Weyl semimetals (WSMs) exhibit an electronic structure governed by linear band dispersions and degenerate (Weyl) points that lead to exotic physical phenomena. While WSMs were established in bulk monopnictide compounds several years ago, the growth of thin films remains a challenge. Here, we report the bottom-up synthesis of single-crystalline NbP and TaP thin films, 9 to 70 nm thick, by means of molecular beam epitaxy. The as-grown epitaxial films feature a phosphorus-rich stoichiometry, a tensile-strained unit cell, and a homogeneous surface termination, unlike their bulk crystal counterparts. These properties result in an electronic structure governed by topological surface states as directly observed using in situ momentum photoemission microscopy, along with a Fermi-level shift of -0.2 eV with respect to the intrinsic chemical potential. Although the Fermi energy of the as-grown samples is still far from the Weyl points, carrier mobilities close to 103 cm2/(V s) have been measured at room temperature in patterned Hall-bar devices. The ability to grow thin films of Weyl semimetals that can be tailored by doping or strain, is an important step toward the fabrication of functional WSM-based devices and heterostructures.
Weyl semimetals (WSMs) exhibit an electronic structure governed by linear band dispersions and degenerate (Weyl) points that lead to exotic physical phenomena. While WSMs were established in bulk monopnictide compounds several years ago, the growth of thin films remains a challenge. Here, we report the bottom-up synthesis of single-crystalline NbP and TaP thin films, 9 to 70 nm thick, by means of molecular beam epitaxy. The as-grown epitaxial films feature a phosphorus-rich stoichiometry, a tensile-strained unit cell, and a homogeneous surface termination, unlike their bulk crystal counterparts. These properties result in an electronic structure governed by topological surface states as directly observed using in situ momentum photoemission microscopy, along with a Fermi-level shift of -0.2 eV with respect to the intrinsic chemical potential. Although the Fermi energy of the as-grown samples is still far from the Weyl points, carrier mobilities close to 103 cm2/(V s) have been measured at room temperature in patterned Hall-bar devices. The ability to grow thin films of Weyl semimetals that can be tailored by doping or strain, is an important step toward the fabrication of functional WSM-based devices and heterostructures.
Weyl semimetals,
materials with
symmetry-protected gapless electronic bands in which electrons obey
the physics of Weyl fermions, are one of the current most exciting
topics in topological matter.[1,2] The existence of Weyl
fermions was first predicted in material breaking time-reversal symmetry
such as pyrochlore iridates,[3] but their
experimental realization was achieved in compound breaking inversion
symmetry, the transition metal monopnictides.[4−12] So far, these compounds were synthesized as bulk single crystals
in the structural space group I41md and with the composition MX (M = Nb, Ta, X = P, As).
Their identification as Weyl semimetals relies on the observation
of characteristic features in their electronic structure: a linear
dispersion with band crossings (Weyl points) and Fermi-arcs in the
surface states have been conclusively measured by several groups using
angle-resolved photoemission spectroscopy[6−11] and further confirmed by local spectroscopic techniques.[13−16] Moreover, the coupling of Weyl fermions to external electromagnetic
fields results in the nonconservation of chiral charges—the
so-called Adler–Jackiw anomaly.[17] Signatures of this chiral anomaly have been investigated in magnetotransport
experiments, with some concerns regarding the possible role of inhomogeneous
current flow in bulk crystals.[18−20] While major efforts have been
put into microstructuring bulk crystals by focused-ion beam milling,[21−25] thereby enabling advanced thermal transport[21] and nonlinear optical measurements,[25] fabrication-related issues appear when approaching the thin film
limit. In this context, the realization of a bottom-up approach to
synthesize Weyl semimetals would be helpful, making nonlocal transport
experiments[26] a viable route. Furthermore,
thin film growth would allow the control of the topological properties
of WSMs via doping or strain, a parameter space that cannot be explored
with the present bulk crystals. Strain gradients in a WSM crystal
are expected to induce electromagnetic gauge fields,[27] leading to the observation of emergent phenomena such as
landau levels and quantum oscillations in the absence of an applied
magnetic field[28] and a quantization of
the circular photogalvanic effect.[29] Moreover,
there have been a number of fundamental phenomena in WSM thin films
addressed by theory, such as an unusual twisting of the Fermi surface,[30] the emergence of Floquet topological insulator
phases,[31] a metal–insulator transition
upon thickness confinement,[32] or even a
special interplay of long- and short-range surface plasmon-polariton
