Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family

Article abstract of DOI:10.1038/nmat4457

Topological Weyl semimetals (TWSs) represent a novel state of topological quantum matter which not only possesses Weyl fermions (massless chiral particles that can be viewed as magnetic monopoles in momentum space) in the bulk and unique Fermi arcs generated by topological surface states, but also exhibits appealing physical properties such as extremely large magnetoresistance and ultra-high carrier mobility. Here, by performing angle-resolved photoemission spectroscopy (ARPES) on NbP and TaP, we directly observed their band structures with characteristic Fermi arcs of TWSs. Furthermore, by systematically investigating NbP, TaP and TaAs from the same transition metal monopnictide family, we discovered their Fermiology evolution with spin-orbit coupling (SOC) strength. Our experimental findings not only reveal the mechanism to realize and fine-tune the electronic structures of TWSs, but also provide a rich material base for exploring many exotic physical phenomena (for example, chiral magnetic effects, negative magnetoresistance, and the quantum anomalous Hall effect) and novel future applications.

Full text of DOI:10.1038/nmat4457

LETTERS
PUBLISHED ONLINE: 2 NOVEMBER 2015 | DOI: 10.1038/NMAT4457
Evolution of the Fermi surface of Weyl semimetals
in the transition metal pnictide family
Z. K. Liu1 , L. X. Yang
,2,3†
4,5,6†
, Y. Sun , T. Zhang , H. Peng , H. F. Yang , C. Chen , Y. Zhang ,
7†
4,5
5
5,8
5
6
Y. F. Guo1 , D. Prabhakaran , M. Schmidt , Z. Hussain , S.-K. Mo , C. Felser , B. Yan
,2,5
5
7
6
6
7
1,2,7
and Y. L. Chen1
,2,3,4,5
*
Topological Weyl semimetals (TWSs) represent a novel state
In comparison to 3D topological Dirac semimetals (TDSs;
1–4
of topological quantum matter which not only possesses refs 17–20), which possess bulk Dirac fermions, 3D TWSs can
Weyl fermions (massless chiral particles that can be viewed be realized by breaking either time reversal symmetry (TRS) or
as magnetic monopoles in momentum space) in the bulk inversion symmetry in 3D TDSs (refs 1–3,21,22)—thus a Dirac
and unique Fermi arcs generated by topological surface point can be split into a pair of Weyl points of opposite chirality. In
states, but also exhibits appealing physical properties such the past few years, several compounds (for example, Y
2
Ir
(ref. 2)) have been proposed to be TWS candidates
2
O (ref. 1)
7
as extremely large magnetoresistance and ultra-high carrier and HgCr
2
Se
4
5–8
mobility . Here, by performing angle-resolved photoemission with spontaneously broken TRS. Unfortunately, none have been
spectroscopy (ARPES) on NbP and TaP, we directly observed experimentally confirmed so far.
3
,4,22
their band structures with characteristic Fermi arcs of TWSs.
On the other hand, recent theoretical investigations
have
Furthermore, by systematically investigating NbP, TaP and indicated that various compounds with spontaneously broken
TaAs from the same transition metal monopnictide family, we inversion symmetry can also be TWS candidates, with a promising
discovered their Fermiology evolution with spin–orbit coupling family of transition metal monopnictides (including NbP, NbAs,
(SOC) strength. Our experimental findings not only reveal the TaP and TaAs; refs 3,4). In this family of materials, a total of twelve
mechanism to realize and fine-tune the electronic structures pairs of Weyl points are predicted to exist within a 3D Brillouin
of TWSs, but also provide a rich material base for exploring zone (BZ), with each pair residing across one of the two crystalline
many exotic physical phenomena (for example, chiral magnetic mirror planes (Fig. 1a) and connected by unique surface Fermi arcs
eꢀects, negative magnetoresistance, and the quantum anoma- (Fig. 1b). In the formation of the TWS, the spin–orbit coupling
3
,4,9–11
lous Hall eꢀect) and novel future applications
.
