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

Abstract

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-functionbased 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 TI 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 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.

Electric and magnetic fields tuned spin-polarized topological phases in two-dimensional ferromagnetic MnBi$_4$Te$_7$

“…Here, |ψ k are Bloch states over the k space, R is the Bravais lattice vector, and t αβ (R − 0) are the hopping parameters from orbital β at site s β in the home cell at R = 0 to orbital α at site s α in the unit cell located at R. Note that we here ignore the Peierls phase in the hopping parameters t αβ or Landau levels. This approach is reliable and effective for studying the magnetic field induced evolution of topological states [74,75]. Our DFT calculations on the electronic properties indicate that the MnBi 4 Te 7 monolayer possesses a FM groundstate with a saturation magnetic moment of ∼5.00 µ B , which matches well with prior results [34,76].…”

Optical conductivity and resistivity in a four-band model for ZrTe5 from ab initio calculations

“…We adapted the model to the case of a lattice by using the standard substitutions k i → sin(k i ) and topological invariants of the lattice model are (1,000), which are different from those of the DFT bands. This is unsurprising since the band inversion in ZrTe 5 happens away from [8], whereas the model parameters were obtained by fitting close to ; it is a common issue with k • p theory [45,46].…”

Anomalous Hall effect at the Lifshitz transition in ZrTe5

“…In non-magnetic materials, such as ZrTe 5 and Cd 3 As 2 , the AHE is generally attributed to the intrinsic Berry curvature of the electronic bands [14,15]. In a magnetic field, ZrTe 5 has a large Zeeman splitting with Landé gfactor of ∼ 21, which in turns produces a large AHE [11,[16][17][18]. Another distinctive feature of ZrTe 5 is its anomalous resistivity peak at temperature T p (≈ 75 K in our sample), shown in Fig.…”