Symmetry Protected Topological Hopf Insulator and its Generalizations

R. H. Fox, Annals of Mathematics 49

1948

Earlier work this paper cites.

F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, 1990)

1990

Earlier work this paper cites.

S.-C. Zhang and J. Hu, Science 294

2001

Earlier work this paper cites.

A. Hatcher, Algebraic Topology (Cambridge University Press, 2002)

2002

Earlier work this paper cites.

J. E. Moore, Y. Ran, and X.-G. Wen, Phys. Rev. Lett. 101

2008

Earlier work this paper cites.

A. Kitaev, AIP Conf. Proc 1134

2009

Earlier work this paper cites.

A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, AIP Conf. Proc. 1134

2009

Cited alongside, same era.

S. Ryu, A. Schnyder, A. Furusaki, and A. Ludwig, New J. Phys. 12

2010

Cited alongside, same era.

J. C. Y. Teo and C. L. Kane, Phys. Rev. B 82

2010

Cited alongside, same era.

T. L. Hughes, E. Prodan, and B. A. Bernevig, Phys. Rev. B 83

2011

Cited alongside, same era.

X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83

2011

Cited alongside, same era.

In our convention, the rank of Sp( OPEN 2 ​ N ) 2N) is N N

Cited in the paper.

At this point, if we impose 𝒯 ′ = 𝒯 × ℐ \mathcal{T}^{\prime}=\mathcal{T}\times\mathcal{I} symmetry, where 𝒯 \mathcal{T} is time-reversal such that 𝒯 2 = − 1 \mathcal{T}^{2}=-1 , then it can be shown that the configuration space is reduced from Sp( 4 ​ N 4N )/U( 2 ​ N 2N ) to Sp ( 2 ​ N ) (2N) , and Σ ​ f \Sigma f is nontrivial element of π 4 ​ [ Sp ​ ( 2 ​ N ) ] = ℤ 2 \pi_{4}[\text{Sp}(2N)]=\mathbb{Z}_{2} in the case N = 1 N=1

Cited in the paper.

D.-L. Deng, S.-T. Wang, C. Shen, and L.-M. Duan, Phys. Rev. B 88

2013

Later among the works it cites.

Y.-Z. You and C. Xu, Phys. Rev. B 90

2014

Later among the works it cites.

Y.-M. Lu and D.-H. Lee, arXiv:1403.5558 (2014)

Original

2014

Later among the works it cites.

D.-L. Deng, Ph.D. thesis, University of Michigan (2015)

2015

Later among the works it cites.

Z. Wang, D. Gresch, A. A. Soluyanov, W. Xie, S. Kushwaha, X. Dai, M. Troyer, R. J. Cava, and B. A. Bernevig, Phys. Rev. Lett. 117

2016

Closest in time.