Transport properties of 2H-NbSe2 synthesized by selenization of Nb thin films

A novel method for the synthesis of 2H-NbSe2 thin films by selenization of precursor Nb thin films is reported. The polycrystalline films grow predominantly in the hexagonal 2H-NbSe2 phase with bulk lattice constants. Their remarkable microstructure consists of a three-dimensional network of flake-like grains substantially stacked vertically on the substrate. The electronic transport between 1.2 K and 300 K in zero and applied magnetic fields up to 14 T has been extensively studied. The study comprises resistivity, magnetoresistance, Hall coefficient, upper critical field, and critical current density. The results are discussed taking account of the coexisting charge-density-wave and superconducting phases.


Introduction
The metallic layer material 2H-NbSe 2 belongs to the material class of transition metal dichalcogenides (TMDs) [1,2].It crystallizes in a highly anisotropic hexagonal (H) layered structure.The unit cell with bulk lattice constants a = 0.344 nm and c = 1.254 nm consists of two (2) single Se-Nb-Se monolayers rotated by 180 • with respect to one another with a thickness of c/2 [3].The Nb atom has as nearest neighbors 6 Se atoms arranged at the apices of a trigonal prism.This trigonal prism layer structure is stacked along the c-axis direction in a hexagonal close-packed AB sequence [4].The intralayer bonding is covalent and strong, while the interlayer Se-Se bonding is weak due to van der Waals interaction between adjacent layers.For this reason bulk three-dimensional (3D) NbSe 2 crystals can be cleaved into two-dimensional (2D) Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.flakes of a few layers and even monolayers [5].Physical properties of the 2D material can be different from those of the 3D material.
The compound 2H-NbSe 2 is a conventional s-wave, phonon mediated, type II superconductor with the highest bulk superconducting transition temperature T c of 7.2 K among the TMDs [6].Two-band superconductivity is suggested by [7,8] although an anisotropic s-wave single-band approximation cannot be excluded since electron-phonon coupling in one of the bands dominates [9,10].For bilayer and noncentrosymmetric monolayer the existence of a Bose-metal and Ising pairing in superconductivity has been reported, respectively [11,12].Superconductivity coexists with charge-density-wave (CDW) order in bulk and even single-layer 2H-NbSe 2 [13,14] by opening the respective energy gaps on different parts of the Fermi surface.However, the magnitude of the gaps remains ambiguous [15][16][17].
The TMD 2H-NbSe 2 is a prototypical CDW system.The CDW phase is a macroscopic quantum state consisting of a periodic modulation of the electronic charge density accompanied by a periodic distortion of the crystal lattice.The triple incommensurate CDW order in 2H-NbSe 2 sets in at the temperature T CDW = 33 K and is manifested, e.g. by an anomaly in the resistivity and a drop with a sign reversal in the Hall coefficient.The transition has also strong optical signatures [18].The resistivity is actually reduced in the CDW-ordered phase [19] that is insensitive to high magnetic fields as evidenced by x-ray scattering studies [20].The origin of the bulk second-order phase transition remains controversial.According to [21] the origin of the CDW in 2H-NbSe 2 is well described by the momentum dependence of the electron-phonon-coupling matrix element, but not by Fermi surface nesting [22] or saddle-point singularities at the Fermi surface [23].
In this study a novel method for the synthesis of 2H-NbSe 2 thin films is reported.The process is composed of two steps: in the first step Nb thin films are deposited onto single-crystalline (001) oriented MgO substrates by conventional dc magnetron sputtering.In the second step these precursor films are transferred to an evacuated and heated reactor made of carbon where they are exposed to Se vapor for only a few minutes resulting in rapidly grown polycrystalline 2H-NbSe 2 thin films.The films are characterized with respect to their crystallographic structure and microstructure.The temperaturedependent resistivity and self-field critical current density are measured in zero magnetic field.Magnetoresistance, Hall coefficient, upper critical field and critical current density are determined for magnetic fields up to 14 T and temperatures down to 1.2 K.
The organization of this article mostly replicates that of a paper previously published by the authors [38].

