Flux response of topological insulators with rotation symmetries

When threading a π-flux quantum into a topological insulator, the system responds by generating a pair of helical electron modes along the flux tube. In this talk, we show that the classification of π-flux helical modes is Z₂ × Z₂, when the system features an n-fold rotation symmetry with n = 2,4,6. In particular, we find that a flux tube in a rotationally anomalous topological crystalline insulator will trap two pairs of symmetry-protected helical modes with distinct angular momenta. Experimental consequences and application of our theory to designing novel topological superconductivity will also be discussed.