Insights into dwave superconductivity from quantum cluster approaches. c = 1 Perfect diamagnetism (Shielding of magnetic field) (Meissner effect). AndréMarie Tremblay. CuO 2 planes. YBa 2 Cu 3 O 7 d. Experimental phase diagram. Hole doping. Electron doping. Stripes.
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Insights into dwave superconductivity from quantum cluster approaches
c = 1
Perfect diamagnetism (Shielding of magnetic field)
(Meissner effect)
AndréMarie Tremblay
1
Hole doping
Electron doping
Stripes
Optimal doping
Optimal doping
1.3 1.2 1.1 1.0 0.9 0.8 0.7
3
n, electron density
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
The Hubbard model approaches
Simplest microscopic model for Cu O2 planes.
t’
t’’
m
U
LSCO
t
No meanfield factorization for dwave superconductivity
4
A. Macridin et al., condmat/0411092
5
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
A( approacheskF,w)
T
A(kF,w)
w
U
w
U
LHB
UHB
Mott transition (DMFT, exact d = )
U ~ 1.5W (W= 8t)
t
Effective model, Heisenberg: J = 4t2 /U
Weak vs strong coupling, n=1
6
Mott Insulator
1.3 1.2 1.1 1.0 0.9 0.8 0.7
7
n, electron density
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
8
9
10
DCA
Variational
Th. Maier, M. Jarrell, Th. Pruschke, and J. Keller
Phys. Rev. Lett. 85, 1524 (2000)
T.A. Maier et al. PRL (2005)
Paramekanti, M. Randeria, and N. Trivedi
Phys. Rev. Lett. 87, 217002 (2001)
11
12
15
+ ….
+
+
Universality
H.F. if approximate F
by first order
FLEX higher order
Then W is grand potential
Related to dynamics (cf. Ritz)
Luttinger and Ward 1960, Baym and Kadanoff (1961)
16
Still stationary (chain rule)
17
M. Potthoff, Eur. Phys. J. B 32, 429 (2003).
With F[S]
Legendre transform of LuttingerWard funct.
is stationary with respect to S and equal to grand potential there.
For given interaction, F[S] is a universal functional of S, no explicit dependence on H0(t). Hence, use solvable cluster H0(t’) to find F[S].
Vary with respect to parameters of the cluster (including Weiss fields)
Variation of the selfenergy, through parameters in H0(t’)
18
M. Potthoff, Eur. Phys. J. B 32, 429 (2003).
M. Potthoff et al. PRL 91, 206402 (2003).
CDMFT
DCA, Jarrell et al.
V
Savrasov, Kotliar, PRB (2001)
Georges Kotliar, PRB (1992).
M. Jarrell, PRL (1992).
A. Georges, et al.
RMP (1996).
19
1D Hubbard model: Worst case scenario
Excellent agreement with exact results in both metallic and insulating limitsCapone, Civelli, SSK, Kotliar, Castellani PRB (2004)Bolech, SSK, Kotliar PRB (2003)
20
U/t = 4, = 0.2, n = 0.89
Kyung, Kotliar, Tremblay, PRB 2006
21
/(4t)
Parcollet, Biroli, Kotliar, PRL (2004)
22
24
25


+
+
+
+


Sarma Kancharla
No Weiss field on the cluster!
Caffarel and Krauth, PRL (1994)
26
t’= t’’=0
Dwave OP
Kancharla, Civelli, Capone, Kyung, Sénéchal, Kotliar,
AM.S.T.condmat/0508205
Sarma Kancharla
27
t’= t’’=0
D = y Z
Kancharla, Civelli, Capone, Kyung, Sénéchal, Kotliar,
AM.S.T. condmat/0508205
28



