Significant improvement of the lower critical field in Y doped Nb: potential replacement of basic material for the radio-frequency superconducting cavity

The research of high energy and nuclear physics requires high power accelerators, and the superconducting radio-frequency (SRF) cavity is regarded as their engine. Up to now, the widely used practical and effective material for making the SRF cavity is pure Nb. The key parameter that governs the efficiency and the accelerating field (E_acc) of a SRF cavity is the lower critical field Hc1. Here, we report a significant improvement of Hc1 for a new type of alloy, Nb_{1-x}Y_x fabricated by the arc melting technique. Experimental investigations with multiple tools including x-ray diffraction, scanning electron microscopy, resistivity and magnetization are carried out, showing that the samples have good quality and a 30%-60% enhancement of Hc1. First principle calculations indicate that this improvement is induced by the delicate tuning of a Lifshitz transition of a Nb derivative band near the Fermi energy, which increases the Ginzburg-Landau parameter and Hc1. Our results may trigger a replacement of the basic material and thus a potential revolution for manufacturing the SRF cavity.


Introduction
The SRF cavity was firstly proposed for accelerating charged particles and widely used for the research of high energy and nuclear physics [1]. A lot of research have been conducted on the SRF cavities over the past decades. The performance of a state-of-art SRF cavity is mainly determined by two key parameters [2][3][4]: the quality factor Q and the accelerating gradient of the electric field Eacc. The quality factor Q is inversely proportional to the cavity radio-frequency (RF) surface resistance Rs as Q = G/Rs (G is a geometrical factor independent on the cavity material) [2][3][4][5]. Generally, it is the energy loss in the skin layer of the cavity that restricts the RF application of superconductors when the RF electromagnetic wave is applied, and this power dissipation is characterized by the surface resistance Rs. Thus, Q determines the energy dissipation on the cavity per RF cycle. In principle, Rs is closely related to the normal state resistivity ρn (with the Bardeen-Cooper-Schrieffer theory in the dirty limit: Rs ~√ ) and the superconducting gap [2][3]. The former measures the quasiparticle scattering rate and latter influences the excited quasiparticle numbers at a certain temperature. In this case, Q can be evaluated by the normal state resistivity and the superconducting gap [2]. On the other hand, the maximal energy gained during each RF cycle is determined by Eacc which is proportional to the peak magnetic field Bpk in the way that Eacc = Bpk/g (g is a factor dependent on the cavity shape, e.g. g = 4.26 mT MV −1 m for TESLA-shape cavity) [2,4]. In principle, Bpk reflects the highest amplitude of the magnetic field for flux to penetrate the interior of the superconducting cavity. Thus, Bpk is limited by the maximum field for the superconductor to remain in Meissner state and resist flux penetration. For type-I superconductors ( <1/√2,  is the Ginzburg-Landau (GL) parameter), Bpk is limited by the thermodynamic critical field Bc, and for type-II superconductors ( > 1/√2 ), Bpk is limited by the lower critical field Bc1 [6,7]. While in practice, due to the existence of surface Bean-Livingston barrier, the superconductor can hold the metastable Meissner state up to the superheating field Bsh (> Bc1) if the surface is very smooth [8][9][10][11][12][13]. Bsh is dependent both on the GL parameter  and the thermodynamic critical field Bc. However, Bsh is difficult to be reached in practice because of surface roughness of the superconductor [14][15][16].
Up to now, Nb is still regarded as the most promising material for manufacturing the SRF cavities due to its relatively high critical temperature [2,17], rather high lowercritical field Bc1 [2,9], large superfluid density among all the element or alloy superconductors, and the high residual resistivity ratio [2,18]. Meanwhile, its high ductility allows for easy manufacturing. However, in practical, the pure Nb cavity is approaching its fundamental limit in terms of the magnetic flux entry field Bsh [19][20][21], and it is highly desired to have materials with better performance than Nb for making the SRF cavity [2,9]. In order to improve the peak magnetic field or quality factor of Nb cavity, some treatments have been carried out, such as the so-called International Linear Collider (ILC) recipe with the combination of the electro-polishing and baking at 120 o C for 48 h [22][23][24][25], nitrogen-doping [26][27][28][29], nitrogen-infusion [21,30], Nb3Sn coating [31][32][33], rare earth elements doping [34], etc. Besides, some ideas for achieving higher energy barrier of flux entry were also proposed [2]. But the improvement of Bc1 due to the aforementioned methods is still very limited. Meanwhile, the multilayer-structure proposed by Gurevich [35,36] and Kubo et al. [37][38][39] has been under extensive research [40,41]. The multilayerstructure consists of a superconducting and an insulating layer coated on the inner surface of the Nb cavity. The thickness of superconducting layer should be in the scale of London penetration depth which is tens of nanometers for Nb [2]. These ideas definitely deserve to be tested, but it is technically very hard for the manufacturing. Other candidate materials for SRF applications have also been explored, such as thin films of Nb [42,43], NbN [3,44], NbTiN [2], FeSe [45], MgB2 [46] and some A15 compounds (Nb3Sn, etc) coated on Nb or Cu substrates [47][48][49]. Besides the high demand for the quality factor and the peak magnetic field, the candidate materials for SRF applications also need to be tough, easy refreshing and polishing. Thus, we focus on the manipulation of material properties by slightly doping other elements to Nb. Our goal is to increase the lower critical field, but maintain the high Tc, large RRR and toughness of Nb. After trying doping with many different elements, it is found that the Nb1-xYx alloys can achieve a lower critical field of about 30-60% higher than Nb. This shows a great potential for the Nb1-xYx alloys to replace the existing Nb for achieving improved performance of the SRF cavity in the future.

