Electronic and Magnetic Characterization of Epitaxial VSe$_2$ Monolayers on Superconducting NbSe$_2$

Vertical integration of two-dimensional (2D) van der Waals (vdW) materials with different quantum ground states is predicted to lead to novel electronic properties that are not found in the constituent layers. Here, we present the direct synthesis of superconductor-magnet hybrid heterostructures by combining superconducting niobium diselenide (NbSe$_2$) with the monolayer (ML) vanadium diselenide (VSe$_2$). More significantly, the in-situ growth in ultra-high vacuum (UHV) allows to produce a clean and an atomically sharp interfaces. Combining different characterization techniques and density-functional theory (DFT) calculations, we investigate the electronic and magnetic properties of VSe$_2$ on NbSe$_2$. Low temperature scanning tunneling microscopy (STM) measurements demonstrate a reduction of the superconducting gap on VSe$_2$ layer. This together with the lack of charge density wave signatures indicates magnetization of the sheet, but not of a conventional itinerant ferromagnet.

and magnetic properties of VSe 2 on NbSe 2 . Low temperature scanning tunneling microscopy (STM) measurements demonstrate a reduction of the superconducting gap on VSe 2 layer. This together with the lack of charge density wave signatures indicates magnetization of the sheet, but not of a conventional itinerant ferromagnet.
Keywords transition metal dichalcogenides, vertical heterostructure, superconductor, magnetism, vanadium diselenide VSe 2 , niobium diselenide NbSe 2 , scanning tunneling microscopy There has been a surge of interest in designer materials that would realize electronic responses not found in naturally occurring materials. There are many routes towards this goal and they are all being explored vigorously: e.g., artificial atomic lattices, [1][2][3][4][5] atomically precise graphene nanoribbons, [6][7][8] and controlled heterostructures of two-dimensional materials. [9][10][11][12][13][14][15] The designer concept is well illustrated in systems combining magnetism with superconductivity to realize topological superconductivity. [16][17][18][19][20] Individual magnetic impurity atoms give rise to so-called Yu-Shiba-Rusinov states, 21 which can be coupled in extended structures to give rise to bands (inside the superconducting gap). Eventually, the system can be driven into a topological phase in the presence of certain spin textures or spin-orbit coupling. 18,[22][23][24][25][26] Topological superconductors are a distinct form of matter that is predicted to host boundary Majorana fermions. Experimental realization of Majorana fermions is exciting in its own right, but this is compounded by the proposal that systems with non-abelian statistics can serve as the basis for topological quantum computation. 27-29 Experimentally, these systems have been realized in one-dimensional chains of magnetic adatoms on the surface of s-wave superconductors 18,23,30 and this has been extended to two-dimensional systems by using magnetic metal islands. 31,32 However, these types of systems can be sensitive to disorder and interface engineering through, e.g., the use of an atomically thin separation layer, might be required. 32 Issues with interface inhomogeneities can potentially be avoided in van der Waals (vdW) heterostructures, where the different layers interact only through vdW forces. 9,10 Layered materials that remain magnetic down to the monolayer (ML) limit have been recently demonstrated. 11,12 CrI 3 and Cr 2 Ge 2 Te 6 have very desirable magnetic properties; however, they are not readily amenable to in-situ growth in ultra-high vacuum (UHV) leading to clean edges and interfaces (through, e.g., molecular-beam epitaxy (MBE)). Very recently, monolayer magnetism was suggested in the transition metal dichalcogenide (TMD) vanadium diselenide (VSe 2 ), which can be readily grown using MBE on various layered materials. 13 Later reports have questioned the existence of magnetism in VSe 2 as no magnetic signal was detected in X-ray magnetic circular dichroism (XMCD) experiments. 33,34 Angle-resolved photoemission spectroscopy revealed an enhanced charge-density wave (CDW) transition at a higher temperature than in the bulk, and it was suggested that the presence of CDW driven by Fermisurface nesting removes the usual mechanism for achieving a magnetic ground state. 33,[35][36][37] While there still is no consensus on the nature of the possible magnetic ground state of VSe 2 , it is clear that there is a delicate balance between different competing interacting states and phases in monolayer transition-metal dichalcogenides, which may also depend on the nature of the substrate. 33,34, [37][38][39][40][41] Combining 2D magnetic and superconducting TMDs would create a promising material platform for investigating the coexistence of superconductivity, magnetism and the resulting emergent quantum phases of matter. The inherent lack of surface bonding sites due to the layered nature of these materials prevents chemical bonding between the layers and results in a better control of the interfaces. We report growth of single layer vanadium diselenide (VSe 2 ) by molecular beam epitaxy on superconducting niobium diselenide (NbSe 2 ) substrate and study the magnetic and electrical properties of these heterostructures. MBE growth under UHV conditions facilitates the formation of clean edges and interfaces and we characterize the electronic structure of the resulting hybrid materials down to the atomic scale using lowtemperature scanning tunneling microscopy (STM) and spectroscopy (STS). Our results give further experimental information on the magnetic properties of VSe 2 and demonstrate a clean and controllable platform for creating superconducting-magnetic hybrid TMD materials with great potential of integrating TMDs into future electronics devices.

