Energy-band structure ofCd3As2at low temperatures and the dependence of the direct gap on temperature and pressure

Electron-effective-mass values obtained from low-temperature Shubnikov-de Haas, magneto-Seebeck, and Hall measurements on ${\mathrm{Cd}}_3$ ${\mathrm{As}}_2$ have been gathered from the literature. Using Kane's model for an HgTe-type inverted energy-band structure, the dispersion relation for the conduction band has been obtained along with a ${\Gamma }_8-{\Gamma }_6$ energy gap of 0.11 eV. The heavy-hole valence band is split from the conduction band at $\Gamma$ by a residual gap of ∼0.01 eV. There is a second conduction band whose minimum at $\Gamma$ is approximately 0.6 eV above the ${\Gamma }_8$ valence band and perhaps a third one ∼0.4 eV above the latter. Theoretical estimates of the variation of the energy gap at $\Gamma$ as a function of temperature and pressure are obtained. Those are found to be consistent with our band model as well as with our analysis of existing temperature data ($\frac{\partial E_0}{\partial T}\sim 5\times {10}^{-4\mathrm{}}$ eV/K) and pressure data ($\frac{\partial E_0}{\partial P}\sim -2\mathrm{}\times {10}^{-5\mathrm{}}$ eV/bar).