Experimental
In the first step Nb precursor films with a typical thickness of 900 nm were deposited onto 5 × 5 mm 2 (001) oriented singlecrystalline MgO substrates by high-power dc magnetron sputtering of a circular Nb target (99.9%purity, 75 mm diameter).The residual pressure in the vacuum chamber before deposition was 1 × 10 −7 mbar.During deposition the substrate temperature was held at 850 • C, and the Ar operating pressure was 4 × 10 −3 mbar.The Nb deposition rate amounted to 1 nm s −1 .The films were patterned in situ to 250 µm long and approximately 100 µm wide stripes by using metal masks fixed over the substrate.For the Hall measurements the pattern was like a cloverleaf [39].The normal-and superconducting properties of the Nb stripes were excellent.The residual resistivity ratio RRR =ρ (300 K) /ρ (9.5 K) amounted to a high value of 22. T c = 9.4 K with a transition width less than 0.1 K was even higher than the bulk value of 9.25 K [40] probably due to strain.
In the second step the vacuum chamber was vented with high-purity Ar.The freshly prepared patterned Nb precursor film was transferred to the reactor shown in figure 1 as fast as possible to minimize the exposure to nitrogen, oxygen, and moisture.The exposure to dry air was no longer than 5-10 min.The Se vapor source consisted of two amorphous Se shots with 99.999% purity (Alfa Aesar, 3-4 mm diameter, 60 mg weight per shot) placed next to the Nb film.The reactor mounted on a heater plate was made of carbon (alumina and BN were not suitable) that does not react with Se vapor at high temperature.The pressure in the reactor was reduced to 10 −7 mbar in a second vacuum chamber.Thus, the NbSe 2 film was synthesized clean of nitrogen, oxygen, and water.As demonstrated in figure 2 the temperature of the reactor was increased to 800 • C within approximately three minutes and held for a few seconds.After switching off the heater the reactor with the fast-grown NbSe 2 film cooled down to 100 • C within 30 min.With 900 nm thick Nb precursor films the thickness of the resulting 2H-NbSe 2 films came to 3400 nm.This thickness increase by a factor of 3.8 corresponds to the ratio of the caxis lattice constant of 2H-NbSe 2 (c = 1.254 nm) and the lattice constant of bcc-Nb (a = 0.32986 nm).
The film thickness was measured by a surface profilometer.X-ray (XRD) diffraction scans at room temperature revealed the crystallinity of the films.Scanning electron microscopy (SEM) enabled the study of the surface morphology.Direct current (dc) four-probe resistance and transport critical current measurements in the normal and superconducting state, respectively, were carried out from room temperature to 1.2 K. Applied static magnetic fields normal and parallel to the film plane varied between zero and 14 T. The Hall measurements were performed by using the van der Pauw method [39,41].

Film crystallinity
A typical Θ−2Θ XRD scan measured on a 3400 nm thick 2H-NbSe 2 film on a (001) oriented MgO substrate is shown in figure 3. The film grows in the hexagonal 2H-NbSe 2 phase (P6 3 /mmc, space group No. 194) with lattice constants a = 0.344 nm and c = 1.254 nm in accordance with the values for bulk powder samples [42].The reflections with the strongest intensities can be indexed by (00ℓ) (ℓ = 2, 4, 6, 8, 14) and reveal a rudimentary epitaxial c-axis growth of NbSe 2 [001] ∥ [001] MgO with a broad mosaic spread of 1.3 • and an in-plane oriantational relationship NbSe 2 [100] ∥ [100] MgO inferred from the respective ω-and Φ-scans.There are, in addition, a textured growth of (110) oriented grains with a broad mosaic spread of ω = 5.5 • and polycrystalline grains.A tiny admixture of foreign phases, among them presumably Se and Nb 2 Se 3 , can also be found.

Film surface
The SEM micrograph in figure 4 displays flake-like flat grains that are presumably single-crystalline and consist of parallel Se-Nb-Se layers.The size of the flakes and their thickness are estimated at a few microns and 400-1000 monolayers.A substantial amount of the flakes are stacked vertically on the substrate with random azimuthal orientation.They form a 3D network with the remaining randomly tilted or horizontally stacked flakes, which the observed epitaxy can be ascribed to.
A similar microstructure is also reported in [36] for bulklike polycrystalline 2H-NbSe 2 films prepared by selenization  of Nb precursor films on SiO 2 / Si substrates in a two-step vapor-phase reaction under ambient pressure by using a twozone furnace.

