Circular Dichroism As A Probe For Topology In 3D Semimetals

Higher-pseudospin fermions associated with multiple band crossings in topological semimetals are condensed-matter analogues of higher-spin fermions in high-energy physics. In this paper, we demonstrate that analyzing the response of a circular drive is an effective way to detect the topology of the lowest-energy Bloch band, as it can be connected to a frequency-dependent probing function $\Gamma^{int}$. This response crucially hinges on the differential excitation rates induced on the filled band, by the left- and right-circular orientations of the drive, because of the geometrical properties of the Bloch bands. Our analytical approximation reveals that $\Gamma^{int}$ is quantized for rotationally-invariant Hamiltonians, when the frequency of the drive is above a critical value, and thus correctly infers the ground state Chern number. We demonstrate this through explicit numerical computations by considering three kinds of semimetals with pseudospin values of 1/2, 1, and 3/2, respectively, and all having linear dispersions. Furthermore, we investigate the effects of tilt and anisotropy on the systems, and find that although tilt does not have any effect on the response, the presence of anisotropy can drastically hamper the quantization. Our scheme thus provides an important methodology for designing future experiments to detect the topology of band structures.