Qi Yang, Fu Liang
Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China.
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Phys Rev Lett. 2015 Dec 4;115(23):236801. doi: 10.1103/PhysRevLett.115.236801. Epub 2015 Dec 2.
The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number n=4, its surface can be gapped out by an anomalous Z_{2} topological order, where all anyons carry mirror-symmetry fractionalization M^{2}=-1. The identification of such anomalous crystalline symmetry fractionalization implies that in a two-dimensional Z_{2} spin liquid, the vison excitation cannot carry M^{2}=-1 if the spinon carries M^{2}=-1 or a half-integer spin.
三维拓扑电子系统的表面通常存在对称性保护的无隙表面态。在电子相互作用的影响下，这些表面态可以在不破坏对称性的情况下被一种表面拓扑序打开能隙，其中任意子激发携带反常对称性分数化，这在真正的二维系统中无法实现。我们表明，对于具有镜陈数(n = 4)的镜面对称性保护的拓扑晶体绝缘体，其表面可以被一种反常(Z_{2})拓扑序打开能隙，其中所有任意子都携带镜面对称性分数化(M^{2} = -1)。这种反常晶体对称性分数化的确定意味着，在二维(Z_{2})自旋液体中，如果自旋子携带(M^{2} = -1)或半整数自旋，则vison激发不能携带(M^{2} = -1)。