Electronic transport in zero magnetic field
3.3.1.Resistivity.The temperature-dependent dc resistivity ρ from 7 K to room temperature of a 100 µm wide 2H-NbSe 2 stripe is shown in figure 5(a).The profile looks similar to those reported in [43,44] for single crystals.The resistivity ρ RT at room temperature (RT ≈ 300 K) of 478 µΩ cm and the residual resistivity ρ res at 7.5 K of 35 µΩ cm in the polycrystalline film are significantly higher than the corresponding values for the single crystals in [43,44].The residual resistivity ratio RRR =ρ RT /ρ res of 13.6 is substantially lower than RRR of the single crystals, nevertheless, relatively high for a thin film.Between 7.5 K and 18 K, above the transition temperature T c to superconductivity and below the transition temperature T CDW to the CDW phase, the temperature dependent part of the resistivity ρ T = ρ − ρ res displays a cubic T 3 -dependence in accordance with [44,45].In a two-band model by Wilson [46] a cubic temperature dependence is expected for electronphonon interband scattering between bands of high and low mobility (see also 3.4.2.)In the low-temperature range below 18 K the resistivity also manifests adherence to Matthiessen's rule ρ = A + BT n that expresses the temperature-independent contribution to ρ due to scattering by lattice imperfections and the separate contribution due to a temperature-dependent process such as electron-phonon scattering.The value of the exponent n depends on the specific scattering mechanism.Above T CDW up to ≈110 K ρ T reveals a linear behavior CT + D with D< 0 suggestive of usual electron-phonon scattering.In a normal metal, however, D = 0 and ρ T is generally proportional to the temperature above the Debye temperature Θ D .For 2H-NbSe 2 , Θ D ≈ 160 K [44] is much above the temperature range of the observed linearity, questioning that 2H-NbSe 2 is a normal metal.Above 110 K ρ T deviates from linearity with a negative curvature up to 300 K.
The resistive transition to superconductivity together with the residual resistivity is demonstrated in figure 5(b).The 90% ρ res onset temperature, the 50% ρ res midpoint temperature and the 10% ρ res downset temperature amount to 7.37 K, 7.30 K, and 7.23 K, respectively, resulting in a 90% to 10% transition width ∆T c = 0.14 K.Such a small value hints to a homogeneous sample.
The anomaly at T CDW = 32 K in figure 5(c) is the signature of the onset of CDW ordering.At this temperature the first derivative dρ/dT has a minimum as shown in figure 5(d).With the onset of the CDW phase ρ (T) changes the slope and drops more rapidly below T CDW .This is explained in terms of van Hove singularities driving the CDW phase and acting as scattering centers above T CDW which are removed from the CDW phase [19].In [44] the more rapid drop is explained by phase ordering of the CDW, i.e. the absence of impurity-like phase disorder scattering due to local CDW fluctuations.The observation of the anomaly in the polycrystalline film with a relatively low RRR of merely 13.6 might be astonishing, since in [47,48] the authors argue that single crystals with RRR around 30 or higher are needed to observe a CDW anomaly in the temperature dependent resistivity.The weakness or vanishing of the anomaly is ascribed to a distortion of the CDW phase order in samples with lower RRR [48].In our opinion figures 5(c) and (d) confirm a high CDW phase order with large CDW domains and few domain boundaries that enable the observation of the anomaly in the resistivity despite the low RRR.

