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 midinfrared (FIR/MIR) band (8--12 \textmu{}m, 0.15--0.1 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 eV) with high optical gain and absorption. In this work, a narrow-gap semiconductor, ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$, is demonstrated to exhibit an optical response >10\ifmmode\times\else\texttimes\fi{} larger than that of ${\mathrm{Hg}}_{x}{\mathrm{Cd}}_{1\ensuremath{-}x}\mathrm{Te}$ (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 ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$ measured using temperature-dependent spectroscopic ellipsometry over a wavelength range 1.7--20 \textmu{}m (0.73--0.062 eV). These measurements demonstrate a large enhancement in extinction coefficient and refractive index, which are 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/MIR range.