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  • Topological Surface States in Three-Dimensional Magnetic . . .
    This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model
  • [0804. 4527] Topological surface states in three-dimensional . . .
    This paper gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model
  • Topological surface States in three-dimensional magnetic . . .
    This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model
  • [0804. 4527] Topological surface states in three-dimensional . . .
    We give an explicit cubic-lattice model with a nontrivial three-dimensional topological invariant (the Hopf invariant in momentum space) and extended surface states and discuss in closing which materials might realize the “Hopf insulator” phase
  • arXiv:0804. 4527v2 [cond-mat. mes-hall] 18 Nov 2008
    a speci c model of a Hopf insulator, we review brie y the basic ideas of Chern number and the Hopf invariant and give an algorithm to compute the Hopf invariant for any two-band model
  • Physical Review Journals
    @article{PhysRevLett 101 186805, title = {Topological Surface States in Three-Dimensional Magnetic Insulators}, author = {Moore, Joel E and Ran, Ying and Wen, Xiao-Gang}, journal = {Phys Rev Lett }, volume = {101}, issue = {18}, pages = {186805}, numpages = {4}, year = {2008}, month = {Oct}, publisher = {American Physical Society},
  • Topological Surface States in Three-Dimensional Magnetic . . .
    Another topological insulator which exists beyond the ten-fold classification is the Hopf insulator, first investigated in static 3D magnetic topological insulator with two energy bands





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