Self-field critical current density.
The self-field transport critical current density j c (T) = I c (T) /A of the superconducting stripe was measured in dependence on the temperature.I c is the critical current determined from voltage-current characteristics, and A = 4.1 × 10 −6 cm 2 is the cross-sectional area of the stripe measured by using a surface profilometer.The I c criterion is the well-recognized field-strength E c = 1µV cm −1 .j c (T) is shown in figure 6 from 1.3 K to 7 K together with the resistivity from 7 K to 14 K (cf Figure 5(b)).j c is in the order of magnitude 10 5 A cm −2 which is a factor of 10 larger than 10 4 A cm −2 reported for 2H-NbSe 2 single crystals of stoichiometric composition in zero magnetic field [49].This comparison with single crystals suggests that the grain boundaries in the polycrystalline film (the contacts between the flakes in figure 4) function as strong links enabling a high j c .
For a quantitative description of j c (T) a proximity-effect model based on de Gennes' theory is employed [50,51].The model predicts a power-law dependence of j c (t) = j c (0) (1 − t) β with the reduced temperature t = T/ T c .The The j c (T) measurement and particularly its analysis build upon our previous work on FeSe thin films [38].In that work a different exponent β = 2 was found suggesting normal conducting grain boundaries.
Concerning the larger j c values in comparison to a single crystal an explanation alternative to the proximity-effect model is provided by enhanced pinning of vortices in the self-field at corrugations of the inherently rough film surface [52,53].This approach is supported by the results discussed in 3.4.4.Where surface pinning turns out an important pinning mechanism in the mixed state.A static magnetic field was applied perpendicular (B ⊥ ) and parallel (B ∥ ) to the film plane.In the figures 7(a) and (b) the resistivity ρ (T, B) for B ⊥ and B ∥ is shown for temperatures T from 1.2 K to 8 K with the magnetic induction B as a parameter from 0 to 14 T.With increasing B T c is stronger reduced for B ∥ than for B ⊥ .There is a parallel shift of the transition curves at low fields.A significant broadening of the transition occurs beyond 7 T for B ⊥ and 1 T for B ∥ .Regarding the low-field shift the 2H-NbSe 2 film resembles low-T superconductors [54].In the normal state, just above T c , the residual resistivity increases with decreasing T and increasing B. The increase is visibly stronger for B ⊥ .
The resistive transition to superconductivity, i.e. the field and temperature dependent drop of the resistivity in figure 7, is analyzed in terms of thermally activated flux flow (TAFF) [55,56].The TAFF model assumes pinning of the flux line  The inset in (a) shows the temperature dependence of the effective mobility µ (T) that is used as a fitting parameter for the parabola in (a).The dashed line is a power-law fit.
matter leads to a specific field dependence of U. The logarithmic dependence, that was also found for mono-and bilayer 2H-NbSe 2 [11,58] with clearly lower activation energies compared to our bulk-like films, suggests a quasi 2D 'pancake' vortex matter as it is expected for layered superconductors in a transverse magnetic field [59].The results for the field parallel to the film plane (B ∥ ) are very similar to those in figure 8. U 0 = 730 K is higher and B 0 = 11.4T lower.The small difference suggests that the pinning forces weakly depend on the field orientation.
The transverse (B ⊥ ) magnetoresistance MR(B, T) = (ρ(B, T) − ρ(0, T))/ρ(0, T) in the normal state from 70 K to 8 K is shown in figure 9. MR is small, positive, symmetric to vertical axis and increasing with increasing field and decreasing temperature.At T > 33 K (figure 9 2 ] that is reduced to MR (B, T) ≈ (µ (T) B) 2 for µB ≪ 1 (solid lines in figure 9(a)).µ is an effective MR mobility of electrons and holes.In a semiclassical approach for a two-charge-carrier system such as 2H-NbSe 2 (cf 3.4.2.) µ depends on the electron and hole carrier densities n e , n h and mobilities µ e , µ h : The quadratic growth for µB ≪ 1 is predicted by the conventional theory of MR in a metal with nonequal densities of electrons and holes [60].Since µB ≫ 1 is not met in this study, saturation or further quadratic growth in the case of compensation, i.e. equal densities of electrons and holes, is not observed.The temperature dependence of the mobility µ (T) is displayed in the inset of figure 9(a).µ increases with decreasing T up to a small value of 125 cm 2 V −1 s −1 at 33 K.A power-law dependence µ (T) ∝ T −δ with δ ≈ 1.9 ± 0.1 is an appropriate fit to the data points.The exponent δ close to 2 points to Fermi-liquid behavior.
The value of MR increases significantly with decreasing T below T CDW and reaches a value of 18% at 8 K and 12 T (figure 9(b)).The shape of the curves remarkably changes from weak-field quadratic below B ≈ 2 T to high-field linear for B ≳ 2 T (solid lines in figure 9(b)), possibly triggered by the CDW order.The anomalous linear dependence on magnetic field strength was already observed for 2H-NbSe 2 single crystals [61,62].The slope of the linear MR increases from 25 K to 8 K by almost a factor of 3.There are many reports on linear MR in various materials such as potassium [63], the heavily disordered silver chalcogenides Ag 2−δ Se and Ag 2−δ Te [64], graphene [65], 2D layered SrMnBi 2 [66], the topological insulator Bi 1.5 Sb 0.5 Te 1.7 Se 1.3 [67], and the iron-based superconductors Ba(Sr)Fe 2 As 2 [68] and FeSe 0.4 Te 0.6 [69].
Linear or quantum MR can be interpreted in terms of a quantum limit [70] where all the charge carriers occupy only the lowest Landau level.It is associated with the existence of high-mobility Dirac fermions that dominate the electronic transport.A certain possibility of linear MR, however, exists in a polycrystalline metal with an open Fermi surface [60].Regarding the 2H-NbSe 2 films in this work further studies are needed to investigate the scenario of Dirac fermions, in particular the study of the temperature dependence of the crossover field from quadratic to linear behavior of MR.Since linear MR in 2H-NbSe 2 occurs below T CDW it is suggestive that the charge density wave is responsible for the effect.In [61][62][63] it is pointed out that the existence of CDW energy gaps provides a scattering mechanism, and the linear MR has been tentatively attributed to magnetic breakdown of the gaps.R H of the films can be compared to R H of 2H-NbSe 2 single crystals and bilayers.In pure high RRR single crystals R H is positive and nearly constant down to 50 K to 40 K where a rapid drop starts accompanied by a sign reversal at around 25 K to 30 K [3,[71][72][73].On the other hand no sign reversal and increase with and without a drop is observed in impure low RRR single crystals and bilayer 2H-NbSe 2 [72][73][74].
In order to estimate the hole and electron carrier densities n h , n e and their mobilities µ h , µ e the magnetoresistance MR of the same sample was also measured at 200 K where R H starts to be constant with increasing temperature (see figure 11).In a semiclassical approach R H and MR of a two-charge-carrier system in the low field region are given by [75,76]: ) /(n h µ + n |µ e |) 2 and A simultaneous fit of the experimental ρ xy (200 K) (see figure 10(a)) and MR (200 , µ e /µ h = 7.7.Using the formulae of Wilson's two-band model [77] and assuming temperature-independent carrier densities Huntley and Frindt [72] determined for their single crystals n h = (8.8± 0.8) ×10 21 cm −3 and n e = (4.2± 0.6) ×10 19 cm −3 with n h /n e = 210 corresponding to about 1 hole per 2 Nb atoms and 3 electrons per 1000 Nb atoms.The carrier mobilities were assumed to be temperature dependent due to scattering with phonons at high temperature and impurities at low temperature, e.g.µ h = 10 cm 2 V −1 s −1 , µ e = 80 cm 2 V −1 s −1 with µ e /µ h = 8 at 200 K and µ h = 100 cm 2 V −1 s −1 , µ e = 2000 cm 2 V −1 s −1 at 20 K.The reasonable agreement with our values above confirms the scenario of holes of high density and low mobility and electrons of much lower density and much higher mobility also in the thin films.The existence of electron and hole bands is compatible with the T 3 dependence of the resistivity at low temperature (see 3.3.1).

