changes with the magnetic field direction.
These real-space patterns yield two distinct
classes of Fourier images, respectively showing
two and four of the six original high-intensity
segments. When the field is applied alongGK,
two bright segments are found along the per-
pendicularGM direction, whereas the remain-
ing four are strongly suppressed. When the
field is directed alongGM, the corresponding
two segments are dark, whereas the other four
segments are bright.
These QPI patterns can be understood di-
rectly from the picture of a segmented Fermi
surface in the superconducting state under
an in-plane magnetic field. Because of the
direction-dependent pair-breaking effect, only
a portion of the normal-state Fermi surface
becomes gapless, and thus only the hotspots
located in this gapless segment are activated
for scattering at zero energy. To illustrate this,
in Fig. 4, G to I, we present the spectral func-
tion of the normal state, the superconducting
state with magnetic field alongGK, and the
superconducting state with magnetic field
alongGM, respectively. In the normal state,
we observe a hexagonally warped contour,
which gives rise to six symmetric segments
in the QPI pattern (Fig. 4A) associated with
scattering between the hotspots at the neigh-
boring tips of the star. In the superconducting
state at zero field, there is no Fermi surface,
owing to the hard gap. Nevertheless, it re-
emerges atBext=40mT,asaresultofthe
gap being filled with quasiparticle states.
However, this new Fermi surface consists of
only segments of the normal-state Fermi sur-
face, whose size and location are controlled by
the field strength and orientation (Fig. 4, H
and I). Scattering between the available hot-
spots on the segmented Fermi surface gives
rise to those bright segments in the observed
QPI pattern (Fig. 4, B and C), as represented
by the indicated momentum transfer vectors
Qi. By contrast, the gapped hotspots cannotparticipate in quasiparticle scattering processes,
leading to suppression of QPI intensity at cor-
responding wave vectors.
Notably, scattering between Bogoliubov
quasiparticles on the segmented Fermi surface
is strongly dependent on the superconducting
coherence factors. Zero-energy quasiparticles
that originate from theE> 0 andE<0branches
at zero field are the symmetric and anti-
symmetric superpositions of electron and
hole states, respectively. In the presence of
nonmagnetic impurities, scattering between
the two opposite branches is constructively
enhanced, whereas scattering within each
branch is destructively suppressed. For this
reason, even though the wave vectorQ 1 con-
nects the same pair of hotspots in both Fig. 4H
and Fig. 4I, quasiparticle scattering at this
wave vector is present in the former case but
suppressed by coherence factors in the latter.
This can be clearly seen in Fig. 4, B and C,
indicating that the gapless excitations are
Bogoliubov quasiparticles rather than normal
electrons. To further substantiate the above
theoretical analysis, we perform a full numer-
ical simulation of the proximitized topological
surface state under an in-plane magnetic field.
By using recursive Green’s functions ( 22 ), we
calculatethelocalDOSinthepresenceofran-
dom disorder and construct its Fourier image.
Our numerical QPI patterns (Fig. 4, D to F) show
good agreement with the experimental data.
Our results reveal the strong impact of
Cooper pair momentum caused by screening
supercurrent on the quasiparticle energy dis-
persion. The observation of the segmented
Fermi surface of Bogoliubov quasiparticles
paves the way for further STM study of
pair density wave and Fulde-Ferrell-Larkin-
Ovchinnikov states in unconventional super-
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1384 10 DECEMBER 2021•VOL 374 ISSUE 6573 science.orgSCIENCE
Fig. 4. QPI patterns of the segmented Fermi surface.(A) QPI at zero magnetic field outside of the
superconducting gap. The six bright segments correspond to scattering between the tips of the normal-state
Fermi surface. (B) QPI atB= 40 mT alongGK atV= 0 mV. The two bright segments correspond to
vertical scattering between the tips of the“star”indicated in (H). (C) QPI atB= 40 mT alongGM
atV= 0 mV. The four bright segments correspond to diagonal scattering between the tips of the“star”
indicated in (I). (DtoF) Numerical simulations ( 22 ) for QPI in a hexagonally warped disordered Dirac surface
state corresponding to the magnetic fields as in (A) to (C). (GtoI) Spectral function displaying Fermi
surface contours corresponding to the magnetic fields as in (A) to (C).Q 1 ,Q 2 , andQ 3 indicate momentum
transfer vectors.
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