Realization of Epitaxial NbP and TaP Weyl Semimetal Thin Films

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.

W eyl 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 timereversal 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 I4 1 md 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 socalled 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 midinfrared 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 E F , which effectively increases the carrier density due to multiple band crossings. Furthermore, a phosphorusterminated 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 I4 1 md 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 1a 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  Figure 1b 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 ACS Nano www.acsnano.org Article 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 (caxis; see cross-section in Figure 1b). 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 singlecrystalline orientation without twinning/twisting of in-plane crystalline domains. Ex situ X-ray diffraction measurements ( Figure 1c) 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 2 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 2a), 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 2b. 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 2c, 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 2c, 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 2d), 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 ACS Nano www.acsnano.org Article Figure 2a) 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-bylayer growth on the MgO(001)/Nb(001) surface. Figure 2e shows the thickness-dependent Raman spectra of NbP thin films. Besides the elastic peak, the characteristic vibrational modes (E 1 , B 1 , E 2 , A 1 ) are observed, which correspond to the NbAs structure type (space group Im4c). The most prominent peak belongs to the A 1 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 A 1 mode as the thickness of the films increases (inset of Figure 2e), 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 A 1 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 B 1 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. 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 3a,b) show that Nb and P shift in opposite directions compared to the neutral Nb 0 and P 0 valence state, consistent with the expected chemical shifts due to electron transfer in the NbP compound (Nb III and P V 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 (Nb 0.49 P 0.51 ) 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 3c) 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  3d).
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 4 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 4). Square and rectangular shaped grains can be identified with two preferred orientations, along 45°and −45°o n 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 4b (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  4c,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  4d) 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).
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 5 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   Figure 5d shows the energy dispersion cut along A → A′, which is expected to cross the location of one pair of Weyl points in NbP (k x = 0.54 Å −1 , E b = −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 x −k y contour at the Weyl points cannot be mapped in our NbP films due to the E F 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 highresolution 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 Fermilevel 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 E F , in order to get a full understanding of Fermi-level engineering of Weyl semimetals achieved by epitaxial design. 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 6a) 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 xy ) as a function of the magnetic field have been fitted by the two-carrier model to extract the densities of the electrons (n e ) and holes (n p ), as well as the electron (μ e ) and hole (μ p ) mobilities as a function of temperature, summarized in Figure 6b,c. Being energetically 0.2 eV below the Weyl points, the density of states at E F encompasses mainly hole-like bands, as shown in the bulk band structure calculations (Figure 6e), and thus the majority carriers are holes with a carrier density (10 21 − 10 22 cm −3 ) higher than in the bulk crystals (10 20 cm −3 ). 47 The resulting electron (hole) mobilities are close to 900 cm 2 /(V s) (300 cm 2 /(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 (E F = −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 6e). At high magnetic fields, a linear, nonsaturating behavior of the resistivity sets in (Supporting Information Figure S6), typically observed in high-mobility compensated semimetals.

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 Ptermination, 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 E F 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 O 2 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 custommade UHV chamber (p base = 1 × 10 −10 mbar), with a regeneration system for residual P 2 (red) and P 4 (white phosphorus). The GaP compound cell is employed to reduce the amount of pyrolytic white phosphorus upon evaporation (P 2 /P 4 ∼ 100). A cross-beam mass spectrometer (XBS Hiden) is used to calibrate the atomic fluxes and monitor the amount of P 2 /P 4 species. No Ga species have been detected under evaporation conditions (T cell = 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 P 2 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, p base < 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 highresolution 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.
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 exchangecorrelation 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 kmesh 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.