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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 25-29 April 2011, San Francisco, CA Session VV4.2 Room 2020 9:00 AM Tuesday, 26 April 2011 2 2 2

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**Transition Metal Oxides **

“Should be Metals, But Aren’t” (Charge Transfer Insulators, Instead) After Imada, et al, RMP 70, 1039 (1998) 3

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**Direct and Reciprocal Lattices**

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

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**Cubic Rocksalt Divalent TMOs**

TMO 3d Config Properties MnO MH-CTI (5.6) FeO MH-CTI (5.9) CoO MH-CTI (6.3) NiO MH-CTI (6.5) CuO 9 XX Doesn't Exist! Why Not? See Imada, Fujimore, Tokura, RPM 70 (1988) 5

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**Tenorite (Monoclinic CuO)**

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**Can Application of DFT (LDA+U) Help Unravel the Cubic Rocksalt CuO Enigma?**

…Let’s see… DFT & (LDA + U) Implemented in LMTO by Anisimov, et al, JPCM 2, 3973 (1990) Applied to NiO, MnO, FeO, CoO and La2CuO4 Plane-Wave Pseudopotential Implementation by Cococcioni and de Gironcoli, PRB 71, (2005) Applied to FeO and NiO Download open-source package from 7

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**Tools QUANTUM-ESPRESSO Suite of Codes “Dial-in” Parameters Hardware**

DFT (LDA+U) plus electron-phonon Graphics by Tone Kolalj (XCrysDen) “Dial-in” Parameters G2 = 40 Ry ρ = 320 Ry Convergence ≤ 10-6 Ry “Smearing” = Methfessel-Paxton Psuedopotentials: Ultrasoft, XC = Perdew-Zunger Cu: 3d94s2 O: 2s22p4 Hardware 3.33 GHz Intel Core i7 – 12 GB+

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**Rocksalt CuO Band Widths**

Note Degeneracies! 9

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**Rocksalt CuO Fermiology (Combined)**

Note (Near) Degeneracies! Jahn-Teller Unstable? Alex M? 10

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**Non-Magnetic Cubic Rocksalt CuO -- Electron-Phonon Properties --**

α2F(ω) λ ~ 0.6 – 0.7 Other sc’s… TC (K) λ μ* K3C60 16.3 0.51 - Rb3C60 30.5 0.61 Cs3C60 47.4 0.72 σ = 0.04 11 11

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**Proto-TMO AF-II Rocksalt**

[111]

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**Proto-TMO AF-II Rocksalt**

[-1-1-1]

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**Tetragonal Distortion**

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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**“Fermi Liquid” “Dilute Triplon Gas”**

“Whatever!” “SDW” “NEEL” “A-F” “Whatever!” The Great Quantum Conundrum T “Non-Fermi Liquid” ‘Nematic Fermi Fluids’ “Whatever!” g* “QCP” “Insulator” “Conductor” g ρlocal

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**The Colossal Quantum Conundrum**

“Real Metal” “Fermi Liquid” “Funny Metal” “Pseudogap” “Fond AF Memories” “SDW” “NEEL” “A-F” Superconductivity T g g* “QCP” “Insulator” “Conductor” ρlocal CuO Perovskites Fe Pnictides Bechgaard Salts

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n 0.00 +0.15 -0.15 U 3 6

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**The Colossal Quantum Conundrum**

“Real Metal” “Fermi Liquid” “Funny Metal” “Pseudogap” “Fond AF Memories” Superconductivity “SDW” “NEEL” “A-F” T g g* “Insulator” “Conductor” U~U0 exp(-α g), g < g*; 0, g > g* U = 3 U = 6 U = 0 Somewhere in here there has to be “BCS-like” pairing!

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**Shakes or Spins or Both? …just another Conundrum?**

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

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**Generalized Linhard Function**

HO (1989)

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**Dielectric Response Function**

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

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**Other CuO Proxy Structures**

- Studies in Progress -

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**2 CuO segments per quadrant**

Films & Tubes 5.226 Å 2.00 Å 2 CuO segments per quadrant 16 Å between tubes a = b = Å c = 6 x = Å

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Films & Tubes Zones

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Films & Tubes States Landauer – Buettiger?

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**3D phase diagram of overdoped La2-xCexCuO4 with 0.15 ≤ x ≤ 0.19.**

Shakes & Spins Copacetic, Competitive or Conundrum? That is the question…anon 3D phase diagram of overdoped La2-xCexCuO4 with 0.15 ≤ x ≤ 0.19. 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! 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…

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**“Real Metal” “Fermi Liquid”**

“Superconductivity” “Real Metal” “Fermi Liquid”

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

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Hubbard (eV) “Doping” (-e/CuO) U = 3 n = n = n =

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

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