Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling

We show that the spin-Hall conductivity in insulators is related to a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin-Hall effect. As a result, we theoretically predict that two-dimensional bismuth will show the quantum spin-Hall effect, both by calculating the helical edge states, and by showing the nontriviality of the $Z_2$ topological number, and propose possible experiments.