Results and discussion
VSe 2 was grown on NbSe 2 by MBE and results are illustrated in Fig. 1 (see Methods for details). Briefly, vanadium was evaporated under excess flux of selenium onto a NbSe 2 crystal cleaved in-situ in UHV and held at T = 520 − 540 K during the growth. The samples were characterized in-situ by STM and X-ray photoelectron spectroscopy (XPS). In addition, after capping the films with a thick Se layer, the samples were characterized ex-situ by temperature dependent magnetization measurements. Fig. 1a shows STM characterization of sub-monolayer VSe 2 films on NbSe 2 substrate. VSe 2 grows atomically smooth, large uniform ML islands. Higher coverages result in the formation of a second layer. The profile along the blue line in Fig. 1a shows that the apparent height of the VSe 2 film is 6.5Å (Fig. 1b) consistent with the unit cell height. 42 Atomically resolved STM images of the VSe 2 monolayer and NbSe 2 crystal surface are shown in Figs. 1c and 1d, respectively. While NbSe 2 shows the well-known 3 × 3 charge-density wave modulation in the atomic contrast, we do not detect a charge density wave on VSe 2 (even at temperature of T = 4.2 K). This is in contrast to reports on HOPG and bilayer graphene substrates. 13,33,35 The lattice constants can be measured from the atomically resolved images, as depicted in Fig. 1e. This yields values of 3.5Å and 3.4Å for VSe 2 and NbSe 2 , respectively. These values match well with previous experimental results. 36, 42,43 XPS was used to study the chemical composition of the as-grown VSe 2 films on NbSe 2 .
Characteristic peaks of V, Se and Nb are found in the XPS spectra (see Supporting Information (SI) Fig. S1). The binding energies of the V 2p 3/2 peak at 513.7 eV and the Se 3d 5/2 peak at 53.4 eV are similar to those previously observed for VSe 2 on HOPG. 13,43 The Nb 3d 5/2 peak is found at 203.5 eV which is typical for NbSe 2 . Both VSe 2 and NbSe 2 have similar selenium binding energies and thus they cannot be resolved from the Se 3d spectrum. 44 The V:Se:Nb stoichiometry estimated from the peak areas was roughly 1:5:2 (for a 0.6 ML VSe 2 film). No other elements, such as possible magnetic impurities, were detected above the detection limit of ∼1 atomic percent.
We have complemented the experiments by density functional theory (DFT) calculations (see Methods and SI for details). Fig. 1f shows the fully relaxed geometry of VSe 2 /NbSe 2 heterostructure from the side and top views. The energetically most favourable stacking has the lower layer Se atoms of VSe 2 on top of hollow site of the NbSe 2 (2.94Å from Se in NbSe 2 to Se in VSe 2 ) and V on top of Nb, with a distance of 6.16Å from Nb to V.
We have probed the electronic structure of single-layer VSe 2 /NbSe 2 heterostructure by both scanning tunnelling spectroscopy (STS) and DFT. Fig. 2a shows typical dI/dV spectra taken on the ML VSe 2 and on the bulk NbSe 2 substrate over a large bias range. We will first focus on the NbSe 2 response. At positive bias (empty states) region, the most pronounced features on bulk NbSe 2 are the broad resonances at ∼ 0.3 V and ∼ 1.8 V, while at negative bias the dI/dV signal is broad and rising. The measured dI/dV spectrum on NbSe 2 is in agreement with earlier STS studies on bulk NbSe 2 . 45 The features in our dI/dV spectroscopy also match the simulated spectra on a 3-layer slab of NbSe 2 (Fig. 2b) and can be compared with the bulk density of states (Fig. 2c). The first resonance at positive bias arises from the Nb-derived band, while the broad feature at negative bias overlaps with the mostly selenium derived bands below E F . On VSe 2 , at positive bias, there are pronounced features close to the Fermi level and also at 0.9 V and 1.45 V. At negative bias, we observe a peak at -0.5 V, First focusing on the experimental spectra for monolayer and bilayer VSe 2 in Fig. 3d, we observe peaks close to the Fermi level at both positive and negative bias and they are more pronounced for the bilayer compared to the monolayer. Their energy spacing (gap) is ∼ 0.2 eV with an abrupt edge at positive energy (peak p1) and smoother edge at negative energy that develops to peaks labelled with n1/n2. At larger positive or negative bias, several peaks can be distinguished with the peak positions shifting between the mono-and bilayer spectra.
Starting from the non-magnetic (NM) phase, the band structure shows the partially filled d-band (Fig. 3a). There is a flat region between Γ and K-points, which also happens to coincide with the Fermi-level. This leads to a strong peak at the Fermi-level in the DOS and Fermi-level (feature p1 in the experimental spectra). The FM phase also seems to yield better agreement between the simulated and experimental STS for the peaks p2 and p3 in the monolayer sample. Overall, in the monolayer sample, several features in the STS spectra seem to have better match with the FM phase than the CDW phase. After the electronic characterization of the samples, we will next focus on their magnetic properties. To explore the magnetic properties of ML VSe 2 on NbSe 2 , we carried out magnetization measurements at various sample temperatures (See Methods for details). All the VSe 2 samples measured showed an in-plane magnetic response similar to that shown in As shown in Fig. 4b, the coercive field is vey small and it and saturation magnetization are practically independent of temperature in the range of T = 10 − 300 K. This behaviour is inconsistent with standard ferromagnetism. While the mechanism is different here, there are other systems that exhibit phenomenologically similar magnetic responses. 46,47 It has been argued that there is no conventional ferromagnetism in VSe 2 on graphite and graphene substrates. 33-36, 40 Here, one potentially important difference between our samples and those on graphite and graphene is the absence of a charge-density wave: we find no evidence of CDW in either the STM images or the dI/dV spectroscopy (see below). The stability of the CDW according to our DFT calculations is extensively discussed in the SI.
