In this work we consider whether nonsymmorphic symmetries such as a glideplane can protect the existence of topological crystalline insulators andsuperconductors in three dimensions. In analogy to time-reversal symmetricinsulators, we show that the presence of a glide gives rise to a quantizedmagnetoelectric polarizability, which we compute explicitly through theChern-Simons 3-form of the bulk wave functions for a glide symmetric model. Ourapproach provides a measurable property for this insulator and naturallyexplains the connection with mirror symmetry protected insulators and therecently proposed $Z_2$ index for this phase. More generally, we prove that themagnetoelectric polarizability becomes quantized with any orientation-reversingspace group symmetry. We also construct analogous examples of glide protectedtopological crystalline superconductors in classes D and C and discuss how bulkinvariants are related to quantized surface thermal-Hall and spin-Hallresponses.
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