Skyrmion Phase and Non-Fermi Liquid Behavior in Nonsymmorphic Magnetic Weyl Semimetals

Abstract

We investigate the interplay between complex magnetic orders and topological electronic states in nonsymmorphic magnetic Weyl semimetals of the ReAlX family (Re is a rare earth element and X is Si or Ge). We show that a Skyrmion lattice can fundamentally alter the behavior of Weyl fermions, driving the system into a non-Fermi liquid state and producing large, sign-tunable Hall responses. To this end, we construct a lattice model incorporating conduction Weyl fermions coupled to localized magnetic moments via Kondo interaction. Considering a multi-$\mathbf{Q}$ cycloid magnetic configuration that evolves into a Skyrmion lattice under an in-plane Zeeman field, we analyze its profound impact on the band structure through magnetic Brillouin zone and band-folding. Using the Kubo formula, we calculate the conductivity tensor and examine the transport properties in the clean limit. Our results reveal that the Skyrmion lattice induces significant changes in both longitudinal and Hall conductivities. Remarkably, the temperature-dependent resistivity deviates from standard Fermi-liquid behavior ($\ddot{I}{}_{xx}\sim T^2$), exhibiting a non-Fermi liquid power-law scaling ($\ddot{I}{}_{xx}\sim T^{\hat{I}}\pm$ with $\hat{I}\pm$ between 3 and 5). This work provides a unified theoretical framework connecting multi-$\mathbf{Q}$ magnetic textures, Skyrmion physics, and anomalous transport in topological semimetals, bridging the fields of topological magnetism and topological fermions.

8 pages, 6 figures