RAPID COMMUNICATIONSPHYSICAL REVIEW B 93, 161112(R) (2016)

Direct observation of nonequivalent Fermi-arc states of opposite surfaces in thenoncentrosymmetric Weyl semimetal NbP
S. Souma,1 Zhiwei Wang,2 H. Kotaka,2 T. Sato,3 K. Nakayama,3 Y. Tanaka,3 H. Kimizuka,3 T. Takahashi,1,3 K. Yamauchi,2T. Oguchi,2 Kouji Segawa,4 and Yoichi Ando2,51

WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
2
Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan3
Department of Physics, Tohoku University, Sendai 980-8578, Japan
4
Department of Physics, Kyoto Sangyo University, Kyoto 603-8555, Japan
5
Institute of Physics II, University of Cologne, Köln 50937, Germany(Received 6 October 2015; revised manuscript received 5 March 2016; published 20 April 2016)

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on noncentrosymmetric Weyl semimetal candidate NbP, and determined the electronic states of both Nb- and P-terminated surfaces.
We revealed a drastic difference in the Fermi-surface topology between two types of surfaces, whereas the Fermi
arcs on both surfaces are likely terminated at the surface projection of the same bulk Weyl nodes. A comparisonof the ARPES data with our first-principles band calculations suggests a notable difference in the electronic
structure at the Nb-terminated surface between theory and experiment. The present result opens a platform forrealizing exotic quantum phenomena arising from the unusual surface properties of Weyl semimetals.
DOI: 10.1103/PhysRevB.93.161112

Weyl semimetals (WSMs) manifest a novel quantum stateof matter where the bulk conduction and valence bands cross at
discrete points with linear dispersion in all the momentum (k)directions in a three-dimensional (3D) Brillouin zone (BZ),
which can be viewed as a 3D analog of graphene breaking
time-reversal or space-inversion symmetry [1–9]. The bandcrossing point is called the Weyl node that is effectively
described by the Weyl equation [1,2,6], and is robust against
perturbations expressed in terms of Pauli matrices. The Weyl
node always comes in pairs acting as a monopole (source) or
antimonopole (sink) of Berry curvature in k space, associatedwith positive or negative chirality, respectively [10,11]. The
WSMs can host many exotic physical phenomena suchas anomalous Hall effects, chiral anomalies [12,13], andmagnetoelectric effects [14–17].
The most intriguing prediction for WSMs is the emergenceof Fermi arcs on their surfaces. Unlike 2D metals showing
closed Fermi-surface (FS) pockets, the Fermi arcs in WSMs
are disjoint, open curves [see Fig. 1(a)]; they must startand end at the projections of a pair of bulk Weyl conesof opposite chiralities onto the surface BZ, independent of
surface orientations and terminations. The shape of the Fermi
arcs in two opposite surfaces in WSMs is not equivalent witheach other due to the breaking of time-reversal or inversion
symmetry. Such a surface state is a characteristic of WSMs,
leading to the predictions of intriguing phenomena such as
quantum interference [18] and quantum oscillations [19], inwhich the propagation of electrons across the top and bottom
surfaces through the bulk plays an essential role. Thus, asimultaneous consideration of both surfaces is necessary tounderstand the unusual physical properties of WSMs.
Recently, density functional theory predicted thattransition-metal monopnictide family TaAs, TaP, NbAs, and
NbP are WSMs with 12 pairs of Weyl nodes in bulk BZ [20,21].
These compounds crystallize in a noncentrosymmetric structure [the I 41 md space group; Fig. 1(b)], distinct from the
WSM candidates which break time-reversal symmetry [1,4,5].
Angle-resolved photoemission spectroscopy (ARPES) of
2469-9950/2016/93(16)/161112(6)monopnictides, in particular, TaAs, confirmed the existenceof Fermi arcs on anion-terminated surfaces and bulk Weylnodes [22–29], consistent with the theoretical prediction. To
firmly establish the WSM nature of monopnictides and to build
a basis for the proposed exotic phenomena, it is of particularimportance to experimentally establish the fermiology of both
surfaces.
In this Rapid Communication, we report ARPES resultson NbP in which ultrahigh carrier mobility and extremely
large magnetoresistance [30,31] were recently reported. We
determined the electronic states of both Nb- and P-terminatedsurfaces. At the P-terminated surface, we observed a tadpoleshaped FS at the BZ corner, whereas such a signature
is absent at the Nb-terminated counterpart, demonstrating
nonequivalent electronic states between two types of surfaces.
We discuss the implications of our findings in terms of thebulk Weyl nodes and physical properties related to the surface
Fermi arc of WSMs.
We have carried out first-principles band calculations (seeSec. 3 of the Supplemental Material [32] for details), andconfirmed that NbP is a WSM with two kinds of Weyl-nodepairs W1 and W2 [20,21,33] [see Fig. 1(c)]. The Weyl-conelike dispersion is recognized from the bulk bands in Figs. 1(d)and 1(e) calculated along cuts crossing W1 or W2.
At first we explain how to distinguish the Nb- and Pterminated surfaces. NbP crystal has two possible cleaving
planes, as indicated by the dashed or solid arrows in Fig. 1(b).
Among these, the cleave occurs easier by breaking two Nb-P
bonds per unit cell (orange line) [24,25,33], rather than bybreaking four bonds (dashed line), which is supported by
our atomic-force-microscopy measurements (see Sec. 2 of the
Supplemental Material for details). This is also consistent withour calculations in which a slab with a fourfold coordinatedsurface is 2.5 eV per unit cell more stable than that with twofold
coordination. Therefore, when we cleave the surface with the[001] axis directed upward as in Fig. 1(b), the Nb-terminated(001) surface must always appear. This in return indicatesthat the other side of the crystal, i.e., the (001̄) surface, is161112-1©2016 American Physical Society

