Phase stability, electronic structures, and superconductivity properties of the BaPb_1−xBi_xO₃ and Ba_1−xK_xBiO₃ perovskites

With extensive first-principles calculations, we investigate the phase stability, electronic structures, and superconductivity properties of the BaPb_1−xBi_xO₃ (BPBO) and Ba_1−xK_xBiO₃ (BKBO) perovskites with the cubic (C), tetragonal (T), and orthorhombic (O) phases. Our calculations show that the tetragonal superconducting phases of both perovskites are metastable. However, the orthorhombic phase of the BPBO perovskite in the superconductivity region is only slightly more stable than the tetragonal phase. The small energy difference between the T and O phases and the discontinuous T-to-O phase transition account for the experimentally observed coexistence of the T and O phases. On the other hand, the BKBO perovskite involves a large energy difference between the T and O phases, which induces a low equilibrium temperature of the discontinuous T-to-O phase transition, in agreement with the experimental observation that the tetragonal BKBO is maintained down to low temperatures. Moreover, the electronic structures of both BPBO and BKBO superconductors show a flat band near the Fermi level, which is favorable for superconductivity. Furthermore, we find that the longer the total length of the flat band segment is, the higher the critical temperature of the BPBO or BKBO perovskite is. This key finding could be generalized straightforwardly to other unconventional superconductors and can be used to design and find optimal composition with maximum T_c for new unconventional superconductors.