(SOC) plays an essential role, and the splitting between the Weyl
Three-dimensional (3D) topological Weyl semimetals (TWSs) points and the Fermi arcs should increase with the strength of the
3
represent a new state of quantum matter recently proposed with SOC in different compounds (Fig. 1b) , as confirmed by our ab initio
unusual electronic structures that resemble both a ‘3D graphene’ calculations (Fig. 1c).
and a topological insulator (TI). On one hand, a TWS possesses
In this work, we first investigated the electronic structure of the
bulk Weyl fermions, unique chiral particles that disperse linearly TWS candidates NbP and TaP by angle-resolved photoemission
along all three momentum directions across a point—the Weyl spectroscopy (ARPES) (see Methods for details of the measurement)
point—which can be viewed as a magnetic monopole in momentum and observed the characteristic surface Fermi arcs in both
12
space . As a Weyl fermion possesses half the number of degrees compounds. The excellent agreement between our experiments and
3
,4
of freedom as a Dirac fermion, they always appear in pairs (with ab initio calculations (as well as other theoretical investigations )
1,3,4,12
opposite chirality) in materials
. On the other hand, a TWS also confirmed that NbP and TaP are TWSs. More importantly, we
possesses non-trivial topological surface states that form unique systematically studied the evolution of the band structures of NbP,
1,3,4
‘
Fermi arcs’ —unusual Fermi surfaces (FSs) consisting of un- TaP and another compound (TaAs) in the same family (which was
closed curves that start and end at Weyl points (Fig. 1b). The unusual recently confirmed as a TWS (refs 5,7,23–25)) and discovered a clear
bulk and surface electronic structure of 3D TWSs can give rise to increase in the separation between the Weyl points and Fermi arcs
many exotic phenomena, such as negative magnetoresistance, chiral from NbP to TaP, and to TaAs. Our result demonstrates for the first
magnetic effects, the quantum anomalous Hall effect, novel quan- time the crucial effect of the SOC in the formation and fine-tuning
tum oscillations (in magneto-transport) and quantum interference of the electronic structure of TWSs, including the Fermi-arc splitting
1
0,13–16
(
in tunnelling spectroscopy)
properties have also been discovered in some 3D TWS candidates, TWS materials with tailored electronic properties.
such as the ultra-high carrier mobility and extremely large mag- The crystal structure of NbP and TaP are illustrated in
. In addition, appealing transport and Weyl point separation—which will facilitate the design of new
5–8
netoresistance , making 3D TWSs not only ideal for fundamental Fig. 1d, showing they have the same crystal symmetry but
research, but also promising materials for novel applications.
slightly different lattice constants (NbP: a=b=3.33 Å, c =11.37 Å,
1
2
School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China. CAS-Shanghai Science Research Center, 239 Zhang Heng
3
4
Road, Shanghai 201203, China. Diamond Light Source, Didcot, Oxfordshire OX11 0QX, UK. State Key Laboratory of Low Dimensional Quantum Physics,
Collaborative Innovation Center of Quantum Matter and Department of Physics, Tsinghua University, Beijing 100084, China. Physics Department, Oxford
University, Oxford OX1 3PU, UK. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. Max Planck Institute
for Chemical Physics of Solids, D-01187 Dresden, Germany. State Key Laboratory of Functional Materials for Informatics, SIMIT, Chinese Academy of
5
6
7
8
†
Sciences, Shanghai 200050, China. These authors contributed equally to this work. *e-mail: yulin.chen@physics.ox.ac.uk
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NATURE MATERIALS DOI: 10.1038/NMAT4457
LETTERS
a
b
c
M
Y
X
NbP
TaP
TaAs
Γ
K
Surface
Fermi-arc
0.2
.4
0.6
.8
TaAs
High
Low
TaP
NbP
0
WP+
WP−
Dirac
point
Mirror
plane
(
001)
010)
100)
(
0
−
0.1 0 0.1
−0.1 0 0.1
−0.1 0 0.1
Increasing SOC/increasing splitting (ΔK)
(
kx (Å−1)
kx (Å−1)
kx (Å−1)
Mirror planes
d
e
g
h
1
00
1.5
1.5
NbP1
(
i)
01
1 mm (ii)
NbP2
NbP3
NbP4
0.5
0.5
0.5
−0.5
−1.5
0
010
β
β
α
−
α
(iii)
(iv)
f
Nb3d
P2s
Nb4s Nb4p
P2p
−1.5
Nb/Ta
−1.5
−0.5
0.5
kx (Å−1)
1.5
Low
Intensity (a.u.)
