Optical Response of 3D Model Topological Nodal-line Semimetal

Abstract

Topological nodal-line semimetals (TNLSM) have attracted significant attention in nanotechnology research due to their novel electronic and optical phenomena. In this work, we present a semi-analytical expression for both longitudinal and transverse optical conductivities of a model TNLSM employing the Kubo formula with emphasis on the optical spectral weight redistribution, deduced from appropriate Green's functions. We considered a simple model of a three-dimensional (3D) TNLSM consisting of a slab containing several nanosheets of single atoms along the $z$ axis. In this semimetal, the conduction and valence bands cross each other along a one-dimensional curve in the 3D Brillouin zone and any perturbation that preserves a certain symmetry group cannot remove this crossing line and open a full direct gap between the two bands. Although the crossing is stable against perturbations, it can be adjusted by continuous tuning of the Hamiltonian with a parameter $\alpha$. When $\alpha>0$, the two bands cross each other near the $\Gamma$ point in the ($k_x, k_y$) plane of the first Brillouin zone making a nodal circle of radius $\sqrt{\alpha}$. The circle shrinks to point when $\alpha=0$ and for $\alpha<0$, the nodal circle vanishes and a gap opens around $\Gamma$. Numerical results for the longitudinal optical response of such TNLSM are investigated by varying the gap due to modifying $\alpha$, the chemical potential $\mu$, temperature $T$ and the dephasing parameter $\eta$. The longitudinal optical conductivity is anisotropic along the direction parallel or perpendicular to the nodal ring due to anisotropic energy band dispersion along the ($k_x, k_y$) plane and the $k_z$ direction. Additionally, the transverse optical conductivity vanishes due to rotational symmetry.