Disorder-induced phase transitions in higher-order Weyl semimetals

We investigate disorder-induced phase transitions in three-dimensional higher-order Weyl semimetals. Using the transfer matrix method to compute the localization length, we map out the global phase diagram. Remarkably, we uncover an emergent intermediate insulating phase separating the higher-order Weyl semimetal and diffusive metal regimes with increasing disorder strength, which is analogous to conventional Weyl semimetals but with a crucial distinction. While the intermediate phase manifests as a higher-order topological insulator in our system, it appears as a three-dimensional Chern insulator (3DCI) in standard Weyl semimetals. The existence of these insulating phases is intimately tied to interorbital disorder correlations: they persist for uncorrelated disorder but vanish when the disorder is magnetically correlated. Additionally, we reveal that the transition between Weyl and higher-order Weyl semimetal phases is mediated either by a 3DCI or by a hybrid Weyl semimetal phase hosting both conventional and higher-order Weyl points, depending crucially on the isotropy of hopping parameters.