cannot be resolved, effectively leading to only
twoobservable arcs. Most photoemission studies
to date ( 20 – 22 ) classify these nodes as having
jCj¼2, whereas recent all-optical measure-
ments ( 25 )findaChernnumbercloseto4.The
second reason is the difficulty in preparing
clean and flat surfaces by cleaving or sputter-
ing and annealing, which has resulted in roughor nonstoichiometric surfaces for all previously
examined candidates, causing band broaden-
ing that can wash out signatures of spin-split
bands caused by SOC. In this work, we overcomeSCIENCEsciencemag.org 10 JULY 2020•VOL 369 ISSUE 6500 181
Fig. 2. Electronic characterization
ofthe bulk electronic structure
of PdGa measured on the
(100) surface of enantiomer A.
(AtoC) Comparison between
ARPES spectra (left) and ab initio
calculations (right) along high-
symmetry lines that pass through
theGand R points. Multifold
fermions are indicated by red
arrows, and spin-orbit splitting is
indicated by black arrows. Spectra
were measured athv= 550, 552,
and 620 eV in (A) to (C), respectively,
all with linear-vertical polarization
(LV). E-EF, the binding energy with
respect to the Fermi-level;
k||, the in-plane wave vector. (Dto
E) Comparison between experimen-
tal Fermi surfaces (left) and ab initio
calculations (right). (D) shows the
Fermi surface in the high-symmetry
plane that contains the G point
(measured withhv= 620 eV, LV polarization), whereas (E) contains the plane that includes the R point (measured withhv= 540 eV, LV polarization). The blue dashed
lines indicate the boundary of the bulk Brillouin zone. Ab initio calculations includekzbroadening of 0.1 Å−^1.
-0.5 0 0.5 1-1. 5-1-0.50k\\ (Å-1)-1X-1.5-1-0.50
M RMX RXE-E(eV)FE-E(eV)FE-E(eV)F-1 -0.5 0 0 .5 1-1-0.500 .51-1 -0.5 0 0 .5 1-1-0.500 .51kx (Å-1) kx (Å-1)ky(Å-1k)(Åy-1)ABCDELow High-1.5-1-0.506-fold fermionX RX-1.5-1-0.50M R M6-fold fermionX X-1. 5-1-0.504-fold fermion0 0.5 1 1.5k\\-1 -0.5 0 0.5 1-1-0.500 .51XM-1 -0.5 0 0 .5 1-1-0.500 .51X
MR-1 -0.5 0 0.5 1-1. 5-1-0.50Fig. 3. Surface electronic struc-
ture of the (100) surface of
enantiomer A.(A) Ab initio slab
calculation of the Fermi surface in
the (100) plane (i.e.,kxversus
kyplane) showing surface Fermi arcs
(indicated by a red arrows),
superimposed by projected bulk
band structure calculation (solid
blue lines). (B) Experimental Fermi
surface measured withhv=60eV
and linear-horizontal (LH) polariza-
tion. Red arrows indicate Fermi arcs,
whereas purple arrows indicate
additional surface states that
overlap with the projected bulk
states atG.(C) Experimental Fermi
surface perpendicular to the sample
surface (i.e.,kyversuskzplane),
showing that the Fermi arcs and
surface states (indicated by red and
purple arrows, respectively) show
negligible dispersion along the
kzdirection. Conversion from photon
energy was performed within free-
electron final state approximation
with inner potential ofV 0 =12eV.
(D) Magnified Fermi surface
measured in the region of the red dashed rectangle shown in (B) withhv= 30 eV and LH polarization. Red arrows indicate spin splitting of Fermi arcs. (E) Band dispersion
measured along the path in momentum space indicated by the red dashed arrow shown in (D) that is crossing the Fermi arcs, and red arrows indicate their spin splitting.
(F) Magnified version of (E). Insets show the momentum distribution curve (MDC) and energy distribution curve (EDC) along the dashed blue lines. a.u., arbitrary units.
00.10.20.30.40.50.60.40.30.20.10-1-0.500.51-1 -0.5 0 0.5 (^1) -1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
Fermi-
arcs
surface
states
Fermi-
arcs
Fermi-
arcs
kx (Å-1) kx (Å-1) k\ (Å-1)
ky
(Å
-1
)
kz
(Å
-1)
kx (Å-1) kx (Å-1)
k
(Åy
-1
)
splitting
cut
0 0. 1 0 .2 0. 3 0 .4
-0.4
-0.3
-0.2
-0.1
0
cut
splitting
0.15 0 .2 0. 25
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
~0.015 Å-1
MDC
intensity (a.u.)
MDC
EDC
E-E
(eV)F
EDC
intensity (a.u.)
kx (Å-1)
~60 meV
A B C
D E F
zoom
surface Low High
spin-up
surface
spin-down
splitting
-2 -1.5 -1 -0.5 0 0.5 1 1.5
3
3.5
4
4.5
5
5.5
6 surface states Fermi-arcs
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