Zeeman-splitting-induced topological nodal structure and anomalous Hall conductivity in ZrTe5

We investigate the topological nodal structure of three-dimensional (3D) ZrTe5 driven by Zeeman splitting as a function of the direction of external magnetic (B) field by using a Wannier-function-based tight-binding (WFTB) model obtained from first-principles calculations. It is known that small external stimuli can drive 3D ZrTe5 into different topological phases including Dirac semimetal. In order to emphasize the effect of Zeeman splitting, we consider 3D ZrTe5 in a strong topological insulator phase with a small band gap. With Zeeman splitting greater than the band gap, the WFTB model suggests that a type-I nodal ring protected by (glide) mirror symmetry is formed when the B field aligns with the crystal a or b axes, and that a pair of type-I Weyl nodes are formed otherwise, when conduction and valence bands touch. We show that a pair of separate Weyl nodes can disappear through formation of a nodal ring, rather than requiring two Weyl nodes with opposite chirality to come together. Interestingly, a type-II nodal ring appears from crossings of the top two valence bands when the B field is applied along the c axis. This nodal ring gaps out to form type-II Weyl nodes when the B field rotates in the bc plane. Comparing the WFTB and linearized k·p model, we find inadequacy of the latter at some B field directions. Further, using the WFTB model, we numerically compute the intrinsic anomalous Hall conductivity σac induced by Berry curvature as a function of chemical potential and B field direction. We find that σac increases abruptly when the B field is tilted from the a axis within the ab plane. Our WFTB model also shows significant anomalous Hall conductivity induced by avoided level crossings even in the absence of Weyl nodes.