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This paper identifies absorbers for multiple transition solar cells that are implemented with nanostructured heterojunctions [e.g., quantum well solar cells with quasi-Fermi-level variations and quantum dot (QD) intermediate-band solar cells]. In the radiative limit, the solar cells implemented with these absorbers are capable of achieving a conversion efficiency ges50% with a geometric solar concentration of at least 1000times. The technical approach enumerates a set of quantitative design rules and applies the rules to the technologically important III-V semiconductors and their ternary alloys. A novel design rule mandates a negligible valence band discontinuity between the barrier material and confined materials. Another key design rule stipulates that the substrate have a lattice constant in between that of the barrier material and that of the quantum-confined material, which permits strain compensation. Strain compensation, in turn, allows a large number of QD layers to be incorporated into the solar cell because each layer is free of defects. Four candidate materials systems (confined/barrier/substrate) are identified: InP0.85Sb0.15/GaAs/InP, InAs0.40P0.60/GaAs/InP, InAs/GaAs0.88Sb0.12/InP, and InP/GaAs0.70P0.30/GaAs. Resulting from the design features, the candidate systems may also find use in other optoelectronic applications.