Topological insulator with negative spin-orbit coupling

Based on the first-principles calculations, we reveal that TlN, a simple binary compound with Wurtzite structure, is a three-dimensional (3D) topological insulator (TI) with effectively negative spin-orbit coupling $\lambda_{eff} < 0$, which makes it distinguished from other TIs by showing opposite spin-momentum locking effect in its surface states. The sign of $\lambda_{eff}$ depends on the hybridization between N-$2p$ and Tl-$5d$ states, and can be tuned from negative to positive by lattice strain or chemical substitution, which drive the system into a Dirac semimetal with 3D Dirac cones in its bulk states. Such topological phase transition can be realized by electronic mechanism without breaking any crystal symmetry.