Robust Bulk Superconductivity by Giant Proximity Effect in Weyl Semimetal-superconducting NbP/NbSe2 Composites

We synthesize Weyl semimetal/superconductor NbP/NbSe 2 composite and observe stable bulk superconductivity at T c = 7.2 K, 6.9 K, and 6.8 K for NbSe 2 crystal, NbP/NbSe 2 (1:1), and NbP/NbSe 2 (2:1) composites, respectively, despite large volume fraction of non-superconducting NbP phase. From the Ginzburg-Landau theory, the H c2 (0) is significantly enhanced in NbP/NbSe 2 composites [22 T (1:1) and 18.5 T (2:1)] comparing with the pristine NbSe 2 crystal (8 T). The bulk superconductivity in Weyl semimetal/superconductor composite cannot be simply described by the de Gennes-Meissner theory in a proximity effect. From the electrical transport, magnetization, and heat capacity measurement, we obtain various superconducting parameters. The superconducting properties indicate that the NbP/NbSe 2 composite is far from the conventional BCS superconductivity. It suggests that the Weyl semimetal/superconductor composite can have giant proximity effect, resulting in the stable bulk superconductivity in a composite with sizable volume fraction of non-superconducting Weyl semimetals. The giant proximity effect in Weyl semimetal/superconductor interface can have a platform to investigate the proximity induced Weyl semimetallic superconducting states. coincide with the standard Bragg peaks with coexisting phases of NbP [PDF#17-0882] and NbSe 2 [PDF#18-0921], indicating the mixed phase composite not a doping. The lattice parameters of NbP phase in the composites are a = 3.332 Å, c = 11.638 Å, V = 126.19 Å 3 [NbP/NbSe 2 (1:1)] and a = 3.326 Å, c = 11.408 Å, V = 126.19 Å 3 [NbP/NbSe 2 (2:1)]. The lattice volume of the NbP is not changed for different molar ratio concentrations of NbP/NbSe 2 composites. The lattice parameters of the 2H-NbSe 2 phase on the composites are a = 3.450 Å, c = 12.530 Å, V = 128.36 Å 3 [NbP/NbSe 2 (1:1)] and a = 3.443 Å, c = 12.550 Å, V = 128.85 Å 3 [NbP/NbSe 2 (2:1)], respectively. The lattice volume of hexagonal 2H-NbSe 2 little bit increased by increasing the c-axis lattice parameter for increasing NbP concentration, but it is close to the lattice parameters of single crystalline NbSe 2 (a = 3.45 Å and c = 12.544 Å ). It shows the stable phase mixing of NbP in NbSe 2 matrix. system. Specific heat was also measured by the PPMS-14 T Dynacool system using the thermal relaxation method.


Introduction
Since the discovery of topological insulator, the search on the various topological insulators such as topological crystalline insulator 1 , topological Anderson insulator 2,3 , topological Mott insulator 4 , etc. have been sought out for new state of matter in condensed matter physics. The topological materials have unusual physical properties resulting from massless Dirac fermion, which can control the fascinating transport properties. On the other hand, the detection of surface properties is limited by using the bulk transport measurements because surface to volume ratio is negligible in bulk compounds. Instead, Dirac and Weyl semimetals show topologically protected states in bulk transport properties. A Weyl semimetal is driven by the symmetry breaking either time reversal symmetry or inversion symmetry from Dirac semimetal 5 . Weyl semimetals have a band structure with two Weyl points as one pair, which makes Fermi arcs on a Fermi surface. Weyl points keep opposite chirality and can be either a source or a sink in the form of topological charge, which can be viewed as a monopole. In particular, the bulk properties of Weyl semimetals with the exotic features like chiral anomaly [5][6][7] , ultra high carrier mobility 8 , and large magnetoresistance 9 are unconventional anomalous transport behavior in terms of robust band topology.
Superconductivity in Weyl semimetals is of great interest but there are not many investigations on the coexistence of bulk superconductivity and a type-I Weyl semimetal (WSM). Type-I Weyl semimetal TaP becomes superconductor under high pressure above 100 GPa, accompanying structural phase transition at 70 GPa 10 . On the other hand, there have been several reports on the coexistence of superconductivity in type-II Weyl semimetals such as MoTe2 and WTe2 [11][12][13][14] .
