Chemistry Reference
In-Depth Information
where
a
k
σ
,b
k
σ
are electron operators on the A and B sublattices,
k
runs
over the Brillouin zone of the triangular Bravais lattice,
a
α
,α
3
are vectors that go from an A site to the three nearest B sublattice
sites. The free electronic dispersion is determined by the function
=1
,
2
,
(
k
)=
−t
α
e
i
k
·
a
α
, and the superconducting gap function ∆(
k
)=
α
∆
α
e
i
k
·
a
α
.
The
ε
symmetry motivated by the meanfield solution
[
40
]
provides
d
+
id
i
2
π
(
α−
1)
3
∆
α
=∆
µ
f
is a “Hartree shift”.
Starting from this mean field theory, we construct a BCS state
e
where ∆ is the “gap parameter”,
|BCS
N
with an appropriate number
N
of electrons.
If we work with a lattice
with
L
sites, this corresponds to a hole doping of 1
− N/L
. Our candi-
|
is now a state with a Gutzwiller-Jastrow factor
[
47;
date ground state
Ψ
48
]
g
g
D
|BCS
N
|
Ψ
=
(21)
=
i
(
n
i↑
n
i↓
n
i↑
n
i↓
where
) is the operator that counts the number
of doubly occupied sites. The wavefunction (21) with partial Gutzwiller
projection has three variational parameters: the gap parameter ∆, the
Hartree shift
D
+
µ
f
, and the Gutzwiller-Jastrow factor
g
. The ground state
is calculated using quantum Monte Carlo method
[
46
]
,
and is optimized with respect to the variational parameters.
energy
Ψ
|H
H
|
Ψ
25
20
15
1
0
5
0
2
3
4
5
6
7
Distance, r
Fig. 9. Zero temperature coherence length, as extracted from the cooper pair correlation
function.
We monitor superconductivity by calculating the following correlation
function using the optimized wavefunctions
F
αβ
(
R
i
−
b
i
a
α
b
j
a
β
R
j
)=
(22)
b
i
a
α
is the
electron
singlet operator that creates a singlet between
the
A
site in the
i
-th unit cell and the
B
site connected to it by the vector
where