Upper critical field.
The temperature dependent upper critical field B c2 (T) is determined from the ρ (T, B) curves in figure 7 as the field at which ρ is 90% of the residual resistivity.The result is shown in figure 12 for B ⊥ and B ∥ from 0 to T c = 7.3 K and 0-14 T. B ⊥ and B ∥ mean the applied magnetic field perpendicular and parallel to the substrate surface or film plane, respectively.In our polycrystalline 2H-NbSe 2 thin films these field orientations are not necessarily perpendicular and parallel to the Se-Nb-Se layers, in contrast to single crystals and c-axis oriented epitaxial thin films.Just below T c there is a fairly good agreement with the single crystal data by Leupold et al [78] (dashed lines in figure 12).However, whereas B c2 (T) of the single crystal increases linearly with c2 (here, ∥ and ⊥ mean parallel and perpendicular to the Se-Nb-Se layers) when T decreases, our B c2 (T) thin-film curves have a crossing point at 6.4 K and 2 T where B ⊥ c2 becomes larger than B ∥ c2 (see inset in figure 12).Moreover, the curves show a positive curvature for both field orientations down to the inflection points at 5.3 K and 7 T for B ⊥ and at 5.2 K and 6 T for B ∥ .The temperatures of 5.3 K and 5.2 K are close to the temperature 5.6 K reported in [79].At the inflection points the B c2 (T) curves change from positive curvature to a linear behavior with decreasing T. The extrapolation of the linear fit to zero temperature results in B ∥ c2 (0) = 23 T and B ⊥ c2 (0) = 32 T.These values are larger than those reported for the single crystal (16 T for B ∥ and 6 T for B ⊥ ).
Although not observed in the single-crystal data of [78], positive curvature and, in addition, extended linearity down to low temperature seem to be typical for 2H-NbSe 2 , as reported in [80][81][82].Positive curvature is also observed in other layered superconductors, namely superconducting multilayers Nb/ Nb 0.6 Ti 0.4 [83], electron-doped high-temperature superconductors L 2−x Ce x CuO 4−y (L = Sr, Sm, Nd) [84], K x Ba 1−x BiO 3 high-temperature superconductor single crystals [85] and  [78] where c2 over the entire temperature range.The dotted lines represent polycrystalline thin-film data [36] with due to a dedicated film morphology.The inset also demonstrates the agreement of our thin-film data with the single-crystal data just below Tc = 7.3 K.
Fe-based high-temperature superconductor NaFe 1−x Co x As [86].According to [81] positive curvature and enhanced linearity of B c2 (T) is an intrinsic phenomenon in 2H-NbSe 2 not due to the charge density wave and not due to sample inhomogeneities.The properties can be explained by the anisotropy of the Fermi surface, that consists of open hole-and electronlike undulating cylinders with an additional closed hole-like pocket, and by a strong anisotropy of the electron-phonon interaction in layer compounds [79].A dimensional crossover from bulk-like to 2D-like is also expected to produce a characteristic positive curvature at least in B ∥ c2 (T) [87].The crossing point at 6.4 K and 2 T in our thin-film data remains elusive.A relation c2 is also reported in [36] for bulk-like polycrystalline 2H-NbSe 2 thin films (see dotted lines in figure 12).The authors argue that B ⊥ c2 > B ∥ c2 is reasonable if 2D-flakes consisting of a few parallel Se-Nb-Se layers are to a large extent stacked vertically on the substrate and form a 3D-network with other randomly tilted flakes.Such a particular microstructure is indeed observed in our thin films, as shown in figure 4.

