Supraconductivité avec et sans point critique quantique ...
Transcript of Supraconductivité avec et sans point critique quantique ...
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Supraconductivité avec et sans point critique quantique antiferromagnétique
A.-M. Tremblay
Réunion inaugurale, LIAJouvence 27 octobre 2016
Institut quantique
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Magnetic superconductivity
Bechgaard salts
Canfield et al. (2010)
Pnictides
The Archetype
Pnictides and organics
Nicolas Doiron-Leyraud, Bourbonnais, Taillefer 2010
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Cartoon « BCS » weak-coupling picture
Δ p − 12V ∑ p ′ Up − p ′
Δ p ′
E p ′1 − 2n E p ′
Exchange of spin waves?Kohn-Luttinger
p
p’
Tc with pressure
Béal–Monod, Bourbonnais, EmeryP.R. B. 34, 7716 (1986).
D. J. Scalapino, E. Loh, Jr., and J. E. HirschP.R. B 34, 8190-8192 (1986).
Kohn, Luttinger, P.R.L. 15, 524 (1965).P.W. Anderson Science 317, 1705 (2007)
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High temperature superconductors
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tU
t’t’’
H −∑ij t i,j ci cj cj
ci U∑ i ni↑ni↓H −∑ij t i,j ci cj cj
ci U∑ i ni↑ni↓
Hubbard model
1931-1980
Attn: Charge transfer insulator
tEffective model, Heisenberg: J = 4t2 /U
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Method for strongly correlated matter
Dynamical Mean Field Theory (+ clusters)Concept: atomic localized correlations
consistent with delocalized aspect
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DCA
2d Hubbard: Quantum cluster method
C-DMFTV-
DCA
Hettler …Jarrell…Krishnamurty PRB 58 (1998)Kotliar et al. PRL 87 (2001)M. Potthoff et al. PRL 91, 206402 (2003).
REVIEWSMaier, Jarrell et al., RMP. (2005) Kotliar et al. RMP (2006)AMST et al. LTP (2006)
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Impurity solver
KZ Dd, dexp −Sc − 0
d 0
d ′∑idiΔ i′i , ′di′ ′
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+ and -
• Long range order:– Allow symmetry breaking in the bath (mean-field)
• Included:– Short-range dynamical and spatial correlations
• Missing: – Long wavelength p-h and p-p fluctuations
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Groups using these methods for cuprates
• Europe: – Georges, Parcollet, Ferrero, Civelli, (Paris)– de Medici (Grenoble) Capone (Italy)
• USA: – Gull (Michigan) Millis (Columbia)– Kotliar, Haule (Rutgers)– Jarrell (Louisiana)– Maier, Okamoto (Oakridge)
• Japan– Imada (Tokyo) Sakai
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Superconductivity around an AFM quantum critical point
Wei Wu
W. Wu A.-M.S.T. Phys. Rev. X, 2015
A heavy fermion example
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3D metals tuned by pressure, field or concentration
Magnetic superconductivityKnebel et al. (2009)
Heavy fermions
CeRhIn5
Mathur et al., Nature 1998Quantum criticality
Heavy fermions
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Heavy fermions
W. Wu A.-M.S.T. Phys. Rev. X, 2015
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Weakly vs strongly correlatedsuperconductivity
Analog to weakly and stronglycorrelated antiferromagnets
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Weak vs Strong correlations
n = 1, unfrustrated d = 3 cubic lattice
Heisenberg
t
Mott
Slater
AFM
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Local moment and Mott transition
n = 1, d = 2 square lattice
Understanding finite temperature phase from a mean-field theory down to T = 0
Critical point visible in V2O3,
BEDT organics
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Phase diagram for organics
Phase diagram (X=Cu[N(CN)2]Cl)S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)
40
30
20
10
0
T
(K)
6004002000
P (bar)
AF
U-SCAF/SC
PI
M
F. Kagawa, K. Miyagawa, + K. Kanoda PRB 69 (2004) +Nature 436 (2005)
Powell, McKenzie cond-mat/0607078Bg for C2h and B2g for D2h
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Influence of Mott transition away from half-filling
n = 1, d = 2 square lattice
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Influence of Mott transition away from half-filling
n = 1, d = 2 square lattice
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Spin susceptibility
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Spin susceptibility
Underdoped Hg1223Julien et al. PRL 76, 4238 (1996)
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Two crossover lines
G. Sordi et al. Phys. Rev. Lett. 108, 216401/1-6 (2012) P. Sémon, G. Sordi, A.-M.S.T., Phys. Rev. B 89, 165113/1-6 (2014)
Giovanni SordiGiovanni SordiGiovanni SordiPatrick SémonPatrick SémonPatrick Sémon
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Physics
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Plaquette eigenstates
Michel Ferrero, P. S. Cornaglia, L. De Leo, O. Parcollet, G. Kotliar, A. Georges PRB 80, 064501 (2009)
See also:
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Finite T phase diagramSuperconductivity
Giovanni SordiGiovanni SordiGiovanni Sordi Patrick SémonPatrick Sémon
Sordi et al. PRL 108, 216401 (2012)Fratino et al.