−1.5
−0.5
0.5
1.5
P
High
kx (Å−1)
200
100
0
Binding energy (eV)
Figure 1 | Properties of TWSs and characterization of NbP/TaP single crystals. a, Schematic of bulk and (001) surface Brillouin zones (BZs) of transition
3
,4
metal monopnictides. Twelve pairs of Weyl points predicted by theoretical investigations (see text for details) are marked as red and blue dots. Three
mirror planes of the bulk BZ are indicated. b, Illustration of the separation of a pair of Weyl points (with opposite chirality, marked as WP+ and WP−)
controlled by the SOC strength in diꢀerent compounds of the family. The dotted line represents the crystalline mirror plane, and the grey arcs represent the
surface Fermi arcs that connect the two Weyl points. c, Ab initio calculations show the Weyl points and surface Fermi arcs of NbP, TaP and TaAs,
respectively. The colour bar shows the surface contribution of the FS (white/0% to red/100%; the same scale is used for Figs 2–4. d, Crystal structure of
NbP/TaP, showing the ...A–B–C–D ... stacking of NbP/TaP layers. Red arrows indicate interlayer positions where cleavage possibly takes place. e, (i) Image
of NbP single crystals with the shiny flat surface used for ARPES measurements. (ii–iv) X-ray diꢀraction patterns from the (100), (001) and (010)
directions. f, Core-level photoemission spectrum of NbP shows characteristic Nb (4s, 4p, 3d) and P (2s, 2p) peaks. g, Broad FS mapping of NbP shows
excellent agreement with the ab initio calculations (overlapped red dotted plots). The orthogonal spoon-like and bowtie-like FS pockets are denoted as α-
and β-FSs, respectively. Blue colour bar indicates the ARPES spectra intensity (the same scale is used for Figs 2–4). h, Broad FS mapping of NbP from two
◦
adjacent cleaved NbP layers shows the mixing of two sets of electronic structures rotated by 90 with respect to each other. The orthogonal spoon-like and
bowtie-like FS pockets are denoted as α- and β-FSs, respectively.
TaP: a=b=3.33 Å, c = 11.39 Å). Taking NbP as an example,
its tetragonal unit cell is formed by four NbP layers with The stacking plots of constant-energy contours at different binding
a repeating ...—NbP -NbP -NbP -NbP —... stacking sequence energies (Fig. 2a) show the electronic structure evolution from the
In Fig. 2, we illustrate the detailed electronic structure of NbP.
1
2
3
4
26
without inversion symmetry (Fig. 1d) . As the interlayer distance isolated cross-shape FSs centred at the X and Y points to a more
between the Nb and P planes along the c-direction (0.167c/1.899 Å) complicated interconnected texture at higher binding energies. To
is about twice as large as their intra-layer distance (0.083c/0.944 Å), compare with the ab initio calculations (see Methods for details), in
the crystal can be naturally cleaved between adjacent NbP layers Fig. 2b we present three side-by-side comparison examples which
(
(
Fig. 1d and Supplementary Fig. 1) for the ARPES measurements demonstrate broad agreement: both the spoon-like and bowtie-like
Fig. 1e(i)). The high quality of the NbP crystals (see Methods for FS pockets (Fig. 2b(i)) and their evolution to nested textures at
details on sample synthesis) is verified by the sharp X-ray diffraction higher binding energies (Fig. 2b(ii), (iii)) can be nicely reproduced
patterns from all three crystalline orientations (Fig. 1e(ii–iv)), and by the calculation. Remarkably, the characteristic Fermi-arc type
the core-level photoemission spectrum (Fig. 1f), which clearly FS suggested by our ab initio calculation and previous theoretical
3
,4
indicates different characteristic Nb (4s, 4p, 3d) and P (2s, 2p) investigations clearly shows up as the spoon-like FSs, as we will
peaks. The overall electronic structure of NbP is captured in Fig. 1g discuss in detail later.
