Transcript Unconventional Superconducting Symmetry in Geometrically

Giant Superconducting Proximity Effect in Composite Systems
Chun Chen and Yan Chen
Dept. of Physics and Lab of Advanced Materials, Fudan University, Shanghai 200433, China
Abstract
Searching routes to raise the superconducting transition temperature (Tc) is one of the major pursuits of current research in condensed matter physics. Although until now,
there is not yet a wide-accepted consensus on the electron-pairing mechanism of cuprate materials and iron-pnictides, condensed matter theorists believe that two relevant
quantities: the pairing gap amplitude as well as the phase stiffness determine the Tc of a superconducting material. Turning this logic around, we study a composite system
consisting of a realistic underdoped cuprates layer modeled by a t-t’-J model and a metallic layer. Due to the different correlation nature of two layers, the interlayer
coupling may lead to giant superconducting proximity effect and the superconducting order parameter at the metallic layer could be greatly enhanced at zero temperature.
Formalism
Introduction
Recently S. Kivelson group at Stanford (PRB 78, 094509 (2008)) proposed a
possible route to high-temperature superconductivity in composite systems. They
studied a simple two-component model consisting of a metallic layer and an
underdoped pairing layer modeled by negative-U Hubbard model, and suggested
that Tc of the whole system can be greatly enhanced by increasing the interlayer
coupling. D.H. Lee (Physics 1, 19 (2008)) highlighted the importance of this
theoretical work and gave a lucid paraphrase as follows by making an analogy to
Josephson junction array.
The Hamiltonian of the Model
We choose the well-established t-t’-J model to describe the pairing layer
and the metallic component is modeled by a tight binding Hamiltonian:
H  tc   c c  h.c.  tc
i , j ,
†
i , j ,
 c
i , j  ,
c  h.c.  J  Si  S j    nc,i  t f
†
i , j ,
i, j
i
  f
†
i ,
f j ,  h.c.    n f ,i  t  c f  h.c.
i, j ,
i
i ,
†
i , i ,
Using renormalised mean field theory and Gutzwiller approximation, we
introduce two renormalised factors to replace the projection operators:
ci†, c j ,  gt ci†, c j , , Si ,  S j ,  g S Si ,  S j , , ci†, fi ,  gt ci†, fi , .
To calculate the superconducting order parameters, we utilize an
orthogonal matrix to diagonalize the effective Hamiltonian:
metallic layer
1
    v13v43  v14 v44  v14 v11  v42 v12  cos k ,
N k
1
f
    v23v33  v24 v34  v31v12  v32v22  cos k ,
N k
1
c
    v13v13  v14v14  v14v14  v42v42  cos k ,
N k
1
f
    v23v23  v24v24  v31v31  v32v32  cos k .
N k
c
tf
 ck    v11

  1
 f k     v2
 f †k    v31
 †   1
 c k    v4
t
tc’
tc J
t-t’-J layer
As the left panel shows in the limit of large charge energy, the number of
Cooper pairs within individual islands are strongly localized and the system
becomes insulating, but once this Josephson junction array attached to a nearby
metal, superconductivity could be restored. However this negative-U model is
over simplified and doped Mott insulator physics has not been seriously
considered in such composite systems.
Motivated by this new proposal of higher Tc, we study a similar composite
system consisting of a realistic underdoped cuprates layer modeled by a t-t’-J
model and a metallic layer (illustrated in the above right panel). By using the
renormalized mean field theory of t-J model, we examined the pairing gap
amplitudes of the two layers at zero temperature. Our results show that by
increasing the interlayer coupling, the pairing gap of t-t’-J layer is suppressed
while the gap at the metallic layer Δm could be greatly enhanced. The value of Δm
could be even greater than the superconducting order parameter
of the underdoped cuprates layer.
v12
v13
v22
v23
v32
v33
v42
v43
v14   d k  

4 
v2   g k  
4  †
v3 g  k  
  † 
4 
v4   d  k  
and four distinct mean fields are defined as usual:
 cr  ci†, ci† r ,  ci†, ci† r , ,  rc   ci†, ci  r ,

 rf  fi ,† fi † r ,  fi ,† f i † r , ,  rf   f i ,† f i  r ,

Density of states
After diagonalizing the Hamiltonian, the bare single-particle Green’s
function is given by
4
vim (k )v mj (k )
m 1
in  Em (k )
G0 (k , in )ij  
and the density of states can be calculated from the retarded Green’s
function:
1
 ( )  
Im G (k ,   i )


0
k
11
 G0 (k ,   i ) 22 
Numerical Results
Density of states
Superconducting Order Parameters
When the hopping between these two layers is strong, the SC order parameter of t-t’-J layer
will decrease, while in the metallic layer such a parameter will be enhanced remarkably,
which is even greater than that of a single t-t’-J layer. Meanwhile we notice that such a peak
of the metallic layer appears in the underdoped region of the superconducting layer. The right
panel depicts the SC order parameter as a function of chemical potential.
Here resonance peak in the DOS spectra of the composite does not directly correspond to the
mean field order parameters of two individual layers , but through a complicated relationship.
One salient feature is that the interlayer coupling may split the original single peak.
Summary
1. Due to the different correlation nature of composite system, the SC order parameter at the metallic layer could be greatly enhanced.
2. The LDOS spectra show the splitting of the resonance peak because of the interlayer coupling.