+
+
+
+
+
+



David Sénéchal
See also, Capone and Kotliar, condmat/0603227,
Macridin et al. DCAcondmat/0411092
29
t’ = 0.3 t, t’’ = 0.2 t
U = 8t
1.3 1.2 1.1 1.0 0.9 0.8 0.7
30
n, electron density
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
31
Armitage et al.
PRL 2003
Ronning et al. PRB 2003
15%
10%
4%
t’ = 0.3 t, t’’ = 0 t
U = 8t
Kyung, Kancharla, Sénéchal, A.M.S. T, Civelli, Kotliar PRB (2006)
Bumsoo Kyung
5%
5%
33
See also Sénéchal, AMT, PRL 92, 126401 (2004).
Effect of U
Bumsoo Kyung
Kyung, Kancharla, Sénéchal, A.M.S. T,
Civelli, Kotliar PRB in press
Pseudogap size function of doping
34
See also Sénéchal, AMT, PRL 92, 126401 (2004).
35
H. Kino + H. Fukuyama, J. Phys. Soc. Jpn 65 2158 (1996),
R.H. McKenzie, Comments Condens Mat Phys. 18, 309 (1998)
Y. Shimizu, et al. Phys. Rev. Lett. 91, 107001(2003)
t’/t ~ 0.6  1.1
37
F. Kagawa, K. Miyagawa, + K. Kanoda
PRB 69 (2004) +Nature 436 (2005)
Diagramme de phase (X=Cu[N(CN)2]Cl)
S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)
39
F. Kagawa, K. Miyagawa, + K. Kanoda
PRB 69 (2004) +Nature 436 (2005)
Diagramme de phase (X=Cu[N(CN)2]Cl)
S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)
41
Parcollet, Biroli, Kotliar, PRL 92 (2004)
Kyung, A.M.S.T. (2006)
See also, Sénéchal, Sahebsara, condmat/0604057
42
Kyung, A.M.S.T. (2006)
See also, Sénéchal, Sahebsara, condmat/0604057
43
F. Kagawa, K. Miyagawa, + K. Kanoda
PRB 69 (2004) +Nature 436 (2005)
Diagramme de phase (X=Cu[N(CN)2]Cl)
S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)
45
Sénéchal
X= Cu2(CN)3 (t’~ t)
Y. Kurisaki, et al. Phys. Rev. Lett. 95, 177001(2005)
Y. Shimizu, et al. Phys. Rev. Lett. 91, (2003)
Kyung
OP
Kyung, A.M.S.T. condmat/0604377
Sénéchal, Sahebsara, condmat/0604057
46
Sahebsara
AF multiplied by 0.1
47
Kyung, A.M.S.T. condmat/0604377
Sénéchal, Sahebsara, condmat/0604057
Kyung, A.M.S.T. condmat/0604377
AF
SL
dSC
49
t’/t=0.8t
H. Morita et al., J. Phys. Soc. Jpn. 71, 2109 (2002).
J. Liu et al., Phys. Rev. Lett. 94, 127003 (2005).
S.S. Lee et al., Phys. Rev. Lett. 95, 036403 (2005).
B. Powell et al., Phys. Rev. Lett. 94, 047004 (2005).
J.Y. Gan et al., Phys. Rev. Lett. 94, 067005 (2005).
T. Watanabe et al., condmat/0602098.
50
Sénéchal, Lavertu, Marois,
A.M.S.T., PRL, 2005
Kancharla, Civelli, Capone, Kyung, Sénéchal, Kotliar,
AM.S.T. condmat/0508205
51
U=5.75
U=6.25
U=6.25
U=5.75
52
53
54
57
59
Armitage et al.
PRL 2003
Ronning et al. PRB 2003
15%
10%
4%
t’ = 0.3 t, t’’ = 0 t
U = 8t
7%
7%
4%
Kancharla, Civelli, Capone, Kyung, Sénéchal, Kotliar,
AM.S.T. condmat/0508205
61
1.3 1.2 1.1 1.0 0.9 0.8 0.7
AF
t’ = 0.3 t
t’’ = 0.2t
U = 8t
dSC
Sénéchal, Lavertu, Marois, A.M.S.T., PRL, 2005
62
Aichhorn, Arrigoni, Potthoff, Hanke, condmat/0511460
63
Sénéchal, AMT, PRL 92, 126401 (2004).
64
66