by a broad momentum-space mapping, which shows the global
In addition to the Fermiology and constant-energy contours,
FS topology across multiple BZs of the (001) surface that agrees the band structure for both the spoon and bowtie-like FSs with
excellently with our ab initio calculations (overlapped dotted plots). overlaid dispersions from calculation are presented as a 3D plot
The FS is comprised of two cross-shape features centred at the X in Fig. 2c, which again shows excellent agreement. In fact, the
and Y points, each containing two sets of orthogonal FS pockets: overall agreement between experiment and theory can be seen
the spoon-like and the bowtie-like pockets marked as α-FS and throughout the whole BZ, as illustrated by the comparison in
β-FS in Fig. 1g, respectively. As the broken Nb–P bonds are along Fig. 2d. Finally, to verify the surface nature of the spoon-like
orthogonal directions between adjacent cleaved NbP layers (see and bowtie-like FSs (as suggested by our ab initio calculations
Supplementary Fig. 1 for details), ARPES measurements sometimes and refs 3,4), we carried out photon-energy-dependent ARPES
2
7
show electronic structures from both kinds of layers (Fig. 1h, also measurements to investigate the k dispersion of these bands.
z
see Supplementary Figs 1 and 2 for more discussion).
In Fig. 2e, the ARPES spectra over a broad photon energy range
2
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NATURE MATERIALS DOI: 10.1038/NMAT4457
LETTERS
a
b
c
M
Eb = 0 meV
Γ
(
i)
X
X
X
Γ
X
X
Γ
X
M
Y
(i)
1.5
0.5
0.5
Γ
X
M
X
0.0
Γ
0.00
0
.4
.8
−
0.06
0
−
1.5
1
.2
−0.5
0
.12
Eb = 150 meV
1
.5
0
.0
1.0
(
ii) 1.5
.5
0.5
1.5
k
y
(Å −1
0.5
k
0.18
0.5
−1
)
0
.0
)
(Å
0
x
0
.24
.30
Γ
−
M
(
ii)
Y
Y
M
−
0.0
Y
0
Γ
Eb = 300 meV
0
.4
.8
0.36
(iii) 1.5
.5
0.5
1.5
0
0
0.42
1
.2
−
−
1.5
0.48
1.5
−
−1.0
0.5
−
1.5
0.5
k
y
−
0.5
0.0
−1.5 −0.5 0.5 1.5
kx (Å−1)
X
Γ
X
(Å −
−
0.5
−0.5
X
1
0.0 −0.5
−1
)
0
.5
)
x(Å
k
−
1.5
1
.5
d
e
(i)
M
Γ
Y
M
Y
Γ
Y
1
30
20
0
0
0
0
0
.0
.2
.4
.6
.8
High
1
1
1
.0
.2
Low
110
(ii)
M
X
Γ
Y
M
0
0
.0
.2
High
100
0.4
0.6
0.8
90
1.0
Low
1
.2
−
1.0
−0.5
0.0
k (a.u.)
