Figure 1

The energy dispersions of the lattice Hamiltonian for k_z = 0 with parameters k₀ = \(\frac{\pi }{4}\) and δ = 2, for different values of the ratio r = \(\frac{{t}_{2}}{{t}_{1}}\). (a) Type-I WSM with t₂ = 0.009t and t₁ = t, (b) type-II WSM with t₂ = 0.3t and t₁ = t. Cuts through the Weyl points at k_z = 0 and k_y = \(\frac{\pi }{4}\) (c) for type-I and (d) for type-II WSM using the same parameter values as in (a,b). When r is less than the critical value (r_c), two non-degenerate bands meet at four type-I Weyl points. As r increases, the WPs start to tilt in the x-direction. When r is above r_c = 0.01, the Weyl nodes tilt further and two pairs of type-II WPs are observed. The green dots indicate WPs. Thus by tuning the ratio r, one can go from a type-I to a type-II model.