Transcript Document

Anomalous self-energy and
pseudogap formation near
an antiferromagnetic instability
A. A. Katanina,b,c and A. P. Kampfc
a Max-Planck
b Institute
Institut für Festkörperforschung, Stuttgart
of Metal Physics, Ekaterinburg, Russia
c Theoretische
Physik III, Institut für Physik, Universität
Augsburg
2004
1
Introduction
• What are the changes in the electronic spectrum
on approaching an AF metallic phase in 2D ?
T
T*0
PM
(Fermi liquid,
well-defined QP)
 = C exp(T*/T),
T < T*
RC
2-nd
order QPT
metallic AF
(n  1)
m
T
T*
PM
 = C exp(T*/T),
T < T*
RC
dSC
1-st metallic AF
order QPT
m
Previous studies:
SF model (A. Abanov, A. Chubukov, and J. Schmalian)
2D Hubbard model:
• DCA (Th. Maier, Th. Pruschke, and M. Jarrell)
• FLEX (J. J. Deisz et al., A. P. Kampf)
• TPSC (B. Kyung and A. M.-S. Tremblay)
2
Cuprates: experimental results
Pseudogap regime –
the spectral weight at the Fermi level
is suppressed.
PG
SC
Partly “metallic” behavior even at very low hole doping
From:
T. Yoshida et al.,
Phys. Rev. Lett.
91, 027001 (2003).
3
The model and AF order
The model:
H =  e k ck ck  U  nini
k ,
n 1
i
e k = 2t (cos k x  cos k y )  4t ' (cos k x cos k y  1)  m, t '  0
• Two possibilities to have AF order:
AF order at large U in a nearly half-filled band –
AF Mott insulator
 AF order due to peculiarities of band structure –
Slater antiferromagnetism:

0.5
t'/t
van Hove
band fillings
r(e)
0.5
0.3
0.1
-2
0
2
4
e/t
0.0
0.0
1.0
1.0
n
0.0
• C. J. Halboth and W. Metzner
Phys. Rev. B 61, 7364 (2000)
• C. Honerkamp, et al., Phys.
Rev. B 63, 035109 (2001)
4
Self-energy: mean-field results
S(e ) =
2
e  e k Q  id
n = nvH
A
SA
ek+Q = 0
ReS  2/e
B
e
ImS(e) = ip2d(e)
n  nvH
S
B
ek+Q  0
A
ReS
Q
B
ek+Q
e
ImS
5
The functional RG
.
.
=
V = V * (G  * S  S * G  ) * V
.
.S

=
0
= S *  d' [V ' * S ' * G ' *V ' ]
G =

 (| e k |  )
d (| e k |  )
; S = 
in  e k
in  e k
Discretization of the
momentum dependence
of the interaction
6
Self-energy at vH band fillings



Spectral properties are strongly anisotropic around the
Fermi surface
The quasiparticle concept is violated at kF=(p,0) and
valid in a narrow window around =0 for other kF
The spectral properties are mean-field like for k=(p,0)
while they are qualitatively different from MF results for
other kF
7
Self-energy near vH band fillings
Similiarity with the
PM – PI, U < Uc
Mott-Hubbard DMFT
picture
Hubbard
sub-bands
Quasiparticle peak, Z0


Unlike vH band fillings, magnetic fluctuations suppress
spectral weight, but are not sufficient to drop spectral
weight to zero.
The quasiparticle concept is valid in a narrow window
around =0 for all kF
8
Conclusions



The spectral weight is anisotropic around FS and
decreases towards (p,0).
At the (p,0) point two-peak pseudogap structure
of the spectral function arises.
At the other points the spectral function has
three-peak form
Therefore, at finite t' and away from half filling
Weak U
(p/2,p/2)
(p,0)
Possible scenario for strong coupling regime in the
nearly half-filled 2D Hubbard model
Strong U
(p/2,p/2)
(p,0)
Magnetic sub-bands
Hubbard
sub-bands
Spectral weight transfer
Quasiparticle peak
Spectral weight transfer
9