Experimental details
The Nb1-xYx alloys were prepared by arc-melting method. Three doping levels were chosen, i.e. x=0.05, 0.10, 0.15 for the Nb1-xYx alloys. The Niobium (99.95%,) and Yttrium (99.9%,) were weighed, ground and pressed into tablets to prepare the precursors according to the corresponding molar ratio in a glove box filled with argon. Then the precursors were melted in the arc-furnace filled with high purity argon. The melting process lasts for at least one minute. To improve the homogeneity of the ingots, all precursors were flipped and remelted three times. At last, the well-mixed and high quality Nb1-xYx alloys were obtained. The structural characterization of the Nb1-xYx and Nb was performed with the x-ray diffraction (XRD) measurements on a Bruker D8 Advanced diffractometer with the Cu-Kα radiation. The surface topography and element composition analysis of the Nb1-xYx and Nb were taken on a Phenom ProX scanning electron microscope (SEM).
For DC magnetization measurements, all the samples were cut into rectangular shape by the wire cutting machine and

Results and discussion
Alloys with three nominal doping levels have been prepared, they are Nb0.95Y0.05, Nb0.9Y0.1 and Nb0.85Y0.15. The doping ratio x of the Nb1-xYx alloys is the mole ratio of the precursor during preparation. A bulk sample of high-purity Nb is used as comparison. Figure 1(a) shows the temperature dependence of magnetization measured in zero-field-cooled (ZFC) mode of Nb1-xYx and Nb. All samples are cut into a rectangular shape with almost the same sizes to reduce the interference of demagnetization effect [50,51]. The applied magnetic field is 10 Oe and parallel to the lateral plane of the samples, which is defined as ab-plane. The superconducting transition temperature Tc is determined by the point where the magnetization starts to deviate from the paramagnetic background at high temperatures, and the results are summarized in Table 1. The Tc = 9.35 K of Nb0.9Y0.1 is a bit higher than Tc = 9.17 K of Nb and the Tc of Nb0.95Y0.05 and Nb0.85Y0.15 is extremely close. This indicates that the slightlydoping of Y can slightly raise the Tc of Nb, which is consistent with previous results [52], and the operation temperature of SRF applications by using the new alloy is guaranteed. The very steep magnetization transitions in Figure 1 give details of the resistivity at low temperatures and the inserted images show the samples with electrodes for resistivity measurements. When temperature decreases, the resistivity decreases monotonically and shows a metallic behavior before entering the superconducting state. Meanwhile, when the applied field increases, the transition of the resistivity widens slightly and shifts to the lower temperatures until the superconductivity is suppressed completely. The residual resistivity ratio (RRR) is related with the thermal conductivity of the material and important for the SRF cavities. The RRR of Nb1-xYx is defined as RRR = ρ(300 K)/ρ(10 K).The measured results are RRR = 14.5 for Nb0.95Y0.05, RRR = 14.9 for Nb0.9Y0.1 and RRR = 11.1 for Nb0.85Y0.15, respectively. The RRR of Nb1-xYx are quite large, indicating a good quality of the samples, but these values are smaller than that of high-purity Nb (RRR = 243 in Supplementary Figure S4) [18]. This may be attributed to the slightly doping of Y and the increase of impurity scattering. However, with heat treatment at high temperature, the RRR of Nb1-xYx may be further improved [52]. The temperature dependence of the electrical resistivity of our high-purity Nb is also given in Supplementary Figure S4.
