Pi-flux as a universal probe of two-dimensional topological insulators

We show that the existence of a Kramers pair of zero-energy modes bound to a vortex carrying $\pi$-flux is a generic feature of topologically nontrivial phases in the $M-B$ model, describing HgTe quantum wells, and therefore this vortex represents the bulk probe of the band topology [1]. We explicitly find the form of the zero-energy states by analytically solving Dirac equation which contains a momentum-dependent Schr\" odinger mass, besides the usual Dirac mass term. A particular regularization of the vortex potential yields the modes exponentially localized and regular at the origin that carry nontrivial charge or spin quantum number. \\[4pt] [1] V. Juricic, A. Mesaros, R.-J. Slager, and J. Zaanen, arXiv:1108.3337.