High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ

i
j
20 mV
a
f
c
d
g
e
h
b
q
3
q
1
q
2
q
4
q
5
q
6
q
7
q
1
q
4
q
5
q
6
q
7
q
3
k
x
k
y
k
x
 
(
π/a
0
)
Δ
T
k 
(º)
Fig. 4 | Quasi-particle interference and superconducting gap in monolayer 
Bi-2212. a, Representative conductance ratio map r
Z
E
( , )
obtained at E = 20 meV 
on the same area as in Fig. 3b. b, Illustration of the octet model for Bogoliubov 
quasiparticle interference in Bi-2212 at a given energy. The octet ends of four 
banana-shaped constant-energy contours have maximum density of states. 
Quasi-particle scattering between these eight regions produces seven primary 
scattering q-vectors, q
1
to q
7
, labelled by coloured squares. c–h, Fourier 
transform of the conductance ratio map 
q
Z
E
( , ) . The Fourier transforms are 
mirror-symmetrized and normalized to their average value. E is labelled on each 
panel. In particular, f displays the Fourier transform of the conductance ratio 
map in a. Red solid lines indicate the atomic Bragg vectors at 
a
(2π/ , 0)
0
and 
a
(0, 2π/ )
0
. Of the total of seven independent scattering vectors (coloured 
squares) prescribed by the octet model illustrated in b, five are observed as 
peaks in the Fourier transform; q
4
and q
5
are too weak to be detected. i, Loci of 
the ends of banana-shaped constant-energy contours extracted from dispersion 
of the q-vectors. Locations of the loci represent the underlying Fermi surface. 
Solid line is a fit to the data with a circular arc joined with two straight lines. 
Broken line marks the antiferromagnetic zone boundary. j, Superconducting 
gap Δ
SC
as a function of Fermi surface angle θ
k
. Δ
SC
is extracted from the 
measured position of scattering vectors q
1
to q
7
(excluding q
4
and q
5
) following 
the procedure described in refs. 
24,26
. Solid line is a fit to the data with d-wave 
gap function Δ θ
Δ
A
θ
A
θ
( ) =
[ cos(2 ) + (1 − )cos(6 )]
k
k
k
QPI
, where Δ
QPI
= 47.3 meV and 
A = 0.844 are fitting parameters.

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