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  1. We report studies of the correlated excited states of coronene and substituted coronene within the Pariser–Parr–Pople (PPP) correlated π-electron model employing the symmetry-adapteddensity matrix renormalization group technique. These polynuclear aromatic hydrocarbons can be considered as graphene nanoflakes. We review their electronic structures utilizing a new symmetry adaptation scheme that exploits electron-hole symmetry, spin-inversion symmetry, and end-to-endinterchange symmetry. The study of the electronic structures sheds light on the electron correlation effects in these finite-size graphene analogues, which diminishes going from one-dimensional tohigher-dimensional systems, yet is significant within these finite graphene derivatives. 
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  2. We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity Cu2+ -> Cu1+ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the T' compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and BaBiO3. The unusually high ionization energy of the closed shell Cu1+ ion, taken together with the dopingdriven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small d-p electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive O2- ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell Cu1+ ions, in the doped state. The model thus gives microscopic justification for the two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional T' crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of O1- -Cu l(1+)-O1- spin singlets that coexists with broken rotational C-4 symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit twodimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and ihid. 93, 205111 (2016)]. We posit that a similar valence transition, Ir4+ -> Ir3+, occurs upon electron doping Sr2IrO4. We make testable experimental predictions in cuprates including superoxygenated La2CuO4+delta and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable. 
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  3. The nature and extent of the spin-entanglement in the triplet-triplet biexciton with total spin zero in correlated-electron π-conjugated systems continues to be an enigma. Differences in the ultrafast transient absorption spectra of free triplets versus the triplet-triplet can give a measure of the entanglement. This, however, requires theoretical understandings of transient absorptions from the optical spin-singlet, the lowest spin-triplet exciton, as well as from the triplet-triplet state, whose spectra are often overlapping and hence difficult to distinguish. We present a many-electron theory of the electronic structure of the triplet-triplet, and of complete wavelength-dependent excited state absorptions (ESAs) from all three states in a heteroacene dimer of interest in the field of intramolecular singlet fission. The theory allows direct comparisons of ESAs with existing experiments as well as experimental predictions, and gives physical understandings of transient absorptions within a pictorial exciton basis that can be carried over to other experimental systems. 
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