We have studied the doping concentration dependence of the thermoelectric (TE) properties for the n- and p-doped CaIn₂P₂ layered Zintl phase at two fixed temperatures: T = 600 and 900 K through first-principles electronic band structure calculations combined with Boltzmann's transport theory within charge-carrier relaxation time and rigid band approximations. The band structure calculated using the Tran-Blaha modified Becke–Johnson potential shows a fundamental indirect energy band gap (E_g) of 1.10 eV that comes from the polyanion (In₂P₂)⁻². CaIn₂P₂ exhibit a mixture of flat and dispersive energy bands in the energy window from $-E_g/2$ to $E_g/2$ eV, which is a required characteristic for high electrical transport coefficients. The computed lattice thermal conductivity for CaIn₂P₂ is equal to $1.34\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 900 K and $0.70\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 1250 K. This relatively low lattice thermal conductivity of CaIn₂P₂ can be mainly attributed to its layered crystalline structure. The highest value of the figure of merit of CaIn₂P₂, viz. ZT = 0.73 (0.71), is obtained for an optimal electron (hole) concentration of $6.0\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$ ( $1.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$) at 900 K.

Magnetic Heusler compounds (MHCs) have recently attracted great attention since these types of material provide novel functionalities in spintronic and magneto-electronic devices. Among the MHCs, some compounds have been predicted to be spin-filter semiconductors [also called magnetic semiconductors (MSs)], spin-gapless semiconductors (SGSs) or half-metals (HMs). In this work, by means of first-principles calculations, it is demonstrated that rare earth-based equiatomic quaternary Heusler (EQH) compounds with the formulaMCoVZ(M= Lu, Y;Z= Si, Ge) are new spin-filter semiconductors with total magnetic moments of 3 µ_B. Furthermore, under uniform strain, there are physical transitions from spin-filter semiconductor (MS) → SGS → HM for EQH compounds with the formula LuCoVZ, and from HM → SGS → MS → SGS → HM for EQH compounds with the formula YCoVZ. Remarkably, for YCoVZEQH compounds there are not only diverse physical transitions, but also different types of spin-gapless feature that can be observed with changing lattice constants. The structural stability of these four EQH compounds is also examined from the points of view of formation energy, cohesive energy and mechanical behaviour. This work is likely to inspire consideration of rare earth-based EQH compounds for application in future spintronic and magneto-electronic devices.