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Setup
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China/US Joint Winter School &3rd China/US Workshop on Novel Superconductors
19 – 27 January 2013
University of Hong Kong
A Density-Functional Study of the Electronic and Magnetic Properties of Tetragonal Copper Monoxide as
a Proxy for High Temperature Superconductivity
Paul M. GrantW2AGZ Technologies
www.w2agz.com
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“China/US Joint...”~ 10,000 years ~ 1,000 years
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Zhu Jingwu
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Yao Ming
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Now Let’s Get Started!
Tools
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Bob Laughlin’s “Theory of Everything” (that matters)
Where’s spin, Pauli and Darwin? Ya screwed up,
Bob!Oh yeah, how about
Maxwell, Boltzmann, Gibbs, Fermi,…and finally,
Newton’s Apple.
The crunch comes when I with i >= 3 -> “thermodynamic limit.” “Van Vleck Catastrophe (1936)”
“Size Matters !”B-
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Extended Hubbard Hamiltonian
†
, , ,2ij i j i jsi iij i ij s
VH t c c U n n n n
Qualitative Description of the Physical Properties of Antiferromagnetic Insulators
One-electron “band” term
On-site “Hubbard” double occupation coulomb repulsion
Off-site repulsion
2 24 /NkT t S UMore Later!
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Charge Transfer Insulator
After Imada, et al, RMP 70, 1039 (1998)
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Density Functional TheoryHohenberg – Kohn (NP Chemistry, 1998)
Kohn-Sham Equations (~1965)
Now minimize self-consistently:
obtaining:
where:
W. Kohn
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DFT & (LDA + U)
Implemented in LMTO by Anisimov, et al, JPCM 2, 3973 (1990)o Applied to rock salt NiO, MnO, FeO, CoO
Plane-Wave Pseudopotential Implementation by Cococcioni and de Gironcoli, PRB 71, 035105 (2005)o Applied to rock salt FeO and NiO
But where is rock salt copper monoxide, CuO?
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Copper Monoxide
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Néel Temperature vs. TMO Atomic Number
“Tenorite”~225 K
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Tenorite (Monoclinic CuO)
Cu
O
What God wants…just ask her!
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Comparison of Tenorite (111) to CuO – MgO Proxy (100)
(111) Tenorite (100) MgO
O
Cu
O
Cu
Cu
O
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Anthologies (CuO rs/tet fsc)• Experimental
– Siemons:• “Tetragonal CuO: End Member of the 3d Transition Monoxides,” Siemons, et al., PRB 79,
195122 (2009).
• Computational– Grant:
• “Electronic Properties of Rocksalt Copper Monoxide: A Proxy Structure for High Temperature Superconductivity,” Grant, JOP:CS 129, 012042 (2008).
– Franchini:• “Hybrid Density-Functional Calculations of the Electronic and Magnetic Structure of Tetragonal
CuO,” Chen, et al., PRB 80, 094527 (2009).• “Thickness Dependent Structural and Electronic Properties of CuO Grown on SrTiO3(100): A
Hybrid Density Functional Theory Study,” Francini, et al., JOP:CM 23, 045004 (2011).
– Cococcioni:• “First Principles Study of Electronic and Structural Properties of CuO,” Himmetoglu, et al.,
arXiv:1107:4399v1 (2011).(This is a great paper...see Acknowledgements...and estimate of TN)
• What’s Next?:– Geballe:
• “Optimal TC of Cuprates: The Role of Screening and Reservoir Layers,” Raghu, et al., PRB 86, 094506 (2012).
(I suspect this model/assertion may be “DFT testable”)
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3d9
Cu2+ Ion Cubic Tetragonal
t2g
eg
Cu2+ 3d Multiplet Splitting (Tetra)
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Tetragonal CuO
c/a = 1.36
3.9053.905
5.320
Measurements(Wolter Siemons)
• 2-4 ML epi on STO
• No Fermi Edge
• No Exchange Bias on ferro-SRO (Tc ~ 100-150 K)
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Proto-TMO AF-II Rocksalt Unit Cell
[111]
Applies to:•MnO•FeO •CoO •NiO •CuO ?