modes.[33] On the other hand, promising application
areas of WSMs have been addressed, pointing to them as efficient hydrogen
catalysts,[34] colossal photovoltaic materials,[25] mid-infrared detectors,[35] and most recently, topological magnets.[36−39] But the most important implication
of WSM thin films is the possibility to fabricate atomically engineered
heterostructures and functional interfaces. It allows the interplay
of WSMs with other materials, such as superconductors, (anti)ferromagnetic,
or ferroelectric materials, to be explored. In this respect, there
have been exciting predictions of interfacial effects that make WSMs
appealing for spintronic and superconducting devices, such as a large
topology-driven spin-Hall[40] and Edelstein
effects,[41] as well as a chirality-dependent
Josephson current.[42] It is thus clear that
the fabrication of thin films will boost the impact of WSMs both in
the fundamental and applied research perspectives.In this article,
we report the growth of NbP and TaP thin films
on insulating MgO(100) substrates by molecular-beam epitaxy. Both
phosphide compounds have been conclusively shown to be type-I Weyl
semimetals in the bulk crystal form by angle-resolved photoemission
experiments.[8−11] Our epitaxial layers present clear differences with respect to the
bulk crystals: (i) both in-plane and out-of plane lattice parameters
are larger by more than 1%, (ii) the composition of the films is
slightly in the P-rich regime, and (iii) the film surfaces exhibit
sub-unit cell steps (2.8 Å) that point to a single surface termination.
The resulting electronic properties are marked by a downward shift
of the Fermi energy (0.2 eV) below the calculated intrinsic EF, which effectively increases the carrier density
due to multiple band crossings. Furthermore, a phosphorus-terminated
surface is naturally achieved by the growth method and is consistent
with the nature of the topological surface states in both experiment
and calculations. The successful realization of epitaxial thin films
will allow for the use of strain and controlled doping to tailor the
electronic structure of Weyl semimetals, paving the way towards the
fabrication of functional WSM heterostructures.
Results and Discussion
The NbP (TaP) compounds crystallize in the I41md structural space group, which is a tetragonal
lattice with parameters a = 3.34 Å (3.36 Å)
and c = 11.37 Å (11.41 Å). The method of
choice for epitaxial growth is to use the basal (a–b) plane of the pnictide structure to match
with substrates with a cubic structure, i.e., to grow the films along
the (001) direction. However, for a reasonable lattice matching on
typical cubic oxide insulators, the NbP (TaP) growth has to be stabilized
with an in-plane rotation of 45° in the basal plane with respect
to the substrate. To this end, MgO (100) substrates were selected
and prepared ex situ to achieve an atomically flat
surface prior to growth (more details about the substrate choice can
be found in Supporting Information Note 1). Figure a summarizes
the growth strategy with the help of in situ reflection
high energy electron diffraction (RHEED) patterns: (i) we start from
an atomically flat MgO (100) surface, (ii) a subsequent growth of
a thin Nb (Ta) (001) buffer layer, (iii) the phosphorization of the
metal buffer layer, and finally (iv) the overgrowth of the phosphide
layer. This procedure results in a very streaky NbP (TaP) RHEED pattern
indicative of a quasi layer-by-layer growth. From the analysis of
the diffraction patterns, it is evident that the Nb (Ta) buffer layer
grows 45° rotated with respect to the MgO substrate in the basal
plane, following the epitaxial relationship MgO [100]//Nb [110] and
MgO[110]//Nb[100] (see structural models in Figure b for clarity). After completion of the buffer
layer, the Nb surface is exposed to a controlled phosphorus atmosphere,
until high-order streaks (twice the distance of the main streaks in
reciprocal space) appear. This observation is consistent with the
formation of a NbP monolayer that is shifted by a/2 with respect to the buffer layer, which is inherent to the structure
of NbP along the growth direction (c-axis; see cross-section
in Figure b). The
Nb-surface phosphorization is another crucial step to guarantee a
smooth NbP overgrowth: streaky RHEED patterns indicative of flat epitaxial
NbP layers are observed reproducibly with the adopted growth strategy.
It should be noted that periodic RHEED reflections are only visible
in the high symmetry directions, while there are no coherent patterns
at intermediate angles, indicating that the NbP (TaP) films grow with
a single-crystalline orientation without twinning/twisting of in-plane
crystalline domains. Ex situ X-ray diffraction measurements
(Figure c) corroborate
the single-crystalline order: a sharp 90° periodicity in the
film peaks is observed upon azimuthal rotation (Phi-scan). Furthermore,
by plotting the Phi-scans of the film and the substrate together,
it is shown that the epitaxial relationship (45° rotation in-plane)
does not change throughout the whole film thickness.