Sci. Rep. 6, 22715 (2016)
Lorenzo Fratino
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Crossovers inside the AFM phase
U
n = 1, unfrustrated d = 3 cubic lattice
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Superconductiviy in Doped Mott insulator
n = 1, d = 2 square lattice
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An organizing principleFr
atin
o et
al.
Sci.
Rep
. 6, 2
2715
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3 bands, charge transfer insulator
Fratino et al. PRB 93, 245147 (2016)
Giovanni SordiGiovanni SordiGiovanni Sordi Lorenzo Fratino
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3 bands, charge transfer insulator
Fratino et al. PRB 93, 245147 (2016)
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Organics : Phase diagram, finite T
Made possible by algorithmic improvements
Patrick SémonPatrick SémonCharles-David Hébert
P. Sémon et al.PRB 85, 201101(R) (2012)
PRB 90 075149 (2014);and PRB 89, 165113 (2014)
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Phase diagram for organics
Phase diagram (X=Cu[N(CN)2]Cl)S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)
40
30
20
10
0
T
(K)
6004002000
P (bar)
AF
U-SCAF/SC
PI
M
F. Kagawa, K. Miyagawa, + K. Kanoda PRB 69 (2004) +Nature 436 (2005)
Powell, McKenzie cond-mat/0607078Bg for C2h and B2g for D2h
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Anisotropic triangular lattice
See: Poster Shaheen Acheche
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Phase diagram at n = 1
Y. Kurisaki, et al. Phys. Rev. Lett. 95, 177001(2005)
Y. Shimizu, et al. Phys. Rev. Lett. 91, (2003)
X= Cu2(CN)3 (t’~ t)
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Superconductivity near the Mott transition
n = 1, d = 2 square lattice
/ t
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Superconductivity near the Mott transition
n = 1, d = 2 square lattice
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Superconductivity near Mott transition (n = 1)
C.-D. Hébert, P. Sémon, A.-M.S. T PRB 92, 195112 (2015)
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Doped Organics
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Doped BEDT
H. Oike, K. Miyagawa, H. Taniguchi, K. Kanoda PRL 114, 067002 (2015)
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Doped organics
n = 1, d = 2 square lattice
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Doped organics
n = 1, d = 2 square lattice
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First order and Widom line in organics
C.-D. Hébert, P. Sémon, A.-M.S. T PRB 92, 195112 (2015)
Compare: T. Watanabe, H. Yokoyamaand M. Ogata
JPS Conf. Proc. 3, 013004 (2014)
G. Sordi et al. Scientific Reports, 2, 547 (2012)
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Doped BEDT
H. Oike, K. Miyagawa, H. Taniguchi, K. Kanoda PRL 114, 067002 (2015)
n= 1
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t’ = 0.4t overview
Compare: T. Watanabe, H. Yokoyama and M. OgataJPS Conf. Proc. 3, 013004 (2014)
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Generic case highly frustrated case
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Summary : organics
• Agreement with experiment• SC: larger Tc and broader P range if doped• Larger frustration: Decrease TN much more than Tc
• Normal state metal to pseudogap crossover
• Predictions• First order transition at low T in normal state (B induced)• Crossovers in SC state associated with normal state.