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PHYSICAL REVIEW B 93, 161112(R) (2016)

FIG. 1. (a) Schematics of the Dirac-cone and Fermi-arc surface states at opposite surfaces of the topological insulator (top) and WSM(bottom), respectively. (b) Left: Crystal structure of NbP with two possible cleaving planes (arrows). Right: Side view of the crystal structure.
(c) Bulk and surface BZs of NbP. The green shaded area is a mirror plane which is projected onto the ¯ X̄ line, and red and green dots highlightthe Weyl nodes (W1, W2). (d), (e) Calculated bulk-band dispersion along cuts crossing W1 and W2, respectively. (f), (g) ARPES spectrum
measured at hν = 200 eV for the Nb- and P-terminated surfaces, respectively. (h), (i) Second derivative of ARPES intensity along ¯ X̄ cut
for the Nb- and P-terminated surfaces, respectively. (j), (k) Calculated band structure for a slab of 7-unit-cell NbP, for Nb- and P-terminatedsurfaces, respectively. The radius of circles represents the surface spectral weight. The projection of bulk bands is shown by the yellow shade.
The gray shaded area is outside of the band plots in (h) and (i).

P terminated. In this regard, it can be said that the P- andNb-terminated surfaces are “opposite” surfaces. Two suchterminations do not coexist on a single cleaved surface aslong as the crystal is composed of a single domain. We
accumulated the ARPES data for many cleaves, and confirmedthat the obtained data are always classified into two categories
attributed to either the Nb-terminated or the P-terminatedsurface, suggesting the presence of an easy cleaving plane
and the single-domain nature of our crystal.
Figures 1(f) and 1(g) show the energy distribution curve(EDC) of NbP for the Nb- and P-terminated surfaces,
respectively, measured with hν = 200 eV (see Sec. 1 of
the Supplemental Material for experimental details). In both
surfaces, one can recognize a sharp P 2p core-level feature ata binding energy EB of ∼130 eV. At EB = 32 eV, we observe
another peak originating from the Nb 4p core levels (inset)
which is apparently weaker for the P-terminated surface [notethat the reason why the intensity of Nb 4p is much lower thanthat of P 2p in Figs. 1(f) and 1(g) is due to an approximately
ten times weaker photoionization cross section of the Nb 4p
orbital]. Figures 1(h) and 1(i) display a comparison of the
ARPES intensity between two terminations along the ¯ X̄
cut. At the Nb-terminated surface, there exists a holelike
band at X̄ which has a top of dispersion at EB ∼ 0.25 eV,
together with a V-shaped band within 0.3 eV of EF , whereas
at the P-terminated surface, the V-shaped band is absent and aholelike band touches EF around X̄. As shown by a comparisonof experimental and calculated band dispersions in Figs. 1(i)and 1(k), the calculated surface bands reproduce the overall
experimental band dispersions for the P-terminated surface,whereas the experimental holelike band away from EF ishardly reproduced for the Nb-terminated surface [Figs. 1(h)and 1(j)].
We begin with the electronic states of the P-terminatedsurface. Figure 2(a) displays a schematic summary of theexperimentally observed FS of NbP around X̄. The energy