Figure 1
(a) Evolution of the
RHEED pattern during NbP epitaxial growth:
(i) MgO substrate, (ii) Nb-buffer layer, (iii) phosphorization of
the Nb surface and formation of the first NbP monolayer, and (iv)
NbP growth. (b) Sketch of the NbP/TaP structure and epitaxial relationship
among the substrate, buffer layer, and film. (c) X-ray diffraction
Phi-scan of the NbP (112) and MgO (113) reflections, indicating a
4-fold symmetric, single-crystalline oriented growth rotated by 45°
with respect to the substrate.
(a) Evolution of the
RHEED pattern during NbP epitaxial growth:
(i) MgO substrate, (ii) Nb-buffer layer, (iii) phosphorization of
the Nb surface and formation of the first NbP monolayer, and (iv)
NbP growth. (b) Sketch of the NbP/TaP structure and epitaxial relationship
among the substrate, buffer layer, and film. (c) X-ray diffraction
Phi-scan of the NbP (112) and MgO (113) reflections, indicating a
4-fold symmetric, single-crystalline oriented growth rotated by 45°
with respect to the substrate.Figure shows a
detailed investigation of the structural properties, comprising X-ray
diffraction (XRD), high-resolution scanning transmission electron
microscopy (S-TEM), and Raman spectroscopy. A standard θ–2θ
scan taken on NbP films of various thicknesses (9–70 nm) shows
only (004) and (008) NbP reflections (Figure a), confirming an epitaxial, single crystalline
oriented growth without secondary phases. While the X-ray reflection
pattern from the Nb buffer layer cannot be resolved due to the reduced
thickness (2–5 nm), it can be well visualized in the overview
cross-sectional TEM image in Figure b. As anticipated in the RHEED patterns during growth,
the Nb buffer layer has a certain degree of structural disorder, which
is not present in the NbP layers grown on top. The fine details of
the structure are shown in Figure c, where a high-resolution high-angle annular dark
field (HAADF) STEM image of the NbP film in the [110] direction displays
highly ordered in- and out-of-plane lattice planes, with an excellent
matching to the NbP structural model. The lattice planes are particularly
visible by the high atomic contrast of the Nb atoms, while a faint
contrast corresponding to the light P atoms can be distinguished in
the zoomed-in image (Figure c, right panel) at the expected atomic positions. Taking advantage
of the excellent structural order, a line intensity profile of the
atomic rows has been taken to calculate the average in-plane lattice
parameter of the NbP film (Supporting Information Figure S1). For the [110] direction, a Nb–Nb atom distance
of 2.40 Å has been inferred, which results in an in-plane lattice
parameter a = 3.394 Å. In order to compare the
quantification using both local and global methods, a reciprocal space
mapping (RSM) X-ray diffraction scan has been performed on the (1,1,10)
reflection of NbP (Figure d), yielding an in-plane lattice parameter of a = 3.391 Å, an excellent agreement within the error of the TEM
linescan averaging and the determination of the XRD intensity maxima.
The in-plane lattice parameters do not vary as the thickness is varied
from 15 to 70 nm according to the RSM measurements (see Supporting Information Figure S2), which means
that the films do not change the in-plane strain state in the studied
thickness range. On the other hand, the out-of-plane lattice parameters
extracted from the (004) peak positions (inset of Figure a) decrease only very slightly
(11.50 Å to 11.46 Å) with increasing thickness. The negligible
thickness dependence of both in-plane and out-of-plane parameters
suggests that the films grow fully relaxed from the very early stage.
Interestingly, the lattice parameters (a = 3.39 Å, c = 11.48 Å) sizably differ from the bulk crystal values
(a = 3.34 Å, c = 11.37 Å),
which means that a bigger unit cell is stabilized during the layer-by-layer
growth on the MgO(001)/Nb(001) surface. Figure e shows the thickness-dependent Raman spectra
of NbP thin films. Besides the elastic peak, the characteristic vibrational
modes (E1, B1, E2, A1)
are observed, which correspond to the NbAs structure type (space group Im4c). The most prominent peak belongs
to the A1 mode (around 380 cm–1) while
the other modes present a much lower intensity, in agreement with
the reported bulk spectra and theoretical calculations.[43] We observe a small redshift of the A1 mode as the thickness of the films increases (inset of Figure e), which arises
due to the slightly smaller c-lattice parameter found
on thicker films. While in ref (43), the redshift was measured by applying hydrostatic pressure,
in our case it was achieved by the thickness-dependent epitaxy. Thus,
the shift of the A1 mode can be used as a quick tool to
probe the strain in the films, an important parameter for tuning the
electronic properties of WSMs. Besides, unlike X-ray diffraction,
Raman scattering is able to map different fingerprints for the isostructural
NbP and TaP compounds, as evidenced in the frequency shift of the
B1 mode (Supporting Information Figure S3). It is also worth noting that the asymmetry of the Raman
line shape and its temperature dependence (not measured here) has
been recently found to give insights into electron–phonon coupling
in type-I WSM systems,[44] calling for future
studies in the thin film regime.
