Chirality flip of Weyl nodes and its manifestation in strained ${\mathrm{MoTe}}_2$

Due to their topological charge, or chirality, the Weyl cones present in topological semimetals are considered robust against arbitrary perturbations. One well-understood exception to this robustness is the pairwise creation or annihilation of Weyl cones, which involves the overlap in energy and momentum of two oppositely charged nodes. Here we show that the topological charge can in fact change sign, in a process that involves the merging of not two, but three Weyl nodes. This is facilitated by the presence of rotation and time-reversal symmetries, which constrain the relative positions of Weyl cones in momentum space. We analyze the chirality flip process, showing that transport properties distinguish it from the conventional, double Weyl merging. Moreover, we predict that the chirality flip occurs in ${\mathrm{MoTe}}_2$, where experimentally accessible strain leads to the merging of three Weyl cones close to the Fermi level. Our work sets the stage to further investigate and observe such chirality flipping processes in different topological materials.

Figure 1

Schematic representation of the Weyl node processes. The red (blue) points represent positive (negative) chirality Weyl nodes, the arrows represent their trajectories upon increasing $\alpha$, and the $C_{2}T$-invariant plane is marked in blue. (a) Band structure of Eq. (1) plotted at $k_x=k_y=0$ for three values of $\alpha$. (b) Chirality flip with a three-node process, as occurring in $H_1$. (c) Chirality flip with two-node processes, as happens in the Hamiltonian $H_2$.

Figure 2

Ratio of conductivities in the plane of the three Weyl nodes as a function of the parameter $\alpha$ for different chemical potentials $\mu$. Panel (a) shows the three-node process and (b) shows the two-node process.

Figure 3

(a) Band structure of ${\mathrm{MoTe}}_2$. $W_1^{v,c}$ ($W_2^{v,c}$) is a Weyl node outside (inside) the $k_z=0$ plane, and connects valence and conducting bands. Analogously, $W_1^{v,v}$ and $W_2^{v,v}$ connect the two upper valence bands. Blue (red) corresponds to negative (positive) chirality. (b) Brillouin zone including the Weyl nodes $W_1^{v,v}$ and $W_2^{v,v}$ having positive $k_x,k_y$ coordinates. The $k_z=0$ plane is indicated in blue. (c),(d) Energy and momentum trajectories of $W_1^{v,v}$ and $W_2^{v,v}$ as a function of tensile strain. Green arrows indicate the trajectories upon increasing the tensile strain.