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A DFT (LDA+U) Study of the Electronic Properties of Square-Planar Coordinated Copper Monoxide Structures Paul M. Grant IBM Research Staff Member, Emeritus Aging IBM Pensioner Financial Support From: IBM Retiree Pension Fund Prior to 1990 MRS Spring Meeting Moscone (West) Convention Center April 2011, San Francisco, CA Session VV4.2 Room :00 AM Tuesday, 26 April 2011

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Transition Metal Oxides Should be Metals, But Arent (Charge Transfer Insulators, Instead) After Imada, et al, RMP 70, 1039 (1998)

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TM O Cubic Rocksalt TMO a = b = c Cubic Rocksalt TMOs Direct and Reciprocal Lattices

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Cubic Rocksalt Divalent TMOs TMO3d Config Properties MnO 5 MH-CTI (5.6) FeO6 MH-CTI (5.9) CoO7 MH-CTI (6.3) NiO8 MH-CTI (6.5) CuO9 XX Doesn't Exist! See Imada, Fujimore, Tokura, RPM 70 (1988) Why Not?

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Tenorite (Monoclinic CuO) Cu O

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DFT & (LDA + U) Implemented in LMTO by Anisimov, et al, JPCM 2, 3973 (1990) Applied to NiO, MnO, FeO, CoO and La 2 CuO 4 Plane-Wave Pseudopotential Implementation by Cococcioni and de Gironcoli, PRB 71, (2005) Applied to FeO and NiO Download open-source package from Can Application of DFT (LDA+U) Help Unravel the Cubic Rocksalt CuO Enigma? …Lets see…

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Tools QUANTUM-ESPRESSO Suite of Codes DFT (LDA+U) plus electron-phonon Graphics by Tone Kolalj (XCrysDen) Dial-in Parameters G 2 = 40 Ryρ = 320 Ry Convergence Ry Smearing = Methfessel-Paxton Psuedopotentials: Ultrasoft, XC = Perdew-Zunger Cu: 3d 9 4s 2 O: 2s 2 2p 4 Hardware 3.33 GHz Intel Core i7 – 12 GB+

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Rocksalt CuO Band Widths Note Degeneracies!

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Rocksalt CuO Fermiology (Combined) Note (Near) Degeneracies! Jahn-Teller Unstable? Alex M?

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Non-Magnetic Cubic Rocksalt CuO -- Electron-Phonon Properties -- λ ~ 0.6 – 0.7 Other scs… α 2 F(ω) σ = 0.04 T C (K) λμ*μ* K 3 C Rb 3 C Cs 3 C

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Proto-TMO AF-II Rocksalt [111]

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Proto-TMO AF-II Rocksalt [ ]

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The Answer(s) ! TMO Asymmetric Type II af-CuO Cell LDA+U Calcs Grant, IOP-CS 129 (2008) Tetragonal Distortion Siemons, et al, PRB 79 (2009)

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References Electronic Properties of Rocksalt Copper Monoxide, APS MAR , P. M. Grant, Pittsburgh (2009)

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Non-Fermi Liquid Nematic Fermi Fluids Whatever! Fermi Liquid Dilute Triplon Gas Whatever! SDW NEEL A-F Whatever! T g g* QCP InsulatorConductor ρ local The Great Quantum Conundrum

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Real Metal Fermi Liquid Funny Metal Pseudogap Fond AF Memories SDW NEEL A-F Superconductivity T g g* QCP InsulatorConductor ρ local Funny Metal Pseudogap Fond AF Memories The Colossal Quantum Conundrum CuO Perovskites Fe Pnictides Bechgaard Salts

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n U

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Real Metal Fermi Liquid Funny Metal Pseudogap Fond AF Memories Superconductivity SDW NEEL A-F T g g* InsulatorConductor Funny Metal Pseudogap Fond AF Memories The Colossal Quantum Conundrum U~U 0 exp(-α g ), g g* Somewhere in here there has to be BCS-like pairing! U = 6 U = 0 U = 3

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Shakes or Spins or Both? Are They Copacetic, Competitive…or… …just another Conundrum? What formalism is the HTSC analogy to Migdal-Eliashberg-McMillan? Generalized Linhard Response Function (RPA + fluctuations) Hu and OConnell (PRB 1989) Dielectric Response Function Kirznits, Maximov, Khomskii (JLTP 1972) (In other words, how do I calculate the value of the BCS gap?)

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Generalized Linhard Function HO (1989)

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Dielectric Response Function KMK (1972) In principle, KMK can calculate the BCS gap for general bosonic fields, be they phonons, magnons, spin-ons, excitons, plasmons…or morons!

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Other CuO Proxy Structures - Studies in Progress -

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Films & Tubes a = b = Å c = 6 x = Å Å 2.00 Å 2 CuO segments per quadrant 16 Å between tubes

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Films & Tubes Zones

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Films & Tubes States Landauer – Buettiger?

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Shakes & Spins Copacetic, Competitive or Conundrum? That is the question…anon 3D phase diagram of overdoped La2-xCexCuO4 with 0.15 x Pairing associated with quantum critical energy scales in superconducting electron-doped cuprates K. Jin, N. P. Butch, K. Kirshenbaum, J. Paglione, and R. L. Greene* -submitted to Nature- *will answer all questions… Bottom Line: Can studying CuO proxies with DFT + LDA+U + phonons provide the answer? I say Yes, but… Size Matters… …and I need a… BIGGER COMPUTER!

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Superconductivity Real Metal Fermi Liquid

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U = 0n = 0.00 n = n = Hubbard (eV)Doping (-e/CuO)

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U = 3n = 0.00 Hubbard (eV)Doping (-e/CuO) n = n = -0.15

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U = 6n = 0.00 n = n = Hubbard (eV)Doping (-e/CuO)

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