Strong Long-Wave Infrared Optical Response in a Topological Semiconductor with a Mexican Hat Band Structure

Light sources and photodetectors operating in the far- to mid-infrared (FIR/MIR) band ($8$-$12~\rm \mu m$, $0.1$-$0.15~\rm eV$) remain relatively poorly developed compared to their counterparts operating in the visible and near-infrared ranges, despite extensive application potential for thermal imaging, standoff sensing, and other technologies. This is attributable in part to the lack of narrow-gap materials ($<0.1~\rm eV$) with high optical gain and absorption. In this work, a narrow-gap semiconductor, $\rm Pb_{0.7}Sn_{0.3}Se$, is demonstrated to exhibit an optical response $>10\times$ larger than that of $\rm Hg_{x}Cd_{1-x}Te$ (MCT), the dominant material for FIR/MIR photodetectors. A previous theoretical investigation indicated that chalcogen $p$ and metal $d$ band inversion in this material creates a Mexican hat band structure (MHBS), which results in a dramatic increase in the joint density of states at the optical transition edge compared to typical semiconductors. This prediction is experimentally validated here using single-crystal specimens of $\rm Pb_{0.7}Sn_{0.3}Se$ measured using temperature-dependent spectroscopic ellipsometry over a wavelength range of $1.7$-$20~\rm \mu m$ ($0.73$-$0.062~\rm eV$). These measurements demonstrate a large enhancement in extinction coefficient and refractive index characteristic of a MHBS in the vicinity of the absorption edge, in agreement with theoretical predictions. The realization of topological semiconductors with a MHBS is expected to lead to high-efficiency detectors operating in the FIR/MID range.