Furthermore, in previous studies, 13 monolayer VSe 2 sample exhibits a maximum in M s and H c in a range around T = 100 K and this non-monotonic behaviour is ascribed to the CDW transition. This is in contrast to our data on M s and H c as a function of temperature.
The absence of CDW transation is also independently determined from the magnetization measurement under zero-field-cooled (ZFC) and field-cooled (FC) regimes, where we do not observe noticeable changes in the slope of the ZFC and FC curves due to the CDW (see SI ing diamagnetic behavior as reported previously. 48,49 Moreover, there is no obvious difference between these magnetization curves, which indicates that the signal is mostly dominated by the bulk NbSe 2 . This conclusion is further supported by the temperature dependent magnetization curves for the zero-field cooling (ZFC) of a bulk NbSe 2 and VSe 2 /NbSe 2 heterostructure (see SI). They show a rapid decrease at the onset of the diamagnetic signal below the critical temperature T c for both samples and, again, there is no obvious change in T c , which further indicates that the dominance of the bulk signals. It is worth to mention that T c is very sensitive to the magnetic doping, with studies suggesting that T c drops rapidly upon metal atom doping. 50,51 This suggests that we do not lose any vanadium due to intercalation at the normal growth temperatures. Increasing the growth temperature to T > 300 • C results in intercalation of vanadium, which is clearly seen in atomically resolved images of the NbSe 2 surface and results in the loss of the long range order of the CDW 52 (see SI Fig. S17 for details).
There is a particular interest in the interaction between the superconducting substrate and the magnetic layer both in terms of the proximity effect induced in the single layer VSe 2 and conversely, the effect of the magnetic layer on the underlying superconductor. The superconducting proximity effect can be used to spontaneously drive a non-superconducting material (normal metal) into superconductivity, however, this picture is altered when the superconductor makes a contact with a magnetic layer. In the case of a ferromagnet, the superconducting order parameter is expected to decay exponentially with a very short coherence length ζ F (typically some nm) at the superconductor-ferromagnet (SF) interface.
Moreover, the pairing potential ∆ p inside the ferromagnet shows a strong oscillatory and damped behaviour due to the internal exchange field of the ferromagnet. 53,54 This type of phenomena could also occur in our hybrid VSe 2 /NbSe 2 layers and it will allow us to shed some light on the nature of the magnetism in VSe 2 on the atomic scale. Fig. 5a shows the dI/dV spectra measured on the NbSe 2 substrate as well as VSe 2 layers with different thicknesses. On NbSe 2 , we observe a typical superconducting gap: a pronounced dip in the DOS at the Fermi level and coherence peaks on both sides of the gap. 55,56 The spectra measured on the VSe 2 films with thicknesses of 1 ML and 2 ML also shows a superconducting gap, but the gap width is significantly reduced compared to the bare NbSe 2 substrate. We do not observe oscillatory behaviour of the pairing potential as bilayer VSe 2 is not sufficiently thick for this. To further quantify the reduction of the SC gap width, we use a simple analytical relation between a superconducting gap ∆ and decay length λ: 57-59 ∆ ≈ ∆ NbSe 2 e −d/λ , where the d is the VSe 2 film thickness and ∆ NbSe 2 is the gap of bare NbSe 2 , respectively. We extract the apparent gap widths from the spectra shown in Fig. 5a by fitting them (see SI Fig. S18 for details) and plot the results in Fig. 5b. The decrease of the energy gap follows an exponential dependence with an decay length of λ = 1 nm (1 ML thickness is roughly 0.65 nm). This is a measure of the quasi-particle coherence length associated with Andreev reflections. However, this decay length is much shorter than recent experimental results on Bi 2 Se 3 on NbSe 2 : 60 they observe a decay length of λ = 2 nm, which is shown as a dashed blue line in Fig. 5b. In the case of Bi 2 Se 3 on Nb, an even much higher value of λ = 8.4 nm was reported. 59 The faster decay we observe in VSe 2 is most easily explained by magnetism of the VSe 2 layer. In this case, one would expect a shorter coherence length ζ F governed by the magnetization in the VSe 2 layer and not by the diffusion (which is a case in Bi 2 Se 3 /NbSe 2 ). The reduced gap is very uniform within the VSe 2 islands and also between different islands, which suggests that it is related to bulk properties of ML VSe 2 and not simply an effect arising from impurities, vacancies or structural imperfections (e.g. layer edges).
We have also probed the spatially dependent spectroscopic response over the edges of the VSe 2 islands and typical spectra are shown in Fig. 5c (more results in the SI Fig. S19).
The spectra evolve from the typical gapped structure over the NbSe 2 into a sharp peak at zero bias at the edge of the VSe 2 island. This feature is very localized at the edge of the VSe 2 layer. Furthermore, it is inhomogeneously distributed along the edges of VSe 2 islands and there are strong intensity variations as illustrated in Fig. 5d. In addition to the spatial distribution of the zero bias peak, its width is also strongly position dependent. We observe both zero bias peaks that are confined within the superconducting gap (e.g. Fig. 5c), but on some other locations (see SI Fig. S19), its width can be a couple of times larger than the superconducting gap width. Features inside the superconducting gap could arise from Yu-Shiba-Rusinov bands or topological edge modes, but the broader peaks suggest the presence of free unpaired spins giving rise to the Kondo effect. 21, 61 In any case, the reason is likely related to the changes of the gap structure of the underlying superconductor due to local magnetic fields arising from the edges of the VSe 2 layer. These results suggest importance of edge effects in the magnetism of the VSe 2 layer.

