nanometers in size, andare located at opposite
ends, ~1.5 nm distance from the surface ma-
nipulation. The horizontal line-cut on the
right side of Fig. 4A shows this in more detail.
The most straightforward way to create a
dipole-shaped profile in a difference image is
by subtracting two identical [two-dimensional
(2D)] peaks that are laterally shifted with re-
spect to each other (Fig. 4B). In the context of
our experiment, this would correspond to a
single peak that laterallyshifted by the electric
field manipulation, which upon generating
thedifferencemapisthussubtractedfrom
itself at a slightly different location. The max-
ima of the subtraction, i.e., the lobes of the
dipole, are in the direction of the shift, as we
observe in the experiment. For shifts smaller
than the width of the peak, the lateral extent
of the resulting dipole will depend exclusively
on the width, whereas the magnitude of the
dipole is a function of the size of the shift and
the peak amplitude (Fig. 4B, inset). Using this
simple toy model, we can accurately repro-
duce both the size and shape of the observed
dipole when we use a Gaussian profile for the
peak, as well as simulate the experimental
data (Fig. 2F). Conversely, a Lorentzian pro-
file decays too slowly to properly fit the tails
of the difference image, as can be seen from
the line-cut comparison in Fig. 4A. For a re-
alistic lateral shift of 2 Å (see, for example,
Fig. 1C), the Gaussian requires an amplitudeof ~50 meV, which is not unreasonable given the
average peak-to-peak gap size ofD=96meV.
Lastly, the width of the Gaussian is 1.7 nm,
which is comparable to the superconducting
coherence length.
A Gaussian-shaped gap distribution that
falls off with length scales on the order of the
coherence length is highly suggestive of a lo-
cal pairing potential originating from a point-
like object. When we laterally move this entity
using the electric field of the tip, its local
pairing potential moves with it, leading to a
dipole-shaped feature in the difference image.
The physical origin of the object is possibly
related to the Bi atoms themselves, although
the contribution of the Bi orbitals to the low
energy density of states is limited ( 23 ). More
likely, the apical oxygen atoms directly below
the Bi atoms shift concomitant with the Bi
manipulation, leading to the gap modifica-
tions. The importance of the apical oxygen
atoms in both the tunneling process ( 24 – 26 )
and the gap size ( 10 ) have been stressed pre-
viously. Our observations provide additional
input for further theoretical investigations—
particularly those that take into account on-
site correlations ( 27 , 28 )—into the origin of the
spectral gap, and the tunneling process, in this
cuprate superconductor.
An alternative source of the dipole-shaped
difference image could be the appearance of
topological defects that introduce a 2p-rotation
of the phase of the order parameter ( 29 ). How-
ever, creation and annihilation of topological
defects has to occur in pairs. Given our finite
field of view, it may be that one-half of the pair
is outside our measurement range, but given
the large field-of-view topographic before-and-
after comparison (fig. S5), and assuming that
both pairs will have a signature in topography,
this is unlikely. Furthermore, in our optimally
doped system we do not find a significant cor-
relation between the gap changes and topo-
logical defects in the smectic, or the d-form
factor density wave, reported for underdoped
samples ( 30 , 31 ). Extension of our work to
lower doping concentrations, where the vari-
ous charge- and spin-ordered states are more
predominant, should giveamoredefinitean-
swer to this issue. Additionally, the influence
of dopants and the surface structure on these
(ordered) states themselves can be studied di-
rectly using the field-induced atom manipula-
tion we introduce in this work.
The observation of a profound influence on
the peak-to-peak gap in tunneling experiments
of subnanometer shifts in atomic positions
highlights the importance of the lattice on
the local electronic properties of the cuprates.
The spatial profile of the gap modification we
observe is highly suggestive of the field-induced
lateralmovementofalocalpairingpotentialin
the CuO 2 plane originating from a point-like
object. This work demonstrates an avenue toMasseeet al.,Science 367 ,68–71 (2020) 3 January 2020 3of4
Fig. 3. Atomic position
dependence of gap changes.
(A)D 2 − 1 =D 2 (r)–D 1 (r) image on the
same area as the constant current
images in Fig. 1C. The manipulated Bi
atoms are marked by circles, the
lateral movement upon manipulation
is indicated by an arrow. The right
panel shows the opposite gap
modification upon a reversion of
the atomic configuration after a
subsequentVs= 1.5 V manipulation.
Scale bars, 1 nm. (B) Schematic
of the surface change and its effect
on the gap: One atom moves up
(down), another shifts laterally away
from (toward) it, resulting in gap enhancement in the direction of the shift. More details and examples
can be found in sections 1 and 4 of ( 21 ).
+15
meV-15
meVD2-1 = Δ 2 - Δ 1 D3-2 = Δ 3 - Δ 2
Δ 2 > Δ 1 Δ 2 < Δ 1 Δ 3 < Δ 2 Δ 3 > Δ 2
AB
Bi BiFig. 4. Dipole profile and toy model.
(A) AverageD(r) for all topographic
modifications after aligning their
orientation. The arrow indicates where
the vertical line trace on the right is
taken for the experimental data
(red circles) and for the toy model
using a Gaussian (black dashed line)
and Lorentzian (blue dashed line)
peak profile. (B) A 2D Gaussian
(width = 1.7 nm; top left) is shifted
by a fraction of a nanometer (top right,
shift exaggerated for clarity), leading
to a difference (bottom) upon their
subtraction with the same shape and
length scales as the experimental
data in (A). The inset shows how the
amplitude of the subtracted
Gaussians depends on the shift
distance: a 2-Å shift requires
an amplitude ofD~50meV
(dashed lines).
D(r)
= Δ 2 - Δ 1shift ~ ÅD (meV)1 nmA5 0 -5-3-2-10123distance (nm)Gaussian
LorentziandataVs > 1.2 V~nm~nmxy10100
Δ
(meV)(^0) Shift (nm)1.0
Δ 1 Δ 2
B
Δ 2 > Δ 1
Δ 2 < Δ 1
RESEARCH | REPORT