Enhancement of superconducting properties and flux pinning mechanism on Cr0.0005NbSe2 single crystal under Hydrostatic pressure

Superconducting properties of Cr0.0005NbSe2 (Tc~6.64 K) single crystals have been investigated through the temperature dependent resistivity (~8 GPa) and DC magnetization (~1 GPa) measurements. Further, the critical current density (Jc) as a function of applied magnetic field has been studied from magnetic isotherms. The vortex pinning mechanisms have also been systematically analyzed using weak collective pinning theory as a function of pressure. The Jc corresponds to the flux flow enhanced by the application of pressure due to increase of Tc and vortex changes. We found that the pressure is responsible for the spatial variations in the charge carrier mean free path (δl pinning). We find that core point pinning is more dominant than surface pinning which is caused by the application of pressure. In addition, Jc(H = 0) increases from 3.9 × 105 (0 GPa) to 1.3 × 106 (1.02 GPa) A/cm2 at 2 K as the pressure is increased from normal pressure to 1.02 GPa. The pressure dependence of Tc (dTc/dP) becomes 0.91 K/GPa and 0.75 K/GPa from magnetization and resistivity measurements respectively. We found that the pressure promotes the anisotropy nature, and decrease of coherence length and resulting in pathetic interface of the vortex core with pinning centers.

Superconductivity in the transition metal dichalcogenides (TMDs) and their intercalated layered structure compounds have special features associated with extreme anisotropy of the superconducting materials 1 . Superconductivity and density waves are competing orders that derive from instabilities 2 due to internal and external perturbations such as chemical pressure, external pressure and magnetic field. Spontaneous formation of periodic lattice distortions and Charge Density Waves (CDW) could be thermodynamically favorable under certain conditions in low dimensional metals where the wave vector is generally known to depend on the nesting properties of the Fermi surface 3 . The symmetry breaking suggest that phonon−electron coupling usually occurs at certain transition temperature (T CDW ) and so called Peierls phase transition 2 . Recently, the TMDs are natural layered materials provided with a new platform to study superconductivity due to the tunable nature of the superconducting properties and coexistent with other collective electronic excitations as well as strong intrinsic spin-orbit coupling. The bulk crystals of TMDs are formed of monolayers and bound to each other by van der Waals attraction, which makes it feasible to investigate experimentally. Niobium diselenide (NbSe 2 ) is one of the most studied layered TMDs which has van der Waals attraction between the layers and it has generated much attention due to interplay of superconducting transition temperature (T c ) [4][5][6][7] and T CDW 2,8-10 is around 7 K and 33 K respectively. Anisotropy in TMDs, particularly in NbSe 2 compounds, having the highest T c among TMDs, could be significantly enhanced by introducing foreign atoms or molecules in the interlayer space (intercalation process) 6,9,11,12 . The intercalation ability of these compounds is related to the expected implementation of high temperature superconductivity in the sandwich type structures described by the excitonic mechanism 6,9,13 . Further remarkably, Zeeman-protected Ising superconductivity is expected in NbSe 2 due to non-centrosymmetric Scientific REPORtS | (2019) 9:347 | DOI: 10.1038/s41598-018-36672-x structure with in-plane inversion symmetry breaking and strong spin-orbit coupling and the anomalous large in-plane critical magnetic field has become one important direction in crystalline 2D superconductors 11,12,14,15 . The vortex movement (i.e., vortex entry into or exit from a single-crystalline superconductor) is possibly pinned at the edges when applied very low magnetic field which can be generally attributed to the translational symmetry breaking at the edges and it is dependent on both shape and dimension of the superconductors 13,16 . The applied magnetic field would significantly modify the pinning and subsequently influence the magnetic behavior of the samples. The TMDs superconductors have revealed wonderful superconducting properties including high values of T c , critical current density (J c ), upper critical field (H c2 ) and irreversible field (H irr ). In the presence of strong pinning, the vortex state of type-II superconductors is usually characterized by J c that decreases monotonically with an increasing field (H) or temperature (T). In the weakly pinned superconductors, interplay between intervortex interface and flux pinning produces an unusual peak in J c as a function of both field and temperature which are just below the normal-state boundary and it is usually designated as secondary peak effect 17,18 . Both strong pinning and high J c depend on variation in the grain size and the coherence length (ξ) 19 . Vortex pinning arises from the interplay of several competing energies, namely the self-energy of the flux lines, vortex-vortex interactions, vortex inhomogeneity interactions and thermal excitations 20 . A magnetic field generates an array of vortices in type-II superconductors and the vortices strongly interact with each other forming highly correlated configurations such as the vortex lattice. In high-T c cuprates at relatively high temperatures, vortices move and vibrate due to thermal fluctuations to the extent that the lattice can melt becoming a vortex liquid [21][22][23] . Growth of the structure of the vortex lattice in a weakly pinned high-T c superconductor is of paramount importance, since it determines superconducting properties that are directly suitable for applications 24,25 . As the temperature is raised, the vortex lattice undergoes a first-order transition to a stable disordered state 24,[26][27][28] . A thermal fluctuation permits pinned vortices to fluctuate around the potential energy and reduces the effective pinning energy due to thermal smearing. The vortices also escape totally from the pinning centers through a variety of de-pinning excitations. Vortex motion still occurs for currents lower than J c at a much slower rate. This flux creep mechanism implies a residual dissipation and it is responsible for the time relaxation of persistent currents flowing in a superconducting closed loop.