bands labeled here, S1 –S4 , all of which are surface states [23],obey different selection rules of photoelectron intensity. For
example, band S1 , which is likely connected to the projectionof Weyl pairs W1 and W2 [Fig. 2(a); we will come back to thispoint later], is dominantly seen at hν = 21 eV with verticalpolarization [Fig. 2(b)]. On the other hand, the intensity ofouter band S2 is greatly enhanced with circularly polarized
50-eV photons [Fig. 2(c)]. The intensity difference is also
recognized from a comparison of the band dispersion along
cut A in Fig. 2(d) where the distance between the two kF
points (arrows) is wider at hν = 50 eV than that at 21 eV. Suchband behavior also leads to the difference in the FS topology;i.e., S1 forms a closed pocket away from X̄, as seen from theabsence of EF crossing in cut B, whereas S2 forms a tadpole
FS, as suggested by its EF crossing in cut B [Fig. 2(d)]. Thereexist other dog-bone-shaped FSs, S3 and S4 , elongated along
X̄ M̄ [Fig. 2(a)], which are better resolved with horizontally
polarized 21-eV photons [Fig. 2(e)]. We found that overall the
cross-shaped FS in the experiment is reasonably reproducedby our calculation [Fig. 2(f)]. In particular, the k locationof the “head” of the tadpole FS and its narrow “tail” show
good correspondence with each other (some differences suchas the absence/appearance of S1 and S3 pockets can be also
recognized).
Now we turn our attention to the electronic structure of
the Nb-terminated surface, which has been hardly studied inmonopnictides [27]. Figures 3(a) and 3(b) display ARPESintensity mapping at EF and the corresponding secondderivative intensity of the EDCs, respectively. At first glance,
FS looks very different from that of the P-terminated surface.
The cross-shaped FS is absent, and the finite spectral weight¯ These differences are not attributable tois observed around .
the simple energy shift between opposite surfaces as visible
from several energy slices in Figs. 2(b) and 3(d).
The electron versus holelike nature of the FSs in Fig. 3(c)can be signified by tracing the experimental band dispersion

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PHYSICAL REVIEW B 93, 161112(R) (2016)

FIG. 2. (a) Experimental FS around X̄ for the P-terminated surface. Fermi wave vectors (kF ’s) are plotted with gray dots. The projectionof Weyl nodes estimated from the present experiment is also indicated by circles and diamonds. (b) Second-derivative intensity of the EDCs
at EB = EF , 0.1 and 0.2 eV, measured with vertically polarized 21-eV photons. The polarization vector of lights is indicated by the arrow.
Experimental FSs are overlaid for EB = EF . (c) Same as (b) but measured with circularly polarized 50-eV photons. (d) Second-derivative
intensity in cuts A–C, measured with hν = 21 eV (top) and 50 eV (bottom). The dashed curves are a guide to the eyes to trace the band
dispersions. (e) Second-derivative intensity at EB = 0.1 eV measured with horizontally polarized lights of hν = 21 eV. (f) Calculated FS for
the P-terminated surface around X̄. The surface weight is reflected by the gradual color scale. The k window is the same as (a).

