Thirty years after the discovery of high temperature superconductivity, correlated-electron superconductivity remains an enigma. A necessary condition for superconductivity driven by electron correlations is that electron-electron interactions enhance the superconducting pairpair correlations, relative to the noninteracting limit. No such enhancement has been found to date in any calculation on the weakly doped Mott-Hubbard semiconductor, thought to be a model for the high temperature cuprate superconductors by many scientists. I present a new valence bond theory of electron pairing, that is influenced by Anderson's resonating valence bond theory, and is yet substantively different. The ground state of the quarter-filled band, in the presence of geometric lattice frustration, is a paired-electron crystal, which is a Wigner crystal of spin singlets [1]. With further increase in frustration, the singlets become mobile to give a paired-electron liquid, which is a precursor to true superconductivity. I report high-precision numerical calculations that for the first time show enhancement of pair-pair correlations by electron-electron interactions at or close to quarter-filling, in six different lattices [2,3]. At all other fillings electron-electron interactions suppress pair correlations. Our work provides a key ingredient to the mechanism of superconductivity in organic charge-transfer solids and many other unconventional superconductors with frustrated crystal lattices. The talk does not assume background knowledge on correlated-electron superconductivity; all key concepts are developed within the context of the talk.

[1] S. Dayal, R. T. Clay, H. Li and S. Mazumdar, Phys. Rev. B 83, 245106 (2011).
[2] N. Gomes, W. Wasanthi De Silva, T. Dutta, R. T. Clay and S. Mazumdar, Phys. Rev. B 93, 165110 (2016).
[3] W. Wasanthi De Silva, N. Gomes, S. Mazumdar and R. T. Clay, Phys. Rev. B 93, 205111(2016).

Homepage: http://fp.optics.arizona.edu/Faculty/Resumes/Mazumdar.htm