0.5
1.0
−1.0 −0.5 0.0 0.5
1.0
k (Å−1)
||
|
|
Figure 2 | Overall electronic structure of NbP. a, Stacking plots of constant-energy contours at diꢀerent binding energies showing the band structure
evolution. Red square marks the first BZ. b, Side-by-side comparison of three constant-energy contours between experiments (left panels) and ab initio
calculations (right panels) shows overall agreement. c, 3D intensity plots of the photoemission spectra around the X (i) and Y (ii) points illustrate the
zoomed-in band structure for both the bowtie-like and spoon-like FSs with overlaid dispersions from calculation. d, Comparison of calculated (i) and
experimental (ii) dispersions along the high-symmetry directions across the whole BZ (M–X–0–Y–M). e, Plot of photoemission intensities at the Fermi
energy (EF) along the high-symmetry Y–0–Y direction (measurement position is along the green line marked on the FS in the lower panel) as a function of
photon energy (82–130 eV), showing the kz dispersion of diꢀerent bands.
(
(
52–130 eV) clearly demonstrate the absence of vertical dispersion excellent agreement with the ab initio calculations. The difference
that is, no k -dispersion, more information of photon-energy- between the measured band structure of TaP (Fig. 3) and NbP
z
dependent measurements can be found in the Supplementary (Fig. 2) is mainly quantitative: the bands that generate the spoon-like
Information), proving their surface nature (the photon-energy- FS have larger splitting in TaP (as will be discussed later with Fig. 4).
dependent measurement along both 0–X and 0–Y directions can
be found in the Supplementary Information).
The existence of Fermi arcs on the surface of TaP can also be
verified by counting the number of FS crossings along a closed
Similar measurements were also conducted on another member reference loop in the BZ (ref. 24) and obtaining an odd number
TaP) of the same family of compounds. As can be seen in Fig. 3, of FS crossings (Fig. 3d). As shown in Fig. 3e, along the closed
(
the overall electronic structure, such as the FS topology, including loop of 0–X–M–0, we observe seven (an odd number) FS crossings
the spoon-like and bowtie-like FS pockets (Fig. 3a,b), and the in total, which confirms the existence of the Fermi arcs (further
band dispersions along different directions (Fig. 3c,d), again show discussion and counting of the FS crossings in NbP can be found in
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NATURE MATERIALS DOI: 10.1038/NMAT4457
LETTERS
a
b
Eb = 0 meV
c
M
Γ
M
(i)
X
Y
X
Γ
X
X
Γ
X
X
X
Γ
(i)
1.5
Γ
M
0.00
X
0
.0
.4
0
.5
0
0.06
−
0.5
0
.8
0
.12
−1.5
1.2
Eb = 150 meV
0
.18
−0.5
0.0
1.5
(
(
ii)
1.5
1.0
Y
0
.5
0
.5
0
.0
0
.24
.30
0.5
−
0.5
(ii)
Γ
0
M
Y
−
1.5
M
Y
Γ
0
.0
0
.36
.42
.48
Eb = 300 meV
iii) 1.5
0.4
0.8
1.2
0
0.5
0
−0.5
1
.5
−
1.5
0.5
−0.5
−
0.5
−1.5
−
−1.5
−1.0
−0.5
0.5
1
.5 −1.5
X
Γ
X
0.5
1.5 −0.5 0.5 1.5
kx (Å−1)
0.0
0
.0 −0.5
d
e
Γ
Closed Fermi pocket
M
(
X
3 45
M
Y
M
High
Low
(
ii)
12
67
i)
0
0
0
0
0
.0
.2
.4
.6
.8
High
Low
1
2
3
Reference
loop
1
.0
4
1
.2
Γ
X
k|| (a.u.)
76
5
Fermi arc
Figure 3 | Overall electronic structure of TaP. a, Stacking plots of constant-energy contours of the full BZ at diꢀerent binding energies showing the band
structure evolution. b, Comparison of three constant-energy contours at diꢀerent binding energies between experiments (left panels) and ab initio
calculations (right panels) shows excellent agreement. c, 3D intensity plots of the photoemission spectra around the X (i) and Y (ii) point illustrate the
zoomed-in band structure for both the bowtie-like and spoon-like FSs with overlaid dispersions from calculation. d, Schematic of an arbitrary reference loop
in the momentum space crossing a closed Fermi pocket and a broken Fermi arc, the crossing points are denoted by the red crosses. e, (i) Comparison of
calculated and experimental high-symmetry cuts along a closed reference loop in the momentum space (M–X–0–M). Green arrows denote the Fermi
surface crossings. (ii) Schematic of the closed reference loop in the momentum space as well as the labelled positions of FS crossings along the loop.