¯ we identify
at various k cuts shown in Fig. 3(e). Around ,
two kinds of FSs arising from bands S5 and S6 : Band S5
forms a circular hole pocket, while band S6 has an electronlike¯ as seen from cuts A, C, and D in
dispersion centered at ,Fig. 3(e). Around X̄, we identify a large hole pocket (S8 )with a holelike character (cuts E–G). This large pocket isconnected to a small hole pocket S7 (cut H). We also finda faint signature of anisotropic FS (S9 ) elongated along ¯ X̄
(the band dispersion can be traced by analyzing the momentum
distribution curves, as detailed in Sec. 6 of the Supplemental
Material). It is noted that S8 and S9 are likely connected to the
Weyl pairs, as discussed later (for k cuts crossing the projectionof Weyl nodes, see Sec. 7 of the Supplemental Material).
The FS topology for the Nb-terminated surface is markedly
different between experiment and calculation, as visible from
Figs. 3(c) and 3(f). In particular, the FS at ¯ is absent in
the calculation. Also, the shapes and numbers of FSs aroundX̄ are different. This is not ascribable to a difference in thedoping level between experiment and calculation; possible surface relaxations, reconstructions, and/or enhanced interactions
among the surface Nb 4d orbitals may need to be considered
to explain such differences, as discussed in Secs. 4 and 5 of
the Supplemental Material. To further clarify the origin of
the differences between experiment and calculation, it would
be necessary to determine the surface structural parameters
using, e.g., I -V low-energy electron diffraction and surface
x-ray diffraction, and carry out the band calculations with an
input of these parameters. It would also be useful to performthe ARPES measurements on the transition-metal-terminatedsurface of other monopnictides and compare the results withthe corresponding band calculations to clarify whether or not
the discrepancy is a unique feature of NbP.
Now we discuss the characteristics of observed surface
states in relation to the location of bulk Weyl nodes. Figure 4(a)161112-3

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FIG. 3. (a), (b) ARPES-intensity mapping at EF and second-derivative intensity of the EDCs for the Nb-terminated surface, respectively,plotted as a function of kx and ky measured with hν = 50 eV. (c) Experimental FS for the Nb-terminated surface. kF points extracted by tracing
the band dispersion are plotted with gray dots. The projection of Weyl nodes estimated from the present experiment is also indicated by circles
and diamonds. (d) Second-derivative intensity plots of the EDCs at EB = 0.1 and 0.3 eV. (e) Second-derivative intensity along cuts A–H in (c).
(f) Calculated FS for the Nb-terminated surface.

summarizes the present ARPES result of NbP, highlighting
the significant differences between opposite surfaces. As
mentioned above, there exist two kinds of bulk Weyl pairs
W1± and W2± (± represents the positive/negative chirality)
in NbP [20,21,33]. It is expected that Weyl nodes projected
onto the (001) or (001̄) surface terminate two Fermi arcs
for W2 due to the projection from two pairs, whereas thosefor W1 terminate a single Fermi arc, independent of surface
terminations. This consideration led us to experimentally pin
down the location of Weyl nodes, since the projection of Weylnodes must appear at (or very close to) the intersection of
FSs for opposite surfaces (note that it is essential to determine
the electronic structure for both terminations to apply thismethod, while such a study has not been performed so far
in transition-metal monopnictides). While there exist three
types of such intersections as indicated by the solid and open

circles in Fig. 4(b), the solid circles are most likely due to theprojection of Weyl pair W2± , since (i) the calculated distance
between adjacent Weyl nodes is wider for W2 than that forW1 [20,21,33], and (ii) the outer tadpole FS commonly forms
a Fermi arc in monopnictides [22–26,28,33] [note that the−1
distance between adjacent Weyl nodes for W2 (0.06 Å ) ismuch smaller than that of TaAs (∼ 0.15 Å−1 ) [24], suggesting
the essentially weak spin-orbit coupling in NbP]. It turned out
to be rather difficult to determine the exact location of theW1 pair since the FS for opposite surfaces overlaps with eachother around X̄, as visible in Fig. 4(b). Nevertheless, one canconclude that W1− and W1+ are very close to each other since
the FS is nearly on the ¯ X̄ line. In addition, the W1 pairs
on both sides of X̄ are not likely traversed by the FS, sinceband S2 appears to sink below EF along the X̄M̄ cut, as shownin cut C of Fig. 2(d). From these arguments, we propose in