Nevertheless, there are many theoretical suggestions on the existence of Weyl superconductors 15-17 . According to the theoretical prediction, WSM can be a superconducting phase caused by superconducting proximity in heterostructure consisting of a WSM and a superconductor 18 .
Experimentally, ion irradiation in NbAs induces breaking the Nb and As bond which leads the natural enrichment of Nb at the surface. Because the excessive Nb becomes superconducting state at Tc ~ 3.5 K, the surface proximity effect makes a superconducting state in Weyl semimetal 19 .
Niobium phosphorus (NbP) which has a noncentrosymmetric structure(I41md) is a representative Weyl semimetal [20][21][22][23][24][25] . There are 12 Weyl pairs of Weyl nodes in bulk Brillouin zone of NbP based on the first principle calculation 26,27 . It has been shown that the NbP has an ultra-high carrier mobility and chiral anomaly-induced negative magnetoresistance like as typical features of WSM 24,28 .
As a good candidate superconducting material for a heterostructure with NbP, the NbSe2 exhibits the superconducting transition at Tc = 7.2 K with coexistence of charge density wave at TCDW = 33 K.
It has the similar lattice parameters (a=3.44 and c=12.54) with that of NbP (a=3.3324 and c=11.3705), which anticipates the coherent interface between NbP and NbSe2 due to lattice match.
Superconductivity also can be induced via the proximity effect, through the interface diffusion of Cooper pairs. NbSe2 has been known as a Ising type superconductivity 29,30 . Ising superconductivity has the anomalously large in-plane critical magnetic field 31 . The high spin-orbit coupling (SOC) with inversion symmetry breaking locks the pseudospins near K and K' points which are parallel to the caxis. By the time-reversal symmetry, the pseudospins at K and K' are formed as antiparallel direction with degenerated energy. This unconventional paring of pseudospins can survive under exceedingly high in-plane magnetic fields comparing with the Pauli limit 32,33 .
Here, we investigated the superconducting properties in NbP/NbSe2 bulk composite, to explore the proximity induced superconductivity on the NbP, anticipating the coexistence of Weyl semimetallic property as well as the superconducting properties. The magnetic, electronic transport, and heat capacity properties show the robust type-II superconductivity even large volume fraction of non-superconducting NbP (NbP/NbSe2 = 2 : 1 in molar ratios). In addition, we observed the enhancement of the upper critical field Hc2 and the reduction of coherence length ξ in the composite. Fig. 1a shows the X-ray diffraction patterns of the crystalline NbSe2 (purple) and NbP/NbSe2 composites with different molar concentrations of NbP/NbSe2 = 1:1 (red) and 2:1 (black). The reference peaks are also shown for comparison. All labeled diffraction peaks of the grown single crystal of NbSe2 are aligned along the (00l) peaks, which is indexed by the hexagonal crystalline structure. The diffraction peaks of the composites 1:1   The phase separation of NbP and NbSe2 can be clearly seen in the elemental mapping from the energy dispersive X-ray spectroscopy (EDX), as presented in Fig. 2.    M(T) 3d-f from 2 to 10 K under various applied magnetic fields for the pristine NbSe2 3a and 3d, NbP/NbSe2 (1:1) 3b and 3e, and NbP/NbSe2 (2:1) 3c and 3f respectively. It is noteworthy that the superconducting transitions are observed in the NbP/NbSe2 composites even large volume fraction of NbP (2:1). The onset critical temperatures of NbSe2, NbP/NbSe2 (1:1), and NbP/NbSe2 (2:1) composites are Tc = 7.2 K, 6.9 K, and 6.8 K, respectively. The Tc (7.2 K) of NbSe2 is same with the previously reported one 34   It is very noteworthy that the χ(T) of the NbP/NbSe2 composites displays strong diamagnetic signal for the FC sequence, which is not significantly different with the ZFC measurement. This strong diamagnetic signal in FC measurement is also exceptional in type II superconductors. The FC and ZFC measurement of NbSe2 show the paramagnetic signal in FC measurement with strong diamagnetic signal in ZFC measurement, which is conventional behavior. This small differences between ZFC and FC curves in the NbP/NbSe2 composites indicate a weak flux pinning but strong superconducting state in the composites.