Coloured dots show the position of the Weyl points in the BZ.
a
b
NbP
0
0
0
0
.8
C2
ΔK1
ΔK2
WP−
WP+
0.0
.2
.4
.6 C1
ΔK1
0
(
i)
.4
0
e
(
i)
(ii)
(iii)
ΔK2
C1
C2
.2
0.6
0
.15
ΔK1
−
0.1 0 0.1
0.2 0.4 0.6 0.8
c
TaP
C2
0
.8
0.6 C1
.4
ΔK1
ΔK2
ΔK2
(ii)
0.0
0
.10
NbP
TaP
ΔK1
0
.2
0
(
iii)
iv)
0.4
0.6
0
.05
(
i)
ΔK2
(ii)
C1
(iii)
C2
0
.2
0.8
−
0.1 0 0.1
0.2 0.4 0.6 0.8
d
TaAs
C2
(
0.00
ΔK1
ΔK2
0
.0
.2
TaAs
0
0
0
.6 C1
ΔK1
NbP
TaP
TaAs
0
SOC increasing
.4
Low
High
Low High
Intensity (a.u.)
0.4
0.6
Surface
contribution
(i)
ΔK2
(ii)
C1
(iii)
C2
.2
−
0.1 0 0.1
−0.1 0 0.1
0.2 0.4 0.6 0.8
k (Å−1)
k|| (Å−1)
k|| (Å−1)
|
|
Figure 4 | Evolution of the band structure with SOC. a, (i) Schematic plot shows a pair of Weyl points projected to the (001) surface BZ and the Fermi arc
grey curves) connecting them. (ii–iv) Comparison of the calculated (left) and ARPES measurement (right) of the spoon-like FSs, showing good agreement.
Red/blue dots denote the Weyl points of opposite chirality (labelled as WP+ and WP−). b–d, High-resolution ARPES measurements on the spoon-like FS
i) and associated band dispersions (ii,iii) for NbP, TaP and TaAs, respectively. The positions of the band dispersions presented in (ii,iii) are indicated by the
red dotted lines in (i). 1K1 and 1K2 represent the separation between the Weyl points and Fermi arcs, respectively. e, Summary of the extracted 1K1 and
K2 (from b–d) from the three compounds, plotted against the SOC strength. Error bars of 1K1 and 1K2 are estimated from the uncertainty in the fitting
(
(
1
of the momentum distribution curves at EF.
4
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NATURE MATERIALS DOI: 10.1038/NMAT4457
LETTERS
the Supplementary Information). In addition to the unique surface 6. Shekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in
Fermi arc, we also carried out ARPES measurements with high
photon energy to investigate the bulk Weyl fermions in TaP (see
Supplementary Information).
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7
8
.
.
After establishing the experimental band structures of NbP and
TaP, we now focus on the characteristic spoon-like FS, which 9. Yang, K.-Y., Lu, Y.-M. & Ran, Y. Quantum Hall effects in a Weyl semimetal:
forms the Fermi arcs that connect the two Weyl points of opposite
Possible application in pyrochlore iridates. Phys. Rev. B 84, 075129 (2011).
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chirality, as suggested by recent theoretical investigations and 10. Zyuzin, A. A. & Burkov, A. A. Topological response in Weyl semimetals and the
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our calculations (see Fig. 4a(i)). To investigate the evolution of
Fermi arcs over different compounds in this transition metal
monopnictide family, we also carried out ARPES experiments on
1
1. Hosur, P. & Qi, X. Recent developments in transport phenomena in Weyl
semimetals. C. R. Phys. 14, 857–870 (2013).
1
2. Balents, L. Weyl electrons kiss. Physics 4, 36 (2011).
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Information) in addition to NbP and TaP.