Figure 2
(a) X-ray diffraction (θ–2θ
scan) of NbP thin
films, indicating a (001) oriented film with the absence of secondary
phases. (b) Transmission electron microscopy overview image of a MgO/Nb
(2 nm)/NbP (15 nm) cross-section. A Pt protection layer has been placed
during TEM sample preparation. (c) High-resolution STEM images of
the NbP film region in the [11̅0] direction, resolving the crystal
structure and the location of the Nb and P atoms in the lattice. (d)
Reciprocal space mapping of the (1,1,10) reflection of the same NbP
film studied by TEM. The extracted in-plane lattice parameters match
with the local TEM determination, confirming the large-scale homogeneity
of the films. (e) Thickness dependent Raman spectra of the NbP thin
films. The shift of the A1 mode toward higher frequencies
is highlighted in the inset.
(a) X-ray diffraction (θ–2θ
scan) of NbP thin
films, indicating a (001) oriented film with the absence of secondary
phases. (b) Transmission electron microscopy overview image of a MgO/Nb
(2 nm)/NbP (15 nm) cross-section. A Pt protection layer has been placed
during TEM sample preparation. (c) High-resolution STEM images of
the NbP film region in the [11̅0] direction, resolving the crystal
structure and the location of the Nb and P atoms in the lattice. (d)
Reciprocal space mapping of the (1,1,10) reflection of the same NbP
film studied by TEM. The extracted in-plane lattice parameters match
with the local TEM determination, confirming the large-scale homogeneity
of the films. (e) Thickness dependent Raman spectra of the NbP thin
films. The shift of the A1 mode toward higher frequencies
is highlighted in the inset.The chemical composition and valence states of the NbP (TaP) thin
films have been studied by in situ X-ray photoemission
spectroscopy (XPS). The details of the Nb 3d 5/2 and P 2p core level
spectra (Figure a,b)
show that Nb and P shift in opposite directions compared to the neutral
Nb0 and P0 valence state, consistent with the
expected chemical shifts due to electron transfer in the NbP compound
(NbIII and PV valence). The stoichiometry of
the films has been determined using the area under the curve of the
core levels with the respective sensitivity factors, yielding a slightly
P-rich (Nb0.49P0.51) composition. Complementary
to XPS, which is a surface sensitive technique, the in-depth composition
of the films has been studied by Rutherford backscattering spectroscopy
(RBS). The best fitting to the spectra (Figure c) yields a 47.6% to 52.4% (Nb:P) composition,
indicating that the P-rich composition is distributed homogeneously
across the full NbP layer. Similar results with regard to bonding-related
core-level shifts and P-rich composition have been found in TaP layers
(Supporting Information Figure S4). A real-space
visualization of the layer homogeneity is further shown by energy-dispersive
X-ray spectroscopy along a 15 nm NbP cross section (Figure d).
Figure 3
(a, b) In situ X-ray
photoelectron spectroscopy of Nb 3d and P
2p core levels of NbP, highlighting the energy shifts in opposite
directions due to chemical bonding. (c) Rutherford backscattering
spectra of a 20 nm thick NbP sample. The red curve is the fit for
composition determination. (d) Energy dispersive X-ray spectra on
a TEM cross section, showing a homogeneous distribution of Nb and
P species along the film thickness.