The crystal structures of Nb1-xYx and Nb are examined by x-ray diffraction (XRD) and the XRD patterns are shown in Figure 2(a). The Nb has a cubic (bcc) symmetry and a space group of Im -3 m (number 229) [53]. The Nb1-xYx have the same index peaks with Nb and no other peaks can be observed in Figure 2(a). This indicates that the Nb1-xYx have the same crystal structure with Nb and the slightly doping of Y does not change the structure of Nb significantly. However, the (110) peaks of XRD pattern of Nb1-xYx show a slightly shift to a higher angle compared with Nb in the inset of Figure 2(a). Meanwhile, the lattice parameters a calculated from the XRD patterns are a = 3.3065(3) Å for Nb0.95Y0.05, a = 3.3027(8) Å for Nb0.9Y0.1 and a = 3.3095(9) Å for Nb0.85Y0.15, compared with a = 3.3167(5) Å of Nb. The slightly decrease of lattice parameters and the shift of (110) peaks from XRD patterns both indicate that a measurable amount of Y has been successfully incorporated into Nb. The energy dispersive spectrums (EDS) of Nb1-xYx and Nb from scanning electron microscope (SEM) measurements are shown in Figure 2(b). The corresponding SEM images are given in Supplementary Figure S5. The SEM image in Figure 2(b) shows a quite smooth surface of Nb0.9Y0.1 with no clear grain boundary. The inset in Figure 2(b) shows the enlarged view of the EDS around 1.9 keV and the dashed vertical lines are the characteristic peaks of Nb (olive) and Y (pink) in the vicinity. With increasing ratio of Y in the alloys, the peak around 1.9 keV is elevated and shifts to higher energy, which is indicated by the black arrow in the inset of Figure 2(b). This confirms the existence of Y in the alloys and the atomic compositions of Y from EDS analyses are 1.14% for Nb0.95Y0.05, 1.82% for Nb0.9Y0.1 and 5.46% for Nb0.85Y0.15. This shows a loss of Y in the Nb1-xYx alloys compared with the nominal composition of starting materials and may be attributed to a saturation of solubility of Y in Nb, which is consistent with previous results [52]. Even with this solution limit, the increase of the lower critical field of the alloys can be clearly seen. Figures 3(a)-(c) show the isothermal magnetic-hysteresisloops (MHLs) of Nb1-xYx and Nb measured at the same temperature, respectively. The temperature ranges from 2 K to 6 K and the magnetic field ranges from -1 T to 1 T. The field is parallel to the ab-plane of the samples, for the purpose of reducing the influence of demagnetization effect [50,51]. The MHLs of Nb1-xYx show stronger symmetric feature with respect to the horizontal line than that of Nb, and this indicates a stronger bulk flux pinning of the alloy [51]. The avalanchelike flux jump effect with the flux abruptly entering the sample can be seen in Nb1-xYx, which is closely related to the thermomagnetic instabilities of the critical state, and it becomes more obvious at low temperatures [54,55]. However, this "harmful" flux jump only occurs when the vortices begin to penetrate the sample, thus it may not affect the SRF applications which work mainly in the Meissner state [2,4,9]. On the other hand, the flux trapped during the cooling process significantly degrades the quality factor Q. Understanding the tendency of flux trapping in Nb1-xYx and its sensitivity is one of the tasks for the future [56,57]. The insets in Figures 3(a) Table 1. Hc1(0) = 2055 Oe of Nb0.9Y0.1 is the highest value and 62% higher than Hc1(0) = 1267 Oe of Nb (Table 1).
Concerning the values of Hc1(0) for pure Nb reported in literatures [2,9,60], there are clear discrepancies. The often cited value of Hc1(0) =1700 Oe was adopted from Reference. 60, while we find that the authors there used the fully penetration field on the MHL as the Hc1, not the deviating point of the M(H) curve from the linear Meissner line. In another report with the samples of Nb single crystals, the Hc1 at 1.83K is smaller than 1235 Oe. This is close with our values. If taking the fully penetration field as Hc1, that would give a value beyond 2500 Oe (T = 2 K) for the sample Nb0.9Y0.1. We believe that an appropriate post-annealing of our Nb samples may increase the Hc1(0) value further. But in any case, this value is smaller than that in the Y doped samples. For the Nb samples with polished surfaces, we find that the Hc2(0) values determined from the resistive onset transition temperature is quite high (≥1.5 T) and much larger than that from other literatures [2,8,42], we believe that is probably due to the surface superconductivity. Thus we use the temperature dependent magnetization which usually reflects a bulk property to determine the upper critical field Hc2 (Supplementary Figure S2-S3). The empirical formula H(T) = 2 ] n is used to fit the Hc2 of all samples to extrapolate Hc2(0) (Supplementary Figure S3). The Hc2(0) of Nb1-xYx are twice that of Nb (Table 1). The clear enhancement of Hc1 in Y-doped Nb is of great significance for the application of the alloy. Above all, the new alloys Nb1-xYx can serve as a promising candidate material for SRF applications.