Critical current density.
The critical current densities j c (B, T) are plotted in figures 13(a) and (b) for B parallel and normal to the film surface, respectively, at various temperatures between 1.4 K and 6.5 K.At each temperature the critical current densities for both field orientations decrease over two orders of magnitude from 0.1 T to 10 T. The decay of j c with increasing field is apparently stronger for the parallel field configuration.The dashed lines in figure 13(a) for temperatures up to 5 K are exponential-decay fits j c (B) = j c (0) exp [−(B/B 0 ) 3/2 ] with the normalization field B 0 .The strong exponential decay is typical for pinning of small bundles of vortices in contrast to pinning of single vortices where a power-law dependence of j c (B) is expected [88].The exponential dependence is distinctive of collective pinning with randomly distributed pinning centers [89].The normalization field B 0 is temperature dependent as illustrated in the inset of figure 13(a).B 0 decreases linearly from 3.4 T at 1.4 K to 1.2 T at 5 K.
The data points at 6 K and 6.5 K cannot be fitted by the simple function above.A fit succeeds only with a superposition of two exponential functions with temperature-dependent coefficients A 1 , B 1 , A 2 , and B 2 .
The fitting curves have an indentation at a crossover field B cr .This feature becomes very clear in figure 13(b) for the normal field orientation at all the temperatures.The solid lines are two-exponential-function fits to the data points, and the cross-line connects the points where the indentation occurs in dependence on temperature.B cr (T) is displayed in the inset of figure 13(b).It decreases linearly from 5.3 T at 1.4 K to 0.5 T at 6.5 K.
Scaling the pinning force density F p (T, B) = j c B in the mixed state of a type II superconductor is useful in the study of pinning mechanisms [90].The figures 14(a) and (b) show the scaling of the reduced pinning force density f p = F p /F p max with b = B/B max for both field orientations.F p max (B max ) are the maxima of the experimental F p (B) functions with T as a parameter (not shown here).Apart from the data points above b = 3 and 5 K all the points lie on unique master curves.The significance of these curves is that the critical current density is governed by specific types of pinning [91].The type of pinning is revealed by the characteristic functional form of f p (B) which is sensitive to the pin strength and spacing [92].The positions of the peaks in f p (B) in the figures at low b hint to strong, closely spaced pins.The generic functional form with B max as the scaling field is f p (B) = Cb p (1 − Db) q [93].The solid lines, that fit the data points in figure 14, are the result of a superposition of two pinning types: normal point pinning (p = 1, q = 2, dashed lines) and normal surface pinning (p = 0.5, dotted lines).The weights of normal point pinning and normal surface pinning are approximately 40% and 60%, respectively, in figure 14(a) and vice versa in figure 14(b).Above b = 3 and below 5 K normal surface pinning is apparently the mere mechanism for both field orientations.
The j c (B, T) measurements and their analysis are also based on our work published in [38] (cf 3.3.2).It is worth comparing the results: for the FeSe thin films in [38] no indentation of the j c (B, T) curves was observed.The data could be described by a power-law fit below a crossover field and an exponential-decay fit above.Only one type of pinning was identified, namely normal surface pinning on grain boundaries.

