495–498 (2015)
172. F. Meier, D. Loss, Magnetization transport and quantized spin conductance. Phys. Rev. Lett.
90, 167204 (2003)
173. J. Sugiyama, K. Mukai, H. Nozaki, M. Harada, M. Månsson, K. Kamazawa, D. Andreica, A.
Amato, A.D. Hillier, Antiferromagnetic spin structure and lithium ion diffusion in Li 2 MnO 3
probed by μ + SR. Phys. Rev. B 87, 024409 (2013)
174. T. Takayama, A. Kato, R. Dinnebier, J. Nuss, H. Kono, L.S.I. Veiga, G. Fabbris, D. Haskel, H.
Takagi, Hyperhoneycomb iridate β-Li 2 IrO 3 as a platform for Kitaev magnetism. Phys. Rev.
Lett. 114, 077202 (2015)
175. X.-L. Sheng, B.K. Nikoli´ c, Monolayer of the 5d transition metal trichloride OsCl 3 : A playground for two-dimensional magnetism, room-temperature quantum anomalous hall effect,
and topological phase transitions. Phys. Rev. B 95, 201402 (2017)
176. J. He, X. Li, P. Lyu, P. Nachtigall, Near-room-temperature Chern insulator and Dirac spingapless semiconductor: nickel chloride monolayer. Nanoscale 9, 2246–2252 (2017)
177. M-H. Pan, H. Liu, Z. Wang, J-F. Jia, Q-K. Xue, J-L. Li, S. Qin, U.M. Mirsaidov, X.-R. Wang,
J.T. Markert, Z. Zhang, C.-K. Shih, Quantum growth of magnetic nanoplatelets of Co on Si
with high blocking temperature. Nano Lett. 5(1), 87–90 (2005) PMID: 15792418
178. This work is supported by the NSFC Grants (No. 11974296, 11774296 and 11804045) and
Hong Kong RGC Grants (No. 16301518 and 16301619)