Hydrostatic pressure effects on the T c enhancement shows more advantages that are relevant to the flux pinning compared to other perturbations. The application of high pressure leads to changes in the electronic bands leading to original properties, which may be associated with a structural phase transition. It always reduces the lattice parameters and causes the shrinkage of unit cells, giving rise to the reduction of anisotropy. Grain connectivity improvement should also be expected, as pressure can compress both grains and grain boundaries. The formation of point defects can be more favorable under high pressure, since it is well known that the formation energy of point defects decreases with an increasing pressure. High pressure can cause low-angle grain boundaries to migrate in polycrystalline bulk samples, resulting in the emergence of giant grains, sacrificing surface pinning thereafter. Hence, a ratio of point pinning centers to surface pinning centers is expected to be higher due to an increase of formation energy under high pressure. Several examples can be recalled here. Pressure increases the superconducting transition from 3.5 K to 6.5 K and also the semiconducting to metallic transition in LaO 0.5 F 0.5 BiS 2 single crystals 29 . Whereas a large enhancement of T c from 26 K (0 GPa) to 43 K (4 GPa) in LaO 0.95 F 0.05 FeAs 30 with application of external hydrostatic pressure up to 3 GPa using piston cylinder pressure device, T c was reduced with the application of pressure above 3 GPa to 30 GPa, using a diamond anvil pressure device. Further, pressure induced superconductivity has been observed in the pnictides such as LaFeAsO 1−x F x , LaFePO and SrFe 2 As 2 31 . In the ladder compounds, pressure induces the metal-insulator transition generating hole carriers and eventually superconductivity occurs in Ca 14−x Sr x Cu 24 O 11 32 . Pressure is also an effective approach to improve the J c significantly in FeSe 33 , Sr 4 V 2 O 6 Fe 2 As 2 34 YBa 2 Cu 3 O 7−x 35 superconductors, as the pressure induces more point pinning centers and subsequently affects the pinning mechanism 33,34 . The investigation of the pressure dependence of thermodynamic magnitudes proved to be a useful method of studying the properties of anisotropic compounds. Such investigations were performed on the layered compound NbSe 2 [36][37][38][39] . Pressure not only enhanced T c with a rate of dT c /dP is 0.86 K/GPa (NbSe 2 ) and 1.47 K/GPa (Fe 0.0011 NbSe 2 ) but also increased J c and H c2 38 . In the case of the intercalated NbSe 2 pressure increased T c and simultaneously suppressed T CDW 40 . Suderow et al., described the pressure dependence of anisotropy, of the electron-phonon coupling and Fermi velocities, which influence the peculiar interplay between CDW, Fermi surface complexity and superconductivity in NbSe 2 41 . Pressure induces a transition from spatial variation in the δT c pinning to δℓ pinning mechanism in the undoped NbSe 2 superconductors 38 .
From above, it is clear that high pressure is exclusively unique in fine-tuning superconducting states with the benefit of without introducing disorder effects in comparison with chemical doping. High pressure is, thus, an important tool to study intrinsic properties of the materials to understand the enhancement of T c , J c and other physical properties 23,33,34,36,38,40,[42][43][44] . These facts motivated our present study on the pressure effects on the superconducting properties of single crystalline Cr x NbSe 2 . We anticipated that hydrostatic pressure would increase the superconducting volume, H irr , and H c2 due to enhancement of T c , increase the point defect and reduction in the anisotropy of single crystalline Cr intercalated NbSe 2 samples. Indeed, we observed such interesting properties when pressure was applied to Cr intercalated NbSe 2 is investigated. These findings are reported below.