• Physics• SC dome without an AFM QCP. Extension of Mott• SC from short range J. • Tc dome maximum near normal state 1st order
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Pairing mechanism
Back to high Tc
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Cartoon « BCS » weak-coupling picture
Δ p − 12V ∑ p ′ Up − p ′
Δ p ′
E p ′1 − 2n E p ′
Exchange of spin waves?Kohn-Luttinger
p
p’
Tc with pressure
Béal–Monod, Bourbonnais, EmeryP.R. B. 34, 7716 (1986).
D. J. Scalapino, E. Loh, Jr., and J. E. HirschP.R. B 34, 8190-8192 (1986).
Kohn, Luttinger, P.R.L. 15, 524 (1965).P.W. Anderson Science 317, 1705 (2007)
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A cartoon strong coupling picture
H M F ∑k ,
kck ,† c k , − 4Jmm̂ − Jdd̂ d̂ † F 0
J∑⟨i,j
S i S j J∑⟨i,j
12 c i
†c i 12 c j
†c j
d ⟨d̂ 1/N∑kcos k x − cos k y ⟨c k ,↑c −k ,↓
Pitaevskii Brückner: Pair state orthogonal to repulsive core of Coulomb interaction
Miyake, Schmitt–Rink, and VarmaP.R. B 34, 6554-6556 (1986)
P.W. Anderson Science 317, 1705 (2007)
More sophisticated Slave Boson: Kotliar Liu PRB 1988
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Extended Hubbard model
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Strongly correlated: From J, yet retarded
Sénéchal, Day, Bouliane, AMST, Phys. Rev. B 87, 075123 (2013)
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Antagonistic effects of V at finite T
A. Reymbaut et al. PRB 94 155146 (2016)
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Summary
• AFM QCP for a heavy-fermion model• No QCP: First order transition that extends
Mott physics away from half-filling• Is an organizing principle for
– The normal and superconducting states – Cuprates and organics are examples– Predictions for organics
• Mechanism: J short-range
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Mammouth
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C’est fini…
A.-M.S. Tremblay“Strongly correlated superconductivity”
Chapt. 10 : Emergent Phenomena in Correlated Matter Modeling and Simulation, Vol. 3, E. Pavarini, E. Koch, and U. Schollwöck (eds.)
Verlag des Forschungszentrum Jülich, 2013
Review: A.-M.S.T. arXiv: 1310.1481
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Collaborators for this work
Patrick SémonPatrick SémonCharles-David Hébert
Wei Wu
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Weakly vs strongly correlatedsuperconductivity
Analog to weakly and stronglycorrelated antiferromagnets
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Weak vs Strong correlations
T
U
n = 1, unfrustrated d = 3 cubic lattice
J = 4t2 /UAFM
Heisenbergt
Mott
Slater
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Local moment and Mott transition
T
U
n = 1, d = 2 square lattice
M I
Understanding finite temperature phase from a mean-field theory down to T = 0
Critical point visible in V2O3,
BEDT organics
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Doped organic: experiment
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Doped BEDT
H. Oike, K. Miyagawa, H. Taniguchi, K. Kanoda PRL 114, 067002 (2015)
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Doped BEDT
H. Oike, K. Miyagawa, H. Taniguchi, K. Kanoda PRL 114, 067002 (2015)
n= 1
n = 0.90
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Method
Concept: Cluster - DMFTTools: Impurity solver
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CTQMC impurity solver (tool) (T finite)
K
P. Sémon et al.PRB 85, 201101(R) (2012)
PRB 90 075149 (2014);and PRB 89, 165113 (2014)