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

Abstract

We investigate the interplay between complex magnetic orders and topological electronic states in nonsymmorphic magnetic Weyl semimetals on the ReAlX family (Re is a rare earth element and X is Si or Ge). We construct a lattice model incorporating conduction Weyl fermions coupled to localized magnetic moments via Kondo interaction. By considering a multi-${\bf Q}$ cycloid magnetic configuration, which can evolve 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 electrical and Hall conductivities. Furthermore, the temperature-dependent resistivity deviates from the standard Fermi-liquid behavior ($ρ_{xx}\sim T^2$), showing a power-law scaling ($ρ_{xx}\sim T^α$ with $α$ between 3 and 5), indicative of non-Fermi liquid behavior. This work provides a theoretical framework connecting multi-${\bf Q}$ magnetic textures, Skyrmion physics, and anomalous transport in topological semimetals.

Figures (4)

• Figure 1: (color online) The band structures of $k_z=0$ plane of (a) $H_0$ and (b) $H$. $m_1=m_2=3$, $u_1=v_2=4$, $v_1=u_2=2$, $v_0=1$, $a=b=0$, and $K=0.2$. In (a), the Weyl nodes are located near $(\pm\frac{2\pi}{3},\pm\frac{2\pi}{3},0)$. In (b), there are extra Weyl nodes emerge near the $\Gamma$ point, $(\pm\frac{2\pi}{3},0,0)$, and $(0,\pm\frac{2\pi}{3},0)$ due to the band folding caused by the multi-${\bf Q}$ magnetic order ${\bf M}$ (\ref{['eq3']}).
• Figure 2: (color online) The distributions of (a) the $(M_1,M_2)$ and (b) the $M_3$ components of magnetization ${\bf M}$ in a magnetic unit cell. (c) The density distribution of Skyrmion number $N_s$ in a magnetic unit cell. In (a), (b), and (c), the Kondo coupling $K=0.2$ and the Zeeman strength $\lambda_1=0.1$, $\lambda_2=\lambda_3=0$. (d) The dependence of the Skyrmion number $N_s$ with respect to the in-plane Zeeman field and Kondo coupling in a magnetic unit cell.
• Figure 3: (color online) We plot the conductivity tensor in (a) and (b), and the resistance of THE in (d). The black, red, pink, green, blue, purple lines correspond to $T=5K,10K,15K,20K,25K$ and $30K$ respectively. (c) We plot the fitted $\alpha$ versus $\lambda_x$ with blue square and red triganle stands for the free Hamiltonian (\ref{['eq1']}) and the totle Hamiltonian $H$ with Kondo interaction (\ref{['eq2']}). In all mini-figures, the external in-plane magnetic field is applied along $x$-direction.
• Figure 4: (color online) The scaling behavior of anomalous Hall resistance versus the electric resistance. (a) $\rho_{xy}^A$ vs. $\rho_{xx}$, and (b) $\rho_{xy}^A$ vs. $\rho_{xx}^A$. We choose $\lambda_x=0.1$ in (a) and (b), and the data is obtained from different temperatures. $\rho_{xy}^A$ and $\rho_{xx}^A$ is obtained from the free Hamiltonian $H_0$ (\ref{['eq1']}) while $\rho_{xx}$ is from the total Hamiltonian $H$ (\ref{['eq2']}).