Transcript Normal and superconducting properties of high

Effect of quasi-2d dimensionality on
the formation of electronic structure
and normal properties of HTSC
cuprates
Sergey G. Ovchinnikov
In collaboration with
V.Gavrichkov, M.Korshunov, E.Shneyder, I.Makarov, S.Nikolaev,
I.Nekrasov, Z.Pchelkina
L.V. Kirensky Institute of Physics,
Siberian Branch of Russian Academy of Science,
Krasnoyarsk 660036, Russia
Outline
• Strong electron correlations and low dimensionality
of cuprates
• Microscopically derived t-t’-t”-J* model from ab initio
LDA+GTB study of muliband p-d model
• Strongly correlated electrons and spin-liquid with
short AFM order
• Doping evolution of the Fermi surface and two
Lifshitz quantum phase transitions between UD and
OD regions
• Whether ARPES measure the true Fermi surface?
By new norm conserving CPT it depends on energy
resolution. For typical resolution negative answer
What are strong electron correlations?
•
•
•
Е el = Е kin + ЕCoul,
ЕCoul = Е HF + Еcorr
Weak correlations: Еcorr
Е el = Е kin + Е HF
<< Е kin + Е HF
Strong correlations: Еcorr >> Е HF, Е kin
No free electron in any mean field
There are multielectron terms and electron hopping
between them
LEHMANN REPRESENTATION:
electron in strong correlated system as a superposition
of Hubbard-type quasiparticles

G

a
a
Single electron GF 
k
k
written as
G (k ,  )  
m

can be
 Am (k ,  ) Bm (k ,  ) 



 
   m   m 
(1)
where the QP energies are given by


m  Em ( N 1)  E0 ( N )  ,
m  E0 ( N )  Em ( N 1)  ,
and the QP spectral weight is equal to
2
Am (k ,  )  0, N ak m, N  1 ,
Bm (k ,  )  m, N  1 ak 0, N
L.V. Kirensky Institute of Physics, SB RAS, Krasnoyarsk, Russia
2
.
S.G.O. and I.Sandalov, Physica C 1989; V.Gavrichkov etal, JETP 2000
Val’kov,
Ovchinnikov 2001
Band structure and density of states of undoped antiferromagnetic
La2CuO4 at the energy scale E~U ( Ovchinnikov, PRB 49, 9891,1994)
U
EF
x
0
1
2
Hybrid LDA+GTB scheme without fitting parameters
(in collaboration with prof.V.I.Anisimov group,
Ekaterinburg, (Korshunov etal, PRB2005))
• Projection of LDA band structure and construction the
Wannier functions for p-d –model
• Ab initio calculation of p-d –model parameters
• Quasiparticle band structure GTB calculations in the
strongly correlated regime with ab initio parameters
• Comparison of La2CuO4 and Nd2CuO4 band structure
with fitting and LDA+GTB parameters
Parameters of the t-t’-t”-J* model
from the LDA+GTB calculations
• La2CuO4
t=0.93 eV, t’= - 0.12 eV, t”=0.15 eV,
J=0.295 eV, J’= 0.003 eV, J”=0.007 eV
• Nd2CuO4
t= - 0.50 eV, t’=0.02 eV, t”= - 0.07 eV,
J=0.195 eV, J’= 0.001 eV, J”=0.004 eV
Short range AFM in CuO2 plane
• Undoped La2CuO4 has 3d AFM with TN~J/(lnJ/J’)
Where J and J’<<J are in-plane and interplane exchange
• Hole doping destroys 3d AFM at x>.03. 2d short AFM
correlations persists for all doping with correlation length
l~a/x^1/2 (by inelastic neutron scattering). Recent RIXS date
for strongly overdoped La1.6Sr0.4CuO4 reveals magnetic
excitations (Dean etal, Nat.Mater.12, 1019 (2013)
• Isotropic 2d spin liquid model with <Sx>=<Sy>=<Sz>=0 and
Nonzero <Sx(i)Sx(j)>=<Sy(i)Sy(j)>=<Sz(i)Sz(j)>
(Barabanov et al, 1989-2001)
Hole dynamics in SCES at the short range order antiferromagnetic
background. SCBA for Self-energy. At low T correlations are static
(Barabanov et al, JETP 2001, Valkov and Dzebisashvili, JETP 2005, Plakida and
Oudovenko JETP 2007, Korshunov and Ovchinnikov Eur.Phys.J.B, 2007)
(1  x) 2
G (k , E ) 
1 x
1  x2 2
E  0   
t (k ) 
 t01 (k ) U   (k )
2
4
2 1
(
k
)