(a, b) In situ X-ray
photoelectron spectroscopy of Nb 3d and P
2p core levels of NbP, highlighting the energy shifts in opposite
directions due to chemical bonding. (c) Rutherford backscattering
spectra of a 20 nm thick NbP sample. The red curve is the fit for
composition determination. (d) Energy dispersive X-ray spectra on
a TEM cross section, showing a homogeneous distribution of Nb and
P species along the film thickness.The topography and surface structure of NbP and TaP films is of
paramount importance for the observation of topological surface states
(Fermi-arcs) and has been thus investigated by scanning probe microscopy
(Figure and Supporting Information Figure S5). Large-scale
atomic force microscopy images (Supporting Information Figure S5a) reveal a flat topography, yielding root-mean-square
(RMS) roughness values of 0.43 nm. The grain size varies from 50 to
100 nm showing regions of grain coalescence, whereas the intergrain
steps correspond mostly to 1 unit cell height. In order to investigate
the topography inside and between the grains, in situ scanning tunneling microscopy images have been acquired (Figure ). Square and rectangular
shaped grains can be identified with two preferred orientations, along
45° and −45° on the image axis (i.e., along (100)
direction), consistent with the 4-fold in-plane crystal symmetry of
NbP. A closer look to the grain topography reveals the presence of
atomically flat terraces. The height of each step terrace amounts
to 2.8 Å, corresponding to 1/4 unit cell fractions (a single
Nb–P monolayer), as depicted in Figure b (a structural model of the NbP unit cell
along the growth direction (001) is drawn as a guide to the eye).
We rarely find slight deviations of exact unit cell fractions, which
might arise if adjacent grains end in a different (Nb/P) atomic termination
or due to the presence of intergrain stacking faults. From the topography
statistics, a predominantly single surface termination (either Nb
or P) scenario is likely to happen throughout the film surface. Figure c,d shows a zoomed-in
topography image comparing NbP and TaP film surfaces, the latter having
a smaller terrace width. Additional scanning tunneling spectra (STS)
have been acquired on a flat region (marked with a square in Figure d) and reveal a parabolic
behavior with a finite density of states at zero bias, characteristic
of metallic systems. An enhanced conductance (shoulder) is observed
around +0.2 V bias voltage, which points to a larger electronic density
of states above the Fermi energy (unoccupied states).
Figure 4
(a) Overview scanning
tunneling microscopy image (500 nm ×
500 nm, V = 1 V, I = 2 pA) of a
20 nm-thick NbP film, revealing rectangular grains oriented along
the (100) direction (45° in the image) with atomically flat terraces.
(b) Height profile across a NbP grain (marked with an arrow in panel
a), featuring terrace steps of 2.8 Å, which correspond to a NbP
monolayer (1/4 u.c.). The NbP unit cell in the (001) direction is
drawn next to it as guide for the eye. (c, d) Zoomed-in topography
images of NbP (V = 1 V, I = 2 pA)
and TaP (V = 0.3 V, I = 10 pA),
respectively. The terrace size in the TaP films appears to be smaller.
(e) Scanning tunneling spectrum (STS) (V = 0.5 V, I = 10 pA) of a TaP epitaxial grain (marked as a square
in panel d) revealing a finite density of states at zero-bias and
a parabolic behavior with an enhanced conductance around 0.2 V.
(a) Overview scanning
tunneling microscopy image (500 nm ×
500 nm, V = 1 V, I = 2 pA) of a
20 nm-thick NbP film, revealing rectangular grains oriented along
the (100) direction (45° in the image) with atomically flat terraces.
(b) Height profile across a NbP grain (marked with an arrow in panel
a), featuring terrace steps of 2.8 Å, which correspond to a NbP
monolayer (1/4 u.c.). The NbP unit cell in the (001) direction is
drawn next to it as guide for the eye. (c, d) Zoomed-in topography
images of NbP (V = 1 V, I = 2 pA)
and TaP (V = 0.3 V, I = 10 pA),
respectively. The terrace size in the TaP films appears to be smaller.
(e) Scanning tunneling spectrum (STS) (V = 0.5 V, I = 10 pA) of a TaP epitaxial grain (marked as a square
in panel d) revealing a finite density of states at zero-bias and
a parabolic behavior with an enhanced conductance around 0.2 V.Having assessed the properties of the film surface,
momentum-resolved
photoemission spectra have been taken using an in-house designed and
built momentum microscope[45] with a He–I
light source (see Methods for details). Figure summarizes the overall
electronic structure of a 15 nm-thick NbP thin film measured at 100
K, including Fermi-surface topology and band dispersion along relevant
(Weyl point) cuts, together with ab initio calculations
using the experimentally obtained unit cell parameters. At the Fermi-energy
(E = 0 meV), four electronic pockets
with an elliptic shape directed toward the X and Y symmetry points can be identified, as shown in Figure a. A detailed comparison
with the calculation of the termination-dependent surface states (Figure b,c) reveals that
the elliptic and cross-like band features along Γ–X and
Γ–Y are characteristic of the P-terminated NbP surface
states (the features for a Nb termination are radically different).
