Interband response in spin-orbit coupled topological semimetals

Abstract

This study investigates the interband conductivity for nodal line semimetals (NLSMs) in the presence of spin-orbit coupling (SOC) beyond the clean limit, where the disorder reshapes the transport properties. The SOC breaks spin degeneracy, thus fundamentally altering the band dispersion and enabling multiple interband transport channels. Using a quantum kinetic framework, we analyze the interband conductivity originating from disorder-driven (extrinsic) and field-driven (intrinsic) mechanisms. We find that the interband response shows an anisotropic nature due to disorder driven counter parts. Additionally, our predictions show a tunable prominent transition peak arising from non-Pauli-blocked states that can be controlled via band parameters as well as external stimuli. To have an experimental relevance, we provide a numerical estimation for the interband response of TaAs using density functional theory estimated parameters. These results suggest the investigation of disorder-enabled signatures in spin systems.

Figures (4)

• Figure 1: Depicts the two-dimensional (2D) band dispersion of a nodal line semimetal with spin-orbit coupling (SOC) in the regime $k_0>m'$. SOC lifts the spin degeneracy, leading to spin-split bands. The dotted line indicates the chemical potential, and the shaded green region denotes the SOC-induced gap. Here, $k_0$ represents the nodal ring radius, $m'$ is the parameter associated with the SOC-related term. Dispersion is plotted at $\tilde{k}_y=0, \tilde{k}_z= 0.1$, band index $n=\pm1$ and spin index $\beta=\pm 1$.
• Figure 2: Shows the three-dimensional (3D) band dispersion of the NLSM with and without SOC. (a): dispersion without the SOC case, where the nodal ring is symmetry-protected. (b)-(d): depict the evolution of the 3D band structure in the presence of SOC for different regimes of the parameters $k_0$ and $m'$. (b): $k_0>m'$ the system shows a Weyl-like behavior characterized by a pair of Weyl nodes. In the regimes $k_0=m'$ and $k_0<m'$, shown in panels (c) and (d), the Weyl nodes annihilate, and the system becomes gapped. Here, $\tilde{k}_y=0$, $n$ and $\beta$$=\pm 1$.
• Figure 3: (a) and (b) illustrate the real part (solid line) and the imaginary part (dotted line) of the normalized intrinsic $\tilde{\sigma}_{zz}^{\text{Int}}=\sigma_{zz}^{\text{Int}}/\sigma_0$ and extrinsic $\tilde{\sigma}_{zz}^{\text{Ext}}=\sigma_{zz}^{\text{Ext}}/\sigma_0$ interband components, respectively, as a function of the normalized frequency ($\tilde{\omega}$). Here, $\sigma_0=e^2/\hbar(2\pi)^2$. The results are plotted for distinct limits of nodal ring radius $k_0$ and term $m'$ associated with the SOC. The inset in panel (b) shows the variation of extrinsic contribution in the complete range of frequency $\tilde{\omega}=0$ to $4$. All plots are obtained using Eq. \ref{['eqn:total_zz']} and the model Hamiltonian for NLSM with TaAs material parameters and keeping the chemical potential $\tilde{\mu}=1.5$.
• Figure 4: (a) shows the real part (solid line) and imaginary part (dotted line) of the total interband part of longitudinal conductivity due to the field along $z$ direction $\tilde{\sigma}_{zz}^{\text{Inter}}=\sigma_{zz}^{\text{Inter}}/\sigma_0$ where $\sigma_0=e^2/\hbar(2\pi)^2$ as a function of frequency ($\tilde{\omega}$) at distinct values of chemical potential ($\tilde{\mu}$), (b) depicts the comparison of different components of the total interband longitudinal response at fixed $\tilde{\mu}=1.5$. These results are obtained from Eq. \ref{['eqn:total_zz']} by using the model Hamiltonian with the DFT parameters relevant for TaAs. Further, we fixed parameter values as $k_0$ = 0.12$\AA^{-1}$ and $m'$ = 0.01$\AA^{-1}$.