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1
5. Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface
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86, 195102 (2012).
which can be nicely reproduced by our calculations (Fig. 4a),
including each FS piece and its detailed shape, thus confirming the
1
3
three compounds are TWSs as proposed . The detailed FS topology
3
and associated band dispersions are illustrated in Fig. 4b–d, 17. Wang, Z. et al. Dirac semimetal and topological phase transitions in A Bi
indicating a clear increase of the separation between the Weyl points
(A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).
8. Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal,
Na Bi. Science 343, 864–867 (2014).
9. Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal
Cd As . Nature Mater. 13, 677–681 (2014).
1
1
(
1K1 in panel (i) and (ii) of Fig. 4b–d) and the Fermi arcs (1K2 in
3
panel (i) and (iii) of Fig. 4b–d) from compound NbP to TaP, and on
to TaAs. In Fig. 4e we collect the 1K1 and 1K2 values extracted
3
2
and plot them against the SOC strength of the three compounds, 20. Neupane, M. et al. Observation of a three-dimensional topological Dirac
clearly verifying their correspondence and showing that the SOC
3 2
semimetal phase in high-mobility Cd As . Nature Commun. 5, 4786 (2014).
can act as an effective controlling parameter to tune the splitting of 21. Burkov, A. A. & Balents, L. Weyl Semimetal in a topological insulator
multilayer. Phys. Rev. Lett. 107, 127205 (2011).
the Weyl points and Fermi arcs (further discussions can be found in
2
2. Halász, G. B. & Balents, L. Time-reversal invariant realization of the Weyl
semimetal phase. Phys. Rev. B 85, 035103 (2012).
the Supplementary Information).
Our systematic study on the electronic band structures of NbP,
TaP and TaAs and observation of the characteristic surface Fermi
2
3. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi
arcs. Science 349, 613–617 (2015).
arcs, together with the excellent agreement with the theoretical 24. Lv, B. Q. et al. Discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
3,4
prediction and our detailed ab initio calculations, establish the first 25. Yang, L. X. et al. Weyl semimetal phase in the non-centrosymmetric compound
TaAs. Nature Phys. 11, 728–732 (2015).
TWS family in transition metal monopnictides. This discovery and
2
6. Xu, J. et al. Crystal structure, electrical transport, and magnetic properties of
niobium monophosphide. Inorg. Chem. 35, 845–849 (1996).
the SOC-controlled band structure and Fermiology tuning further
pave the way for the exploration of novel phenomena and potential
future applications in TWSs.
2
7. Chen, Y. Studies on the electronic structures of three-dimensional topological
insulators by angle resolved photoemission spectroscopy. Front. Phys. 7,
175–192 (2012).
Methods
Methods and any associated references are available in the online
version of the paper.
Acknowledgements
Y.L.C. acknowledges support from the EPSRC (UK) grant EP/K04074X/1 and a DARPA
(US) MESO project (no. N66001-11-1-4105). C.F. and B.Y. acknowledge financial
support by the Deutsche Forschungsgemeinschaft DFG (Project No.EB 518/1-1 of
DFG-SPP 1666 ‘Topological Insulators’) and by the ERC Advanced Grant (No. 291472
‘Idea Heusler’). Advanced Light Source is operated by Department of Energy, Office of
Basic Energy Science (contract DE-AC02-05CH11231).
Received 16 April 2015; accepted 24 September 2015;
published online 2 November 2015
References
Author contributions
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2
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.
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal
and Fermi-arc surface states in the electronic structure of pyrochlore iridates.
Phys. Rev. B 83, 205101 (2011).
Y.L.C. conceived the experiments; Z.K.L. and L.X.Y. carried out ARPES measurements
with the assistance of T.Z., H.P., H.F.Y., C.C., Y.Z. and S.-K.M.; D.P., M.S. and Y.F.G.
synthesized and characterized the bulk single crystals; B.Y. and Y.S. performed ab initio
calculations. All authors contributed to the scientific planning and discussions.
Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the
2 4
quantized anomalous Hall effect in HgCr Se . Phys. Rev. Lett. 107,
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Additional information
Weng, H., Fang, C., Fang, Z., Bernevig, A. & Dai, X. Weyl semimetal phase in
Supplementary information is available in the online version of the paper. Reprints and
permissions information is available online at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to Y.L.C.
non-centrosymmetric transition-metal monophosphides. Phys. Rev. X 5,
011029 (2015).
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5
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Huang, S.-M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the
transition metal monopnictide TaAs class. Nature Commun. 6, 7373 (2015).
Zhang, C. et al. Observation of the Adler–Bell–Jackiw chiral anomaly in a Weyl Competing financial interests
semimetal. Preprint at http://arXiv.org/abs/1503.02630 (2015).
The authors declare no competing financial interests.
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©

NATURE MATERIALS DOI: 10.1038/NMAT4457
LETTERS
Methods
Angle-resolved photoemission spectroscopy. ARPES measurements
were performed at beamline 10.0.1 of the Advanced Light Source (ALS)
at Lawrence Berkeley National Laboratory, and beamline I05 of the
Diamond Light Source (DLS). The measurement pressure was kept
Sample synthesis. Single crystals of NbP and TaP of high quality were grown via
chemical transport reaction using iodine as the transport agent. The compound
NbP was first synthesized by a direct reaction of the elements niobium (Chempur
◦
−11
−10
9
9.9%) and red phosphorus (Heraeus 99.999%) at 800 C in evacuated fused silica
below 3×10 /1.5×10 torr in ALS/DLS, and data were recorded by
Scienta R4000 analysers at a sample temperature of 10 K at both facilities.
The total convolved energy and angle resolutions were 16 meV/30 meV and
tubes for 48 h. Starting from this microcrystalline powder, NbP crystallized by a
◦
chemical transport reaction in a temperature gradient from 850 C (source) to
◦
−3
◦
◦
950 C (sink), with a transport agent concentration of 13.5 mg cm iodine (Alfa
0.2 /0.2 at ALS/DLS, respectively. Fresh surfaces of single crystals for ARPES
measurement were obtained by cleaving the sample in situ along its natural (001)
cleavage plane.
Aesar 99.998%). TaP is prepared using the elements tantalum (Alfa Aesar 99.9%)
and red phosphorus (Heraeus 99.999%) using the same method as for NbP.
Precursor polycrystalline TaAs samples were prepared by mixing high-purity
(
>99.99%) Ta and As elements. The mixture was sealed into a quartz tube under
Ab initio calculations. Electronic structures were calculated by the density
functional theory (DFT) method as implemented in the Vienna ab initio
Simulation Package (VASP). The exchange–correlation was considered in
the generalized gradient approximation (GGA) and spin–orbital coupling
(SOC) was included self-consistently. Experimental lattice parameters were
used in the construction of a slab model with a thickness of seven unit cells to
simulate a surface, in which the top and bottom surfaces are terminated by P/As
and Ta/Nb, respectively. The surface band structures and Fermi surfaces were
projected to the top unit cell of the P/As-terminated side, which fits the
experimental band structure well. We adopted a dense k-point 400×400 grid
in the Fermi surface calculations.
high vacuum, which was then sealed into another evacuated tube for extra
◦
◦
−1
protection. First, the vessel was heated to 600 C at a rate of 50 C h , then after
1
◦
◦
−1
0 h of soaking it was slowly heated to 1,050 C at a rate of 30 C h and kept at
this temperature for 24 h. Finally the vessel was cooled down to room temperature.
With the polycrystalline precursor, the single crystals were grown using the
chemical vapour transport method in a two-zone furnace. The polycrystalline TaAs
−
3
powder and 0.46 mg cm of iodine were loaded into a 24-mm-diameter quartz ◦
tube and sealed under a vacuum. The charged part of the tube was kept at 1,150 C
◦
and the other end at 1,000 C for three weeks. The resulting crystals can be as large
as 0.5–1 mm in size.
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