title: Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators.
abstract: 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.
authors.affiliation: Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Yang
authors.initials: Y
authors.lastname: Qi
authors.affiliation: Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Liang
authors.initials: L
authors.lastname: Fu