Conclusions
In conclusion, we have demonstrated high-quality epitaxial growth of VSe 2 -NbSe 2 hybrid structures using MBE. We have observed significant and spatially uniform reduction of the superconducting gap of the NbSe 2 substrate on the VSe 2 islands with the reduction being thickness dependent and stronger on bilayer VSe 2 . This would be most naturally explained to result from magnetization of the VSe 2 layer. The other electronic and magnetic characterization results are also more consistent with magnetization than with charge density waves.
Finally, we observe strongly position-dependent, enhanced dI/dV intensity at the Fermi level around the edges of the VSe 2 layer suggesting that the atomic-scale structural details of the edge of monolayer VSe 2 may contribute to its unusual magnetic response. Finally, our work suggests that it will be possible to combine 2D TMDs with different quantum ground states to stimulate new work in the field of 2D-TMDs hybrids. DFT calculations. All density-functional theory calculations are carried out in the plane-wave basis in the projector augmented wave framework as implemented in VASP. [62][63][64] In all calculations, we use 500 eV cutoff and k-point sampling corresponding to 24 × 24 mesh in the primitive cell. High k-point mesh is required to correctly describe e.g. the CDW phases.

Methods
Further computational details are given in the SI.
V tends to exhibit strong Coulomb correlations, which usually necessitates using either hybrid functionals or +U. It was shown in Ref. 40 , that depending on the U-parameter, the monolayer is either in nonmagnetic CDW state or in ferromagnetic no-CDW state. This