H(0)[1-(T/Tc)
In order to study the physical reason of the improved Hc1 in Nb1-xYx compared with Nb, we carry out the first principle calculation. Figure 5(a) illustrates the calculated band structure of Nb. There are both the hole and electron pockets near the  point of the band structure of Nb. When the doping level of the alloy is changed, the Fermi level moves up and down and a Lifshitz transition can occur. This Lifshitz transition occurs most likely for the band between N- in which a band bottom appears very close to the Fermi energy. Figure 5(b) illustrates the total density of states (DOS) of Nb, which consists of the DOS of both p orbit and d orbit. It can be seen that, the DOS of d orbit accounts for the main part of the total DOS of Nb. There is a sharp peak of DOS at slightly negative energy side. This is induced by the shallow band bottom between N-. If doping with holes in the Nb (the substitution of Nb by Y is hole doping), the Fermi energy will drop down (the zero energy point moves left in Figure 5(b)), and thus the DOS will increase to a higher value (the sharp peak on the left of zero energy point in Figure 5(b)). Figure  5(c) illustrates the three-dimensional (3D) Fermi surface of Nb with color-coded Fermi velocities, and the first Brillouin zone (BZ) of Nb has a symmetry of dodecahedron. In principle, the coherence length ξ can be written as ξ = ℏvF/πΔ, vF is the Fermi velocity, Δ is the superconducting gap and ℏ is the reduced Planck constant. The superconducting gap remains almost the same for the alloys compared with Nb and so is ξ. On the other hand, the condensed carrier density ns/m * can be written as ns/m * = σ/e 2   σ/, ns is the superconducting carrier density, m * is the effective mass, σ is the conductivity and  is the relaxation time. As illustrated in Figure 5(d), the condensed carrier density of Nb decreases with slightly doping of Y into Nb (hole-doping). The London penetration depth λ can be written as λ = (m * /μ0nse 2 ) 1/2 and therefore increases slightly [61]. For these reasons, the GL parameter  = λ/ξ increases.
In the case of small  value, the vortex core should be taken into consideration in evaluating the vortex tension energy and the lower critical field. Thus, through theoretical calculation given by Brandt [62,63], the  dependence of the ratio of critical field is Hc1/ Hc2 =[ln + α()]/(2 2 ), α() = 0.5+exp[-0.415-0.775 ln -0.13(ln) 2 ]. The curve is shown in Figure   4(b) and the  ranges from 0.75 to 10. The above formulae is valid when T is close to Tc. Therefore, we use the Hc1 and Hc2  Figure 4(b) and the superheating field Hsh is determined by Hsh =1.26 Hc ( ≈ 1) [12]. For the samples studied here, we have calculated different quantities and the results are summarized in Table 1.
The  of Nb1-xYx are higher than that of Nb (Table 1), and the latter is higher than the values for Nb from other literatures ( ~1) [2,9]. To deal with this difference, we use the fully penetration field as the criteria of Hc1 as adopted by others [60], and we have Hc1 ( [65,66], which reflects the bulk properties of superconductors. With the slight Y doping, the Hc2 of Nb1-xYx is elevated a lot compared with the pure Nb (Table 1). Due to the both increase of Hc2 and , the lower critical field Hc1 is increased as well.
Among all the alloys, Nb0.9Y0.1 gives rises to the highest value of Hc2(0) (=1.71 T) and an increase of  (=2.49), and therefore the highest improvement of Hc1(0) (=2055 Oe). This is consistent with our theoretical argument. Again, here we want to emphasize that, the Hc1(T) here are all determined from the very first deviating point of the M(H) curve from the Meissner linear line. Meanwhile, Hsh(0) of Nb1-xYx are higher than that of Nb in our study, and approach that of Nb3Sn [2,9,38]. All these indicate a promising prospect of Nb1-xYx for SRF applications.

Conclusions
We report systematic investigations on a new type of alloy Nb1-xYx prepared by arc melting method. The lower critical field Hc1 of Nb1-xYx is found to be 30-60% higher than that of high-purity Nb. This may greatly improve the accelerating gradient of the electric field Eacc for a superconducting cavity. Thus the Nb1-xYx alloy may serve as a promising candidate for replacing Nb in the SRF cavity applications.