Summary and conclusions
A novel preparation method is presented where a precursor Nb thin film is rapidly selenized under high vacuum mostly avoiding contamination with nitrogen, oxygen, and moisture.In the near future a complete in situ process will be realized without exposing the precursor film to ambient air.In principle the process may enable the growth of epitaxial thin films by the choice of suitable substrates and adopted process parameters.It is encouraging for material systems consisting of metals and high-vapor pressure components, e.g.transition metal sulfides, selenides, and tellurides such as WS 2 , TaSe 2 , or MoTe 2 .
The polycrystalline films grow predominantly in the hexagonal 2H-NbSe 2 phase.Their microstructure is extraordinary: flake-like flat grains are substantially stacked vertically on the substrate with 3D interconnection.
The main results of the electronic transport measurements can be summarized as follows: The resistivity anomaly at 32 K and the sharp drop at 7.3 K reveal the onset of the coexisting CDW and superconducting phases, respectively.
The resistive transition to superconductivity in a magnetic field is analyzed in terms of thermally assisted flux flow with the result of a quasi 2D pancake vortex matter as expected for layered superconductors.
The linear magnetoresistance in the CDW phase is possibly triggered by the CDW order and hints at the existence of highmobility Dirac fermions.
According to the Hall coefficient and magnetoresistance measurements the electronic transport is dominated by holes of high density and low mobility and electrons of much lower density and higher mobility.The temperature dependent Hall coefficient starts to drop at the onset of the CDW order without sign reversal.
The temperature dependence of the upper critical field is characterized by a change from positive curvature to linear behavior that seems to be an intrinsic phenomenon in 2H-NbSe 2 .The linearity can be explained by the anisotropy of the Fermi surface and the electron-phonon interaction.The anisotropy of the upper critical field can be related to the extraordinary microstructure of the films.
Depending on field direction, field strength, and temperature range the critical current density can be described by strong exponential decay or a superposition of two exponential functions taking the noticeable indentation into account.The critical current density is determined by a superposition of normal point and normal surface pinning with strong, closely spaced pinning centers.Normal surface pinning dominates at low temperature and high fields.

Figure 1 .
Figure 1.Cross section of the cylindrical two-piece carbon reactor (bottom + lid) for the vaporization of solid Se shots (1) and the selenization of Nb precursor films (2).The reactor is mounted on a stainless-steel resistively heated plate.(3) Sheathed NiCr-Ni thermocouple.(4) heater-current source with temperature controller.

Figure 2 .
Figure 2. Temperature versus time profile for the selenization of Nb precursor films in the carbon reactor of figure 1.

Figure 4 .
Figure 4. SEM micrograph of the surface of the 3400 nm thick 2H-NbSe 2 film on (001) MgO substrate showing a combination of vertically and horizontally (parallel to the substrate surface) aligned and randomly tilted flakes.