Discussion
To be a bulk superconductivity in a composite, the Cooper pair should not be scattered near the superconducting/normal metal interface. The only reasonable description on the bulk superconductivity in the NbP/NbSe2 composite is the proximity effect between superconducting and normal interface.
From the De Gennes and Meissner theory, the cooper pair electrons in superconductor can penetrate into a normal metal as a characteristic length scale where it is a coherent length of normal metal as a following relation 35,36 : where is the resistance of the junction in its normal state, Δ is the superconducting energy gap at normal interface, is the superconducting transition temperature of superconducting side, d is the thickness of normal layer. In clean limit ( ≪ ), the characteristic length in normal metal , is presented by , = ℏ /2 , where is the Fermi velocity of normal metal. In dirty limit ( ≪ ), the characteristic length is given by , = √ℏ /6 , where is the mean free path of normal metal and is the coherence length of superconductor.
Many high temperature superconductors showed that the characteristic length in normal metal by proximity effect is less than 10 Å. For example, the YBa2Cu3O7 (Tc = 92 K) and Co-doped PrBa2Cu3O7 interface (normal metal) interface exhibits the = 6 Å. 37    (1:1) and 8.09 nm for NbP/NbSe2 (2:1) composites, respectively. It is also surprising that the stable bulk superconductivity in the NbP/NbSe2 composites even though the coherence length is much shorter than the μm scale mean grain size of NbP. Therefore, the length scale of proximity effect may not be related with the coherence length.  In addition, the magnetic-hysteresis loops within an applied magnetic field range of ± 9 T for all the samples at 2 K is illustrated in Fig. 5a. As expected, the magnetic hysteresis of NbSe2 crystal shows conventional type-II superconducting diamond-like loop. The magnetization of the NbP/NbSe2 composites are decreased by one order of magnitude or more. Fig. 5b, c,  According to the Abrikosov theory, the ( , ) is expressed by 57 where is a constant depending on the vortex arrangement ( =1.16 for triangular lattice and 1.18 for square vortex), = / is the Ginzburg-Landau (GL) parameter, and is a penetration depth. The field derivative of magnetization near Hc2 region can gives rise to the Ginzburg-Landau parameter.
The GL parameters and penetration depths are presented in Table 1   When we plot the log-log scale of the critical current density with magnetic field Jc(H) as depicted in the insets of Fig. 6a-c, the field dependent behavior shows the saturation at low magnetic fields and rapidly decreasing at high magnetic fields, indicating the formation of vortex bundle and vortex melting at high magnetic fields. It indicates the vortex dynamics on the NbP/NbSe2 composites is not significantly different with the pristine NbSe2 crystal.
The vortex pinning force is presented in Fig. 6d Fig. 7), we obtain the Sommerfeld coefficient γ and phonon coefficient β, as presented in Table 1.    Fig. 7d. The electronic entropy is monotonically decreased with decreasing temperature until Tc and is exponentially decreased below Tc. The significant reduction of entropy below Tc is consistent with the condensation of superelectrons, which decreases entropy.
From the α-model, the superconducting gap can be measured from the relation 64 : where the α is the zero-temperature superconducting energy gap scaled by kBTc (∆(0)/kBTc) and BCS = 1.764. By using the superconducting specific heat jump, the scaled zero-temperature superconducting energy gaps (α-value) are 2.07 for NbSe2, 2.01 [NbP/NbSe2 (1:1)], and 1.97 [NbP/NbSe2 (2:1)], respectively, which are not sensitive with the NbP composite concentration and are remarkably similar to the reported ones 65 . The gap parameter α-value in BCS superconductor is known as BCS = 1.764, so the larger α-value in NbSe2 and the composites than BCS indicate that the NbSe2 and the related NbP/NbSe2 composites are not simply described by the BCS superconducting mechanism.

Sample preparation
We separately synthesize the polycrystalline samples of NbP and NbSe2 from the solid-state