Interestingly, the size and shape of the measured elliptical (also
called spoon-like) features at E match
with the calculations and the bulk crystal data in refs (10 , 11 , and 46) only when an energy shift of ΔE = −0.2
eV (E = 200 meV) is considered (highlighted
in a green box, Figure b), suggesting an effective hole doping in the as-grown thin films. Figure d shows the energy
dispersion cut along A → A′, which is expected to cross
the location of one pair of Weyl points in NbP (k = 0.54 Å–1, Eb = −0.026 eV) and thus used to visualize
the surface Fermi arcs.[10,11] A clear linear band
dispersion is observed, in agreement with previous photoemission results
of cleaved monopnictide bulk crystals.[6−11] This dispersion originates from the Fermi-arcs, but their k–k contour at the Weyl points cannot be
mapped in our NbP films due to the EF shift
(−0.2 eV) with respect to the intrinsic Fermi level, and second,
due the intrinsically short separation of the Weyl points in momentum
space (Δk < 0.05 Å–1) for the NbP compound, a detection challenge even for high-resolution
synchrotron ARPES.[10,11,46] It is noteworthy that only these topological surface states (elliptic
shape, A → A′ cut) are observed in our films, whereas
the bowtie features centered at the X and Y points) are completely
absent. This merits further investigation and will be discussed elsewhere.
On the other hand, the origin of the effective hole-doping in the
as-grown thin films can be attributed to residual acceptors (Nb-vacancies)
arising from the MBE growth process, in agreement with the slightly
P-rich composition of the films inferred by XPS and RBS. The strained
lattice parameters of the phosphide thin films will also have an effect
on the Fermi-level position. Although we estimate that the effect
of the lattice parameters (∼1% tensile strain) is rather small,
further studies are needed to disentangle the contribution from strain
and vacancy acceptors on EF, in order
to get a full understanding of Fermi-level engineering of Weyl semimetals
achieved by epitaxial design.
Figure 5
Electronic structure of the NbP thin films (t =
15 nm) revealed by momentum-resolved photoemission spectroscopy. (a)
Constant energy contour at zero binding energy (Fermi surface). The
green square represents the Brillouin zone (BZ). (b, c) Ab
initio calculations of constant-energy contours (surface
projection) at different binding energies for a P-terminated (panel
b) and Nb-terminated surfaces (panel c), respectively. The calculated
energy contours of the P-termination at a 200 meV binding energy (highlighted
in green) match well with the experimental results at EF, evidencing a Fermi-level shift in the as-grown film.
(d) Energy dispersion along the A–A′ direction (defined
in panel a), which corresponds to the cut across the Weyl point projection
(k = 0.54 Å–1).[11,12] A linear dispersion is clearly
observed.
Electronic structure of the NbP thin films (t =
15 nm) revealed by momentum-resolved photoemission spectroscopy. (a)
Constant energy contour at zero binding energy (Fermi surface). The
green square represents the Brillouin zone (BZ). (b, c) Ab
initio calculations of constant-energy contours (surface
projection) at different binding energies for a P-terminated (panel
b) and Nb-terminated surfaces (panel c), respectively. The calculated
energy contours of the P-termination at a 200 meV binding energy (highlighted
in green) match well with the experimental results at EF, evidencing a Fermi-level shift in the as-grown film.
(d) Energy dispersion along the A–A′ direction (defined
in panel a), which corresponds to the cut across the Weyl point projection
(k = 0.54 Å–1).[11,12] A linear dispersion is clearly
observed.Finally, electrical transport
measurements have been analyzed only
for thick films (t = 70 nm), so that shunting effects
of the thin buffer layer can be discarded. The temperature dependence
of the resistivity (Figure a) shows the expected metallic behavior for NbP.[47] We do not observe superconductivity down to
2 K, in contrast to recent reports on platelets formed from bulk crystals
using focused ion beam milling.[24] The carrier
density in the as-grown films has been extracted by standard Hall
effect measurements, and as already anticipated from the Fermi-level
shift determined by photoemission (ΔE = −0.2
eV), both electron and hole bands will contribute to electronic transport.