Figure 5 .
Figure 5. (a) dc resistivity ρ versus the temperature T. (b) Magnification of (a) in the temperature range 7.1 K-7.5 K demonstrating the residual resistivity and the resistive transition to superconductivity.(c) Magnification of (a) in the temperature range 24 K-40 K.The hump at 32 K indicates the onset of the CDW phase.(d) First derivative dρ/dT of (c) to elucidate the onset of CDW order by the minimum at 32 K.

Figure 6 .
Figure 6.Left scale: critical current density jc versus temperature between 1.3 K and 7 K.Right scale: resistivity ρ versus temperature between 7 K and 14 K.The dashed line is a fit jc (t) ∝ (1 − t) with t = T/Tc.

Figure 8 .
Figure 8.(a) Arrhenius plot of the resistivity data in figure 7(a) normalized to the residual resistivity ρres (B) with the transverse magnetic field B ⊥ from 0.1 T to 14 T as a parameter (open circles).The data points are fitted by the solid lines according to the TAFF theory.(b) Thermal activation energy U(B) (full circles) and logarithmic fit (solid line) in a semi-log plot.

Figure 9 .
Figure 9. Magnetoresistance MR (B, T) in the low-field regime µB ≪ 1 at temperatures above (a) and below (b) T CDW .The solid lines are quadratic and linear fits to the data points (open circles).The inset in (a) shows the temperature dependence of the effective mobility µ (T) that is used as a fitting parameter for the parabola in (a).The dashed line is a power-law fit.

3. 4 . 2 .
Low-field Hall coefficient.The magnetic field dependence of the Hall resistivity ρ xy at 200 K, 33 K, 20 K, and 7.5 K is shown in figures 10(a)-(d), respectively.The field range, where ρ xy depends linearly on B, is shrinking with decreasing temperature.Whereas the linear range reaches from −12 T to 12 T at 200 K, it merely reaches from −0.75 T to 0.75 T at 7.5 K.For this low-field region, we define the low-field Hall coefficient R H = ρ xy /B for all the temperatures.The temperature dependence of R H is displayed in figure 11.R H is positive which means that the majority carrier type is hole-like.Above 200 K R H is apparently constant.Between 200 K and the onset of the CDW transition at 32 K R H increases and sharply drops in the CDW phase.A change of the sign of R H is not observed in our films.

Figure 11 .
Figure 11.Low-field Hall coefficient R H versus temperature.The solid line through the data points is a guide to the eye.

Figure 12 .
Figure 12.Anisotropic upper critical field B c2 (T) versus T for B ⊥ and B ∥ perpendicular (up triangles) and parallel (circles) to the film plane, respectively.The blue solid lines left from the inflection points (5.3 K | 7 T) for B ⊥ and (5.2 K | 6 T) for B ∥ are linear fits extrapolated to zero temperature.The red lines right from the inflection points are guides to the eye.The inset demonstrates the crossing point (6.4K | 2 T) where B ⊥ c2 becomes larger than B ∥ c2 with decreasing T. The dashed lines display data measured on a single crystal [78] where B

Figure 13 .
Figure 13.jc (B) (full symbols) for B parallel to the film surface (a) and B normal to the film surface (b) at temperatures from 1.4 K to 6.5 K.The dashed lines in (a) are exponential fits jc(B) = jc (0) × exp [−(B/B 0 ) 3/2 ].The inset in (a) shows the temperature dependence of the normalization field B 0 .The solid lines in (a) and (b) represent a superposition jc(B) = A 1 exp [−(B/B 1 ) 3/2 ]+ A 2 exp [−(B/B 2 ) 3/2 ] with temperature-dependent coefficients A 1 , B 1 , A 2 , B 2 .The cross-line in (b) connects the jc (Bcr, T) points where the curves have an indentation.The crossover field Bcr versus T is displayed in the inset of (b).

Figure 14 .
Figure 14.Reduced pinning force density fp = Fp/Fp max versus the reduced field b = B/Bmax (full symbols) with the temperature as a parameter for B parallel to the film surface (a) and B normal to the film surface (b).The dashed and dotted lines result from normal point pinning and normal surface pinning, respectively.The solid lines through the data points represent superpositions of 40% normal point pinning plus 60% normal surface pinning in (a) and 60% normal point pinning plus 40% normal surface pinning in (b).