We review the remarkable properties, including superconductivity, charge-densitywave ordering, and metal-insulator transitions, of lead-and potassium-doped barium bismuthate. We discuss some of the early theoretical studies of these systems. Our recent theoretical work, on the negative-U, extended-Hubbard model for these systems, is also described. Both the large-and intermediate-U regimes of this model are examined, using mean-field and random-phase approximations, particularly with a view to fitting various experimental properties of these bismuthates. On the basis of our studies, we point out possibilities for exotic physics in these systems. We also emphasize the different consequences of electronic and phonon-mediated mechanisms for the negative U. We show that, for an electronic mechanism, the semiconducting phases of these bismuthates must be unique, with their transport properties dominated by charge ±2e Cooperon bound states. This can explain the observed difference between the optical and transport gaps.We propose other experimental tests for this novel mechanism of charge transport and comment on the effects of disorder.PACS numbers: 74.10+v, 74.65+n * Present address: Mehta Research Institute of Mathematics and Mathematical Physics, 10 Kasturba Gandhi Marg, Allahabad-211002, India.† also at Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560012, India.
1The materials BaPb 1−x Bi x O 3 , and Ba 1−x K x BiO 3 , derived from barium bismuthate, BaBiO 3 , have many remarkable properties [1,2,3,4,5,6,7,8,9,10]. These include structural and metal-semiconductor transitions as x and the temperature T are varied; diamagnetic, semiconducting (CDW ordered?) phases even in the presence of a partially filled Bi 6s-O 2p σ antibonding band, with optical and transport gaps (2 eV and 0.24 eV, respectively, at x = 0) differing by nearly an order of magnitude; and superconducting T c 's (13K and 34K, respectively, for Pb and K doping) that are 3−5 times higher than for other three-dimensional oxide systems with similar, low densities of states at the Fermi level. However, partly because of all the attention devoted to the high-T c cuprates, these bismuthates have not been studied extensively, either experimentally or theoretically.We review here the experimental properties of lead-and potassium-doped barium bismuthate, give a summary of some early theoretical studies of these systems, and then provide an overview of our recent theoretical work [9,10], which uses the negative-U, extended-Hubbard model for these systems. The principal goal of our review is to consolidate what is known (experimentally and theoretically) about these remarkable materials.We have organised the review as follows: Section I is devoted to the phenomenology of lead-and potassium-doped barium bismuthate. Section II is devoted to a survey of the models that have been put forth for these systems and to some of the early theoretical work on them. Sections III and IV are devoted to our work on these systems based on the neg...