Supporting Information Available
The following files are available free of charge.
More experimental and computational details.

Computational details
All density-functional theory calculations are carried out in the plane-wave basis in the projector augmented wave framework as implemented in VASP. S1-S3 In all calculations, we use 500 eV cutoff and k-point sampling corresponding to 24 × 24 mesh in the primitive cell.
High k-point mesh is required to correctly describe e.g. the CDW phases.
V tends to exhibit strong Coulomb correlations, which usually necessitates using either hybrid functionals or +U. It was shown in Ref., S4 the depending on the U-parameter, the monolayer is either in nonmagnetic CDW state or in ferromagnetic no-CDW state. This balance is also affected by the number of electrons S4 and likely also by strain.
We calculated the lattice constants and magnetic moments using several exchange-correlation functionals S5-S7 in order to choose a suitable one. The results are shown in Table   S1 and also in Fig. S2  We also studied the CDW phase stability. We here only considered the √ 3R30× √ 7R19.1 pattern suggested in Ref. S8 As shown in the calculated phonon dispersion curves in Fig. S3, the imaginary frequency modes are located at the same wavevectors, which justifies using the same CDW pattern with all functionals. The energy difference between this phase and the FM phase are also given in Table S1. Only within LDA, CDW phase is slightly lower in energy (by 7 meV/formula unit), whereas PBE and revB86b both slightly favor FM phase (by 4-13 meV/f.u.). Upon adding +U correction the FM phase becomes strongly favored.
We note, that for U values in the range 2-4 eV, a lower energy FM structure with broken symmetry was found (cf. Fig. S2). The unit cell size remains at 3 atoms, but the two lattice constants have different lengths.
As a result, revB86b with moderate U (e.g. 2 eV) gives results in good agreement with HSE and also lattice constant in fairly good agreement with experiments. On the other hand, the CDW phase can be stabilized, or nearly stabilized, only without U.

S4
Electronic structure Band structure of monolayer NbSe 2 is shown in Fig. S4. The valence bands are all formed out of Nb-d and Se-p. Fermi-level crosses one distinct band, which is also responsible for the CDW. Spin-orbit coupling splits this band by 0.19-0.31 eV.
Band structure of monolayer VSe 2 is shown in Fig. S5. There is partly filled V-d band, similar to NbSe 2 . +U parameter controls the separation between the spin-up and -down channels of this band.
The PBE calculated work functions are 5.56 eV for NbSe 2 and 5.02 eV for VSe 2 . Thus, we expect to have electron transfer from VSe 2 to NbSe 2 (hole-doping of VSe 2 ). Comparing these to the Fermi-level position of graphene at 4.39 eV suggests charge transfer from graphene to VSe 2 (electron-doping of VSe 2 ). According to Fumega and Pardo, S4 FM becomes stronger at small hole-doping and weaker at electron-doping (assuming Stoner mechanism).

