Effect of Spin-Texture Dynamics on Three-Dimensional Orbital Dirac Semimetals

Abstract

We consider the minimal coupling of a Dirac semimetal Hamiltonian to a generic spin-texture in this work. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective corrections to the Dirac dispersion. A full function's worth of freedom is obtained as a result. Choosing different pitch vectors, we show that many forms of novel phenomena arise in such systems. For example, a linear pitch vector leads to the generation of type-I Weyl semimetal -- we observe the anomalous Hall effect and the chiral magnetic effect. The anomalous Hall coefficient requires a non-zero pitch vector whereas the CME is proportional to the exchange coupling. The band structure of the model in the presence of a magnetic field shows a Lifshitz transition. The introduction of a suitable time dependent pitch vector leads to the formation of nodal spheres in the Sambe space of effective Hamiltonians. This nodal sphere is robust to all orders in van-Vleck perturbation theory as proven explicitly.

Figures (4)

• Figure 1: Schematic illustrating the signatures of the CME and AHE in an effective Weyl spectrum originating from a 3D orbital Dirac semimetal under spin-texture dynamics.
• Figure 2: Full energy spectrum from Eq. (\ref{['Eq8']}) for an inversion-asymmetric Weyl spectrum in the $k_x$–$k_y$ plane with $J_{ex}=1$, $g_x=g_y=\pi/2$, $k_z=0$, and $v_F=1$.
• Figure 3: Landau-quantized band structure as a function of the longitudinal momentum $k_z$ for several Landau indices $n$. Each Landau level splits into four branches due to exchange hybridization, labeled by $(s,\delta)$. While higher-index subbands exhibit a conventional single-minimum dispersion with a band edge at $k_z=0$, the lower hybridized branch develops a double-minimum structure with degenerate band minima at finite $\pm k_z^\ast$. Parameters used are $J_{ex}=3$, $g=1$, $s=+1$, $\delta=-1$, $l_B=1$ and $\hbar=v_F=1$.
• Figure 4: The Floquet bulk spectrum of a nodal-ring semimetal for $\lambda=\pm 1$ in the $k_x$–$k_z$ plane is shown, resulting from coupled temporal and spatial spin-texture dynamics in a three-dimensional orbital Dirac semimetal. Parameters used are $J_{ex}=0.5$, $g_x=g_y=2.5$, $k_y=0$, $\omega=1$, and $v_F=1$.