 1 x N

q
2
2

1 x
t012 (q)
t01
(k)t01
(q) 
J(k  q)  x
 ( 1  x)
t(q) 
 K(q) 
2
U
U




1 x 
t012 (k  q)  ( 1  x)t01(k)t012 (k  q)  3
 J(q) 
 
t(k  q) 
  C(q)
2 
U
U



 2
K (q)   ei (f g)q X f2 X g2
f g
C(q)   ei (f g)q X f X g  2 ei (f g)q Sfz Sgz
f g
f g
Correlation functions are calculated follow Valkov and Dzebisashvili, JETP 2005
3
1
2
3
short range magnetic order in spin liquid
state up to 9-th neighbor
Self consistent spin and charge correlation
functions in the t-t’- t”J* model,all parameters
from ab-initio LDA+GTB
4
44
Cn  2 S0z S nz  X 0 X n
K n  X 0 0 X n0
Comparison ARPES and LDA+GTB calculations
Korshunov and Ovchinnikov Eur.Phys.J.B, 2007
Ovchinnikov, Korshunov, Shneyder, JETP 2009
ARPES data for Bi2201 Hashimoto etal, PRB77,2008 (left down),
and Meng etal, arXiv may 2009 (right down)
Bulut and Scalapino PRB1996
Barabanov et al, JETP 119, вып.4 (2001)
Spin-polaron approach, Mori-type projection method for spin-fermion model
X=0.06
X=0.11
Shadow band
intensity is smaller
due to spectral
weight redisribution.
No QP damping
X=0.14
X=0.19
Fermi surface
in the p-d Hubbard
model,
SCBA (non crossing
approximation) for the
self-energy,
S(k,) SRe  iSIm
Plakida, Oudovenko
JETP 131, 259 (2007)
Effect of short antiferromagnetic order on the electron
spectrum
(Kuchinskii, Nekrasov, Sadovskii,
JETP Lett. 2005, JETP 2006, JETP Lett. 88, 224, 2008)
Green function for electron interacting with a random
Gaussian spin fluctuation field is given by
   (k  Q)  ik
GD (k ,  ) 
(   (k ))(   (k  Q)  ik ) | D |2
Here D is the amplitude of the fluctuating AFM order , (k) is the electron
dispersion in the paramagnetic state
   x (k  Q)   y (k  Q) ,  x , y (k )   (k ) k xy
In the limit of zero Im part the long range AFM (SDW) is restored
2
1
3
Effective mass predicted by MMK and SGO (2007) and
from quantum oscillations measurements:
+ YBa2Cu3O6.5(p=0.1) Doiron-Leyraud l Nature,2007
* YBa2Cu4O8 (p=0.125) Yelland etal, PRL 100, 2008
x YBa2Cu4O8 Bangura etal, PRL 100, 047004, 2008
T Hg1201 Barisic etal, Nature Physics 2013 (m*/m=2.45)
T
*x
+
Fig. 2. Doping dependent evolution of the chemical potential shift, nodal Fermi velocity, and effective mass.
Density of states near optimal doping
QPT,
N(E)=Nreg(E) + Nsing(E)
Ovchinnikov etal, arXiv 0908.0576
J.Phys.: Condens.Matter 23, 045701 (2011)
Critical behavior near xc1=0.15:
Fsing ~z^2*Log|z|, Ce/T~Log|z|
Nsing(E) ~ Log|z|, z~e-eF~x-xc1~T
Sommerfeld parameter Ce/T~Log T,
Balakirev, PRL 2009
This is a properties of the Lifshitz QPT
in the 2d electron systens (Nedorezov
JETP 1966)
Logz is a tipical van Hove singularity
for 2d free electrons (Ziman 1964)
DOS near pseudogap critical point x=p*=0.24
Ovchinnikov etal, arXiv 0908.0576
J.Phys.: Condens.Matter 23, 045701 (2011)
Ovchinnikov,
Korshunov,
Shneyder,
arXiv 0908.0576
J.Phys.:
Condens.Matter
23, 045701 (2011)
Eg(x)=
J(1-x/p*)
Kinetic energy Ekin(x)/Ekin(p*) as function of doping. Above p* dependence ~(1+x)
is expected for 2D electron gas. Below p* its extrapolation reveals the depletion of
kinetic energy due to pseugogap. Black triangles-fitting with Loram-Cooper
triangular pseudogap model. Red line – exponential fitting E/E* ~ exp(-4Eg(x)/J)
Conclusion: normal state
Concentration
dependence of
the two
characteristic
energy scales in
cuprates:
Tc and T*
From T.Yoshida
etal, PRL137,
037004 (2009),
ARPES
Theory: Ovchinnikov etal
Xc1=0.15
Xc2=0.24
JETP 109, 775 (2009)
2D модель Хаббарда для кластера 2X2
Norm conserving Cluster perturbation theory for 2D Hubbard
model
(S.Nikolaev, S.Ovchinnikov, JETP 111, 634 (2010)
H   H 0c ( f )   H1c ( f , g ),
f
2
H0c