Thus, slightly nonlinear transverse resistances (R) as a function of the magnetic field
have been fitted by the two-carrier model to extract the densities
of the electrons (ne) and holes (np), as well as the electron (μe) and hole (μp) mobilities as a function of temperature,
summarized in Figure b,c. Being energetically 0.2 eV below the Weyl points, the density
of states at EF encompasses mainly hole-like
bands, as shown in the bulk band structure calculations (Figure e), and thus the
majority carriers are holes with a carrier density (1021– 1022 cm–3) higher than in the
bulk crystals (1020 cm–3).[47] The resulting electron (hole) mobilities are
close to 900 cm2/(V s) (300 cm2/(V s)) and feature
a weak temperature dependence similar to heavily doped (degenerate)
semiconductors. Moreover, a positive magnetoresistance is observed
both for in-plane (B // I) and out-of plane (B ⊥ I) magnetic
fields, suggesting the absence of chiral anomaly in the as-grown films.
This result corroborates that the chiral anomaly is highly sensitive
to the location of the Fermi energy (EF = −0.2 eV). The effect of chiral charge pumping is strongly
diminished away from the Weyl points, due to the contribution of
nontopological bands at other locations in momentum space (see Figure e). At high magnetic
fields, a linear, nonsaturating behavior of the resistivity sets in
(Supporting Information Figure S6), typically
observed in high-mobility compensated semimetals.
Figure 6
Electrical and magnetotransport
properties of NbP films and their
relation to the bulk band structure. (a) Temperature dependence of
the resistivity of a 70 nm-thick NbP film. In this thickness regime,
the parallel buffer layer conduction (t = 2 nm) is
negligible. (b) Electron and hole mobility calculated using the two-carrier
model, exhibiting a very shallow temperature dependence. (c) Carrier
density dependence revealing holess as majority carriers throughout
the measured temperature range. (d) Angular dependent magnetoresistance,
exhibiting positive MR dependence under both in and out-of-plane magnetic
fields (absence of chiral anomaly). (e) Bulk band structure calculations
of NbP showing all the relevant bands inside the Brillouin zone, and
highlighting the presence of multiple hole pockets at the experimentally
determined EF (green line), in agreement
with the large hole concentration (>1022 cm–3) obtained by the Hall effect.
Electrical and magnetotransport
properties of NbP films and their
relation to the bulk band structure. (a) Temperature dependence of
the resistivity of a 70 nm-thick NbP film. In this thickness regime,
the parallel buffer layer conduction (t = 2 nm) is
negligible. (b) Electron and hole mobility calculated using the two-carrier
model, exhibiting a very shallow temperature dependence. (c) Carrier
density dependence revealing holess as majority carriers throughout
the measured temperature range. (d) Angular dependent magnetoresistance,
exhibiting positive MR dependence under both in and out-of-plane magnetic
fields (absence of chiral anomaly). (e) Bulk band structure calculations
of NbP showing all the relevant bands inside the Brillouin zone, and
highlighting the presence of multiple hole pockets at the experimentally
determined EF (green line), in agreement
with the large hole concentration (>1022 cm–3) obtained by the Hall effect.
Conclusion
In summary, epitaxial thin films of type-I Weyl semimetals NbP
and TaP have been synthesized via molecular beam epitaxy. A rigorous
structural, morphological, and chemical characterization was carried
out to assess the quality of the films. During the epitaxial growth
process, the layers are stabilized with a larger lattice constant
(1%) and with a slight P-rich stoichiometry with respect to the bulk
crystals. The excellent surface quality, featuring a homogeneous P-termination,
allows the visualization of topological surface states with a linear
dispersion. A Fermi-level shift of around −0.2 eV with respect
to the intrinsic EF is determined by comparing
the photoemission spectra with ab initio calculations
and bulk crystal data; and arises mainly due to the formation of Nb-vacancy
acceptors (P-rich conditions). The realization of high-quality WSM
thin films and the intimate relation between strain, doping, band
structure, and electronic transport discussed here constitutes a route
to access and control topological states in order to design functional
heterostructures and Weyltronic devices.
Methods
Substrate
Preparation and Molecular-Beam Epitaxy Growth
MgO (100) substrates
were soaked in methanol for 20 min and rinsed
with water followed by annealing in O2 atmosphere (1150
°C) for 3.5 h to achieve an atomically flat surface prior to
film growth. The typical substrate dimensions are 5 × 10 mm.