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FIG. 4. (a) (Left) crystal structure of NbP and(right) schematics of experimental FS around X̄
for the opposite surfaces. Bulk Weyl nodes areillustrated by circles. The arrows indicate the Berrycurvature. (b) Direct comparison of experimental
FS between Nb-terminated (blue) and P-terminated(red) surfaces. The projection of Weyl nodes W2
at the intersection of FSs for opposite surfaces isoverlaid by solid circles, whereas other intersections
are shown by open circles. Possible Weyl pairs W1
are also indicated with diamonds. (c), (d) Schematics of Fermi arcs (solid curves) and trivial FSs(gray dashed curves) for the P- and Nb-terminatedsurfaces, respectively. The closed loop enclosing
three Weyl nodes is indicated by a green dashedrectangle. The arrows indicate the crossing points
of Fermi arcs and trivial FSs.

Fig. 4(c) the schematic FS for the P-terminated surface which
explains most consistently the present ARPES result. The FS(S2 ) which connects W2± can be viewed as a combination of
two Fermi arcs. Namely, one arc starts and ends at W2, and theother is connected to W1. It is thus likely that only S2 forms
a Fermi arc and all the others (S1 , S3 , S4 ) form a trivial FS.
At the Nb-terminated surface [Fig. 4(d)], one Fermi arc (S8 )starts and ends at W2, and the other is connected to anotherW2 pair in the opposite kx region. The Weyl nodes for W1 areconnected to each other via a single arc S9 , as inferred from theabsence of its FS crossing along X̄M̄ [cut E of Fig. 3(e)]. Thus,
S6 and S7 are likely the trivial FSs. We emphasize, however,that the Fermi-arc connectivity is not unique and depends onthe details of the surface [20]; hence, at this stage, the above
interpretation is just a likely possibility and its verification
requires higher-resolution data.
To examine the WSM nature of NbP, we choose a closed
k-loop surrounding the odd number of (three) Weyl nodes andcount the total number of FS crossings. Since only an open
Fermi arc can cross this loop an odd number of times, thetotal odd number of FS crossings would be a hallmark of
the existence of Fermi arcs in WSM [23,24,28,33]. For the
P-terminated surface [Fig. 4(c)], the Fermi arc (S2 ) crosses
this loop only once, and the trivial FSs (S1 , S3 , and S4 ) crosssix times. For the Nb-terminated surface [Fig. 4(d)], the Fermi
arcs (S8 and S9 ) cross this loop three times, and the trivial FSs(S6 and S7 ) cross four times. In either case, the FSs cross the
k loop seven times in total, supporting the WSM nature of
NbP.

The observed nonequivalent nature of the Fermi arcs
between Nb- and P-terminated surfaces suggests a possibility
to control the shape of the Fermi arcs by tuning the surface
conditions, laying the foundation for the Fermi-arc engineeringof WSMs. It is also remarked that the nonequivalence ofthe surface states should be seriously taken into account inmonopnictides, as long as the surface transport and spectroscopic properties, such as quantum oscillations in magnetotransport, quasiparticle interference in tunneling spectroscopy,
and possible gating devices utilizing ultrathin films, areconcerned.
In conclusion, we have reported ARPES results on NbP and
elucidated the electronic states of the Nb- and P-terminatedsurfaces. We revealed that the FS topology is considerably different between these two terminations. We also found that thefirst-principles calculations hardly reproduce the experimental
electronic structure for the Nb-terminated surface, unlike
the P-terminated counterpart. The present result provides apathway for exploring exotic quantum phenomena utilizing
the Fermi-arc properties of WSMs.

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We thank D. Takane, N. Inami, H. Kumigashira, K. Ono,
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measurements. This work was supported by MEXT of
Japan (Innovative Area “Topological Materials Science”,
Grant No. 15H05853), JSPS (KAKENHI 15H02105,
26287071, 25287079, 25220708, and Grant-in-Aid for JSPS
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