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Proto-TMO AF-II Rocksalt
[-1-1-1]
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“Zone-ology” of “nm_Tet-CuO”
Actually, “Tet-CuO” is really “Ortho-fcc CuO” with a = b
oh...btw...the red balls are O
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So...
Let’s “Shut up and start calculating.”- David Mermin, Cornell, as quoted by yours truly,
(Nature 4 August 2011)
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Tools
QUANTUM-ESPRESSO Suite of CodesDFT (LDA+U) plus electron-phononGraphics by Tone Kolalj (XCrysDen)www.quantum-espresso.org
“Dial-in” Parameters G2 = 40 Ry ρ = 320 RyConvergence ≤ 10-6 Ry“Smearing” = Methfessel-PaxtonPsuedopotentials: Ultrasoft, XC = Perdew-Zunger
Cu: 3d94s2 O: 2s22p4
Hardware 3.33 GHz Intel Core i7 – 12 GB+
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First EffortsTMO Asymmetric Type II
af-CuO Cell
LDA+U Calcs
Grant, IOP-CS 129 (2008) 102042(Click Here)
Tetragonal Distortion
Siemons, et al, PRB 79 (2009)
195122(Click Here)
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Néel Temperature vs. TMO Atomic Number
“Tenorite”~225 K
“Face-Centered, Rock
Salt CuO”~850 K (wow!)
See Francini, Cococcioni Papers
jiij
BN J
k
SST
3
)1(2
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n
U
0
3
6
0.00 +0.15 -0.15
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“Real Metal”“Fermi Liquid”
“Fu
nn
y Metal”
“Pseu
do
gap
”
“Fo
nd
AF
Mem
ories”
Superconductivity
“SDW”“NEEL”“A-F”
T
gg*“Insulator” “Conductor”“F
un
ny M
etal”
“Pseu
do
gap
”
“Fo
nd
AF
Mem
ories”
The Colossal Quantum Conundrum
U~U0 {1 - (g/g*)2}1/2
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?
• Original Strong Coupling, Eliashberg (JETP, 1960), McMillan (PR, 1968)
• Generalized Linhard Response Function (RPA + fluctuations) Hu and O’Connell (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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McMillan Strong Coupling(Computationally implemented by Wierzbowska, et al., cond-mat/0504077, 2006)
What’s the HTSC
equivalent?
Well!What do I “move?”
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Phonons?(Ask Alex M.)
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Bednorz-Mueller Nobel Lecture
After Chakravarty, (1979)
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Macfarlane, Rosen, Seki, SSC 63, 831 (1987)
Raman Spectroscopy of YBCO
Indeed, they’re there!
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Pyka, et al., PRL 70, 1457, (1993)
Harashima, et al., Physica C263, 257 (1996)
More Evidence
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Ledbetter, Physica C 235, 1325 (1994)
Finally, TC scales (roughly) with D
Nota Bene!
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The Grand(t) Summary: (EM, D ≈ 440 K, * ≈ 0.05)
Note Differences in Tc Scale
(“double-delta) smoothing (“double-delta) smoothing
(“double-delta) smoothing
Tc (K)Tc (K)
Tc (K)
“Tet c/a = 1.36”q = 0.15 holes per CuO
“Cubic”q = 0
“Tet c/a = 1.36”q = 0.15 electrons per CuO
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Doping per CuO (units of (e)
Tc (K)
Conclusions
• Phonons can yield “credible” values of Tc in the cuprates
• Holes are better than electrons
• Can’t account for higher Tc’s in “1-2-3 +” layered compounds (Yet...check out Raghu, et al.)
Computers and the Study of Proxy Structures may finally resolve the mystery of High-Tc...a Future NP for
someone in the audience...much younger than me!
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The End
Well...almost...
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PBCO CNT-5,0
“Ba Channel”“RE Channel”
Come See Mein Baltimore!
Possibilities for Observation of Quantum Transport in
(RE)Ba2Cu3O7-y Perovskites
R43.000032:54 PM, Wednesday, 3/20/2013
Hilton Ballroom 2