Nb (Ta) rods are evaporated via electron-beam heating, and P species
are thermally evaporated from a GaP compound effusion cell in a custom-made
UHV chamber (pbase = 1 × 10–10 mbar),
with a regeneration system for residual P2 (red) and P4 (white phosphorus). The GaP compound cell is employed to
reduce the amount of pyrolytic white phosphorus upon evaporation (P2/P4 ∼ 100). A cross-beam mass spectrometer
(XBS Hiden) is used to calibrate the atomic fluxes and monitor the
amount of P2/P4 species. No Ga species have
been detected under evaporation conditions (Tcell = 850 °C). The substrate temperature is controlled
by radiation heating. The Nb (Ta) buffer layer is grown at 300 °C,
at a rate of 3–5 nm/h and a pressure of p =
4 × 10–10 mbar. The surface of the buffer layer
is then exposed to a P2 flux (BEP: 1 × 10–8 mbar) to achieve phosphorization, whereas the subsequent NbP (TaP)
layer is grown under P-rich conditions (Nb:P flux 1:20), a moderate
substrate temperature (300–400 °C), and a slow rate (<4
nm/h), controlled by the Nb (Ta) flux. The thicknesses of the films
presented in this work range between 9 and 70 nm. After concluding
the growth process, the sample is cooled down very slowly (10 °C/min)
to room temperature under P atmosphere (p = 1 ×
10–8 mbar), to ensure a homogeneous P-termination
at the surface.
In Situ Characterization
The crystallinity
of the films is monitored in situ by reflection high
energy electron diffraction (RHEED), using a 15 kV electron beam.
The layers are further characterized by in situ tools
(XPS, STM, and momentum microscope) with the use of a vacuum suitcase
transfer system (Ferrovac, pbase <
1 × 10–10 mbar) to move the as-deposited film
under UHV conditions from the growth to the analysis chambers. Core-level
X-ray photoelectron spectra (XPS) were taken at room temperature using
Al Kα radiation and a hemispherical analyzer. The STM experiments
were performed on an Omicron VT-STM-XT system operated at room temperature
with a base pressure of 2 × 10–11 mbar. The
mechanically sharpened Pt/Ir tips were treated and checked on the
Au(111) surface before measurements, and the topography images were
acquired at room temperature. A sinusoidal modulation of 30 mV and
713 Hz was added to the bias voltage for the measurements of dI/dV spectra. Momentum-resolved photoemission
spectra were acquired using an in-house designed momentum microscope,[45] using a helium lamp (hv = 21.2
eV), at 100 K and with an energy step of 10 meV.
Ex
Situ Characterization
X-ray diffraction
patterns, including reciprocal space maps, were taken in a commercial
4-circle diffractometer (Bruker) using Cu Kα radiation. Transmission
electron microscopy (TEM) was carried out in an aberration corrected
high-resolution microscope (FEI, Titan). Cross-sectional lamellas
of the MgO/Nb/NbP stack (t = 100 nm) were prepared
by focused ion beam (FIB) with Ga-ion etching. A Pt protection layer
is deposited on the sample before lifting the lamella to the TEM grid.
Raman spectra were acquired using a 532 nm excitation wavelength at
room temperature. Rutherford backscattering spectroscopy using particle
induced X-ray emission was measured using a 1.9 MV alpha+ beam at
a 169° scattering angle in an NEC Pelletron accelerator.
Device
Fabrication and Electrical Transport
Hall-bar
devices were patterned using laser-assisted optical lithography (Heidelberg
Instruments) and etched via an Ar-discharge plasma (500 V DC) under
high-vacuum conditions. Cr/Au (4 nm/80 nm) contacts were deposited
by DC magnetron sputtering. The device sizes ranged from (5 ×
15) μm2 (width × length) to (100 × 300)
μm2 (aspect ratio 1:3).
Ab Initio Calculations
Electronic
structure calculations are performed within the density functional
theory as implemented in the Vienna ab initio simulation
package (VASP).[48,49] The exchange-correlation energy
is treated within the Perdew–Burke–Ernzerhof (PBE) parametrization[50] of the generalized gradient approximation. The
kinetic energy cutoff for the plane wave basis is 300 eV, and a k-mesh of 500 × 500 × 1 is adopted for the Brillouin
zone integration. A six-unit-cell thick slab model is constructed
by cutting NbP along the (001) plane of the conventional cell, and
the in-plane cell size is 1 × 1 for the conventional cell. The
internal coordinates of the atoms in the surface unit cell are fully
relaxed. Spin–orbit coupling is considered in the electronic
structure calculations. All the surface band structures and Fermi
surfaces are projected onto the atoms in the surface unit cell of
the P- and Nb-termination, accordingly.
Authors: Maja D Bachmann; Nityan Nair; Felix Flicker; Roni Ilan; Tobias Meng; Nirmal J Ghimire; Eric D Bauer; Filip Ronning; James G Analytis; Philip J W Moll Journal: Sci Adv Date: 2017-05-24 Impact factor: 14.136