CDW structures
Bulk NbSe 2 adopts incommensurate CDW phase, although nearly commensurate to 3×3, S9 at T < 33 K. Calculations are carried out at 0 K and thus also show CDW-phase when  Figure S5: Band structure of monolayer T-VSe 2 calculated using revB86b (top), revB86b+U(2) (middle), and revB86b+U(5) (bottom), projected on V-sp, V-d, Se-s, and Se-p, respectively in the four columns. Half of k-points are spin up and half are spin down. Energy zero is at Fermi-level.
suitable supercell is used. In 3×3 monolayer supercell, PBE and revB86b calculations yield CDW-phase lower in energy by 4 meV (33 K·k B ) per formula unit.
There are two nearly degenerate phases for the CDW distortion, hexagon-centered (HC) and anion-centered (AC). S10 These are shown in Fig. S6.
Atomic structure of the CDW phase VSe 2 is shown in Fig. S7.  Fixing H-NbSe 2 to BaB, T-VSe 2 can be located at BaC, CbA, and AcB, or inverted at CaB, AbC, and BcA. The binding energies are listed in Table S2, and defined with respect to strained monolayers, so that it only contains the interlayer binding contribution. The results without +U show large changes in the magnetic moment, indicating sensitivity of the S7 system to converge to either FM or NM phase.   The simulated STM image for CDW-VSe 2 is in good agreement with the experimental images reported in, S8 but not observed in our experiments.

Simulated STS
STS is simulated within Tersoff-Hamann approach using LDOS as where ρ i = |Ψ i | 2 is the partial charge density of ith Kohn-Sham orbital, z 0 determines the distance above the surface, and δE sets the energy resolution; here 20 meV.
LDOS (a.u.)  Figure S12: The evolution of simulated STS spectra with increasing +U parameter (revB86b functional) and comparison to the experimental spectrum.
LDA and revB86b in the NM phase show a very prominent peak at Fermi-level that is in poor agreement with experiments. The same is true for the LDA result in FM phase due to S11 very small magnetic moment. The simulated spectra for the CDW phase seems consistent with the dip at the Fermi-level and the step-like structure at positive energies seen in the experimental spectra, although (i) in the calculations the dip is about 0.15 eV above Fermilevel and (ii) the dip appears to be present already in the NbSe 2 spectrum. Point (i) would contradict with the expected hole-doping from the calculated work functions. Although point (ii) suggests NbSe 2 origin for the dip, the dip becomes more pronounced in the bilayer spectrum. These features could be a signature of the CDW phase in the bilayer region, which makes sense as bulk VSe 2 is known to exhibit CDW and also the bilayer regions are very small and thus strongly affected by the edges. On the other hand, these features are fairly weak in the monolayer spectrum and there is also an additional peak at 1.5 eV and the change in the peak shape at around -0.5 eV. These changes are consistent with the change between the revB86b calculated CDW and FM phases. The peak around 1.5 eV becomes more pronounced and the peak at -0.05 eV in CDW phase moves down to -0.3 eV in the FM phase.
Increasing the value of the U-parameter to 1-2 eV the lower energy features appear to be in good agreement with experiment, but there is an extraneous strong peak at about E F + 0.5 eV. At U ≥ 3 eV, the agreement becomes rather poor.
The band structure, density of states, simulated STS, and experimental STS calculated using revB86b+U(2) are shown in Fig. S13 and can be compared to the revB86b calculated results in Fig. 3 in the main paper.
Intensity (a.u.) Expt. 1L Expt. 2L  Figure S13: Band structure, density of states, simulated STS, and experimental STS calculated using revB86b+U (2). The peaks are denoted as in the main text.

S13
Background removal from the VSM measurement For the data shown in Fig. 3a of the main paper a linear background is removed as shown in Fig. S14.

S14
Raw data before and after removing monolayer VSe 2 Figure

S17
The quality of the sample (e.g. the sharpness of the VSe 2 edges) can be improved by growing the sample at a high substrates temperatures. Fig. S17a shows STM characterization of sub-monolayer VSe 2 films on NbSe 2 substrate grown at T = 600 K. The edge of the island is much sharper compare with low growth temperature, which is grown at T = 540 K (Fig. S17c). However, at high temperature growth, the metal atom starts to intercalate NbSe 2 and as a result of that the NbSe 2 substrate loses the long-range charge density wave order as shown in an atomic resolution STM image (Fig. S17b). In our experiment, we have optimized the substrate temperature (T = 540 − 570 K) to insure that the long-range charge density wave order is preserved (Fig. S17d). The metal intercalation not only affects the charge density wave order but also the superconducting gap. Fig. S17e shows the dI/dV spectra measured on NbSe 2 surface with and without a metal intercalation.
Fitting the superconducting gap