states before and after manipulation. These
difference measurements will only show con-
trast where the density of states has been
altered by the atom manipulation, providing
a direct link between single atomic sites and
the local electronic structure.
To generate a difference map of the spectral
gap, we record low-energy differential conduct-
ance maps and extract a map of the peak-to-
peak gap,Di(r), using identical settings before
and after atom manipulation. Figure 2, A and
B, shows one example of a gap map taken
before and after ~10 dopants and Bi surface
atoms have been manipulated. Three subse-
quent electric field manipulation treatments
are shown in section 4 of ( 21 ). Whereas the
topographies and the gap maps are mostly
identical, excluding any change of the tip itself,
select locations show substantial changes, with
gaps increasing and decreasing by >10 meV.
The two spectra in Fig. 2C, which are taken at
the same location before and after the electric
field–induced manipulation, highlight the
significance of these changes. The spectra are
predominantly affected at the peak energies,
whereas the low energy states, |E|<20meV,
are hardly modified, if at all, highlighting the
insensitivity of the latter to disorder ( 22 )(fig.S7).
From the two gap maps, we then calculate the
difference map,D 2 − 1 (r)=D 2 (r)−D 1 (r), which
shows directly where the gap has enhanced
(blue) or decreased (red) upon the electric field
manipulation(Fig.2D).Asthehistogramsof
the gap changes in Fig. 2E show, the average
gap size over the entire field of view is pre-
served: The gap is both reduced and enhanced
in equal measure in the vicinity of the ma-
nipulated atoms.
Using the topographies taken simultaneous-
ly with the gap maps, we can next pinpoint
where surface Bi atoms have been manipu-
lated(fig.S8andS9);thelocationsofma-
nipulated Bi atoms have been marked with
black dots on the two gap maps (Fig. 2, A and
B) and in their difference map in Fig. 2D.
Similarly, from high energy differential con-
ductance maps we can extract the position of
all near-surface oxygen dopants, as well as
determine which dopants have changed [sec-
tion 1 of ( 21 )]. The gap changes in Fig. 2D are
clearly linked to the atomic manipulations,
but in a rather unexpected manner: The al-
tered Bi sites mark the boundary between re-
gions of increasing and decreasing gaps,
whereasthegaponthesitesitselfishardly
affected. Whereas one would expect the ma-
nipulation of oxygen dopants to have a strong
effect on the gap, the contribution to the gap
modifications of the near-surface dopants we
manipulate does not appear to be the dominant
one: The correlation between their location
and where the gap changes is only moderate,
and when we manipulate a single near-surface
dopant atom, the gaps in its vicinity shift by a
few milli–electron volts at most (fig. S6). This
observation is in line with a previous study
that found these dopants (i.e., those with a
resonance at−1eV<E<−0.4 eV) to have a
much weaker correlation to the intrinsic gap
inhomogeneity than the ones closer to the
CuO 2 plane ( 9 ). The dominant contribution
of manipulated Bi atoms and the secondarynature of the manipulated oxygen atoms are
exemplified by the simulation shown in Fig.
2F. As discussed below, the simulation, which
is in good agreement with experiment, uses
a model that takes into account only Bi
manipulations.
Atomic scale difference images of two con-
secutive manipulations of the same Bi atom
are shown in Fig. 3A. Two observations stand
out. First, whenever a surface modification
reverts in a subsequent electric field treatment,
the gap reverts back as well. Consequently,
the difference images between the first and
third map,D 3 − 1 (r), is featureless (fig. S11),
andD 3 − 2 (r)=−D 2 − 1 (r)(Fig.3A,rightand
left, respectively). For isolated manipulation
events, even the full spectrum reverts to the
original configuration (fig. S12). Second, the
direction along which the gap is altered ap-
pears to be linked to the direction of the sur-
face Bi atom repositioning. As can be seen
from Fig. 3A and as shown schematically in
Fig. 3B, each time a Bi atom moves down be-
low (up into) the BiO plane, a neighboring atom
laterally shifts toward (away) from it, leading
to an enhancement of the spectral gap in the
direction of this shift.
To quantify the direction of the gap change
in more detail, we average theD(r)images
around each surface Bi manipulation after
aligning their direction of maximum gap in-
crease [see section 4 of ( 21 )].AsFig.4Ashows,
a clear dipole profile, centered at the sur-
face modification in an otherwise unaffected
environment, is obtained. The two lobes of
thedipolehaveoppositesigns,areafewMasseeet al.,Science 367 ,68–71 (2020) 3 January 2020 2of4
101286420g (nS)-100 -50 0 50 100
Energy (meV)160
meV55
meV
1 nm 1 nm
before
after 1 nm
-15 meV +15 meV-15 meV +15 meVAB C DEDcalc(r)FΔi+1 - Δ (^) i (meV)
8
12
4
0
3
number of pixels (x10 )
-10 010
i = 1
i = 2
i = 3
i = 4
D2-1(r)
Δ
(r
)
Vs > 1.2 V
gap increased
1 nm
Fig. 2. Gap modification.Maps of the peak-to-peak gap,D, taken (A)before
and (B) after field-induced atom manipulation at 1.5 V and ~100 pA. Dots mark
the locations where Bi atoms have been manipulated. (C) Spectrum taken
before and after manipulation on the location indicated by an X in (A) and (B),
showing a clear change inD.(D) Difference of the gap maps taken (A) before
and (B) after manipulation:D 2 − 1 (r)=D 2 (r)–D 1 (r). Black dots mark the
same locations as in (A) and (B), the dashed box indicates the area of Figs. 1C
and 3A. (E) Histograms ofD=Di+1−Difor four consecutive manipulations;
i= 1 corresponds to the difference map in (D). For all maps, the average change
in the gap size is zero. (F) Simulation of the difference map in (D) using our
model of a shifting Gaussian. The fitted dipole profile (Fig. 4B, bottom) is
placed on every manipulated site (blackdots) using the orientation extracted
from fits to the data (fig. S13) [see also section 4 of ( 21 )].
RESEARCH | REPORT