t
1
H tc
f
t’
f g
H1c  H tc  H tc  H tc ,
3
4
H tc
H tc
Norm conserving CPT
1. For 2x2 cluster and 4 local states of the Hubbard model there are
4^4=256 cluster eigenstates.The exact sum rule requires all these states
a
ai    i ( ) X f ,  i ( )  n ai m ,

,
a
i
i



   i ( ) F ( )  1.
2

2. Usually Lanczos method involves only the ground and a few excited eigenstates.
 d A (k,  )    i ( ) F ( )  f
2
Lost spectral weight: f <1

3. It appears that 30 eigenstates is enouph to get f>0.995
We control our CPT to keep f>0.99 and call it the NC CPT
4. Then CPT in X-operator representation
F ( )
1
~
1 ~
0
D  ( ) 
  ,
D k ,   (D ( ))  T k ,
   ( )
N
1
ik ( r  r )

G (k ,  ) 

(

)

(

)
D  (k ,  ),
  i
e
j
N c   i , j 1
(
0
)
()
c
i
j
Зависимость зонной структуры от f-фактора
(Николаев, Овчинников, ЖЭТФ 138б 717 (2010))
Ovchinnikov,
Nikolaev, JETP
Lett 93, 575, 2011
NC CPT
reproduces
CDMFT+ED
method,
(Stanescu,
Kotliar PRB 74,
125110,
2006,
Sakai,Motome,
Imada PRL102,
056404 (2009))
ARPES LSCO
. Yoshida, et al.,
Condens
Matter 19, 125209
(2007). delta = 0:02
eV, t = 0:25 eV,
delta/t=0.08
CDMFT+ED
(Sakai,Motome,
Imada
PRL102, 056404
(2009))
Isotope effect and critical temperature at
different values G/J
Shneyder, Ovchinnikov, JETP 109, 1017 (2009)
Conclusions
• Two quantum phase transition with doping take
are required to go from UD to OD Fermi liquid
• At optimal doping Xc1=0.15 there are log
singularity in DOS which results in maximum Tc
• Second QPT at Xc2=0.24 separates at T=0 FL
at x>xc2 and pseudogap state at x<xc2.\
• The ARPES with modern resolution does nor
show true FS. The order of magnitude
improvement of resolution will give the true FS
• Magnetic and phonon d-pairing works together
and gives aproximately equal contributions in Tc