Results and Discussions
The temperature dependence of resistivity (ρ(T)) in the temperature range from 2 to 300 K under various hydrostatic pressures from 0 to 8 GPa [ Fig. 1(a)], the expanded region near T c [ Fig. 1(b)] and zero-field-cooled (ZFC) and field-cooled (FC) dc magnetization (M(T)) at the constant magnetic field of 20 Oe [ Fig. 1(c)] in the vicinity of the T c under various hydrostatic pressures range from 0 to 1 GPa of the crystal flakes of Cr 0.0005 NbSe 2 are shown respectively in Fig. 1(a,b and c). The T c is defined as an onset, mid and offset of superconductivity with obtained  Fig. 1(a), normal state resistivity gradually decreases with the application of high pressure and it almost shows the metallic nature for all pressures up to ~ 8 GPa. Similar ρ(T) behavior under pressure has been reported for various superconducting materials 33,34,36,38,40 . This is associated with the fact that high pressure brings the layers in the unit cell closer together, and facilitates overlap of wave functions of the conduction electrons in the adjacent layers. The T c (6.64 K) of Cr 0.0005 NbSe 2 is found to be less than undoped NbSe 2 single crystal, and similar trend has been reported for various intercalated compounds Fe x NbSe 2 6,38 , NbSe 2 36,40 , Ga x NbSe 2 11 , Pd x NbSe 2 45 , Cu x NbSe 2 12 , (LaSe) 1.14 (NbSe 2 ) 46 pnictides 34,44 at both ambient and pressure. Figure 1(c) shows M(T) in the ZFC and FC regimes with an applied magnetic field of 20 Oe under various hydrostatic pressures up to ~ 1 GPa in the vicinity of T c up to 10 K; We clearly notice the diamagnetic transition at 6.14 K and 7.07 K at ambient and 1.02 GPa respectively. The diamagnetic transition shifts towards high temperature with the application of pressure as shown in Fig. 2(a). The hysteresis between ZFC and FC regimes indicates that Cr 0.0005 NbSe 2 exhibits weak flux pinning centers. Without correcting the demagnetization factor, we estimate the superconducting volume fraction (ZFC) to be ~ 80% indicative of bulk superconductivity. At ambient pressure the sample shows a T c of 6.14 K from M(T) at constant magnetic field of 20 Oe and it is ∼0.5 K less than that observed from ρ(T) measurements, as shown in Fig. 2(a). Evidently, T c onset and T c offset observed from ρ(T) is higher than M(T) measurements as shown in Fig. 2(a). With the application of high pressure, T c onset steadily increases in entire pressure region due to the reduction of interlayer distances of Cr 0.0005 NbSe 2 as shown in Fig. 2(a).
With an application of pressure, the room temperature resistivity (ρ 300K ) decreases monotonically up to 8 GPa and favours enhancement of metallic nature [ Fig. 1(a)]. However, ρ 300K decreases at a faster rate (0.13 mΩ-cm/ GPa) up to 1.5 GPa and then moderate decrease (0.01 mΩ-cm/GPa) is observed above 1.5 GPa to 8 GPa. Further, ρ T (onset) c decreases with slower rates are 0.01 mΩ-cm/GPa and 0.001 mΩ-cm/GPa at below and above 1.5 GPa respectively. Hence, we found that both ρ 300K and ρ Tc(onset) are sensitive to the low pressure as shown in Fig. 2(b). ρ(T) is found to be almost linear in the high temperature region for various applied pressures. The change in ρ(T) shows metallic behavior at all pressures of up to 8 GPa. The upward curvature in ρ(T) weakens progressively with increasing pressure. Figure 2(a) shows the rapid enhancement of T c in the low pressure region and moderate increase in high pressure region as we observed from both ρ(T) and M(T) for Cr 0.0005 NbSe 2 . One can see that the both T c onset and T c offset shift towards higher temperature with the application of high pressure and the dT c /dP becomes 0.91 K/GPa in the 0 < P < 1 GPa from M(T) measurements. The rate of change of T c with pressure dT c / dP = 0.75 K/GPa for P less than 1.5 GPa and 0.09 K/GPa in the interval 1.5 < P < 8 GPa as observed from ρ(T) measurements. These results suggest that the relative change in the density of states at the Fermi level is profound in low pressure region up to 1.5 GPa and the moderate increase in the high pressure region (1.5 < P < 8 GPa) which leads to corresponding variation of T c . This is associated with the fact that the P brings the layers closer together, and it facilitates the overlap of the wave functions of the conduction electrons in the adjacent layers.
Consequently, an increase in T c is mainly determined by changes in the density of states at the Fermi level and the change in the phonon spectrum plays a minor role. The region above 100 K in Cr 0.0005 NbSe 2 can be described reasonably well by straight line fits with different slopes for various pressures in ρ(T) suggesting that phonon scattering mechanism is dominant. The relationship between interlayer spacing and T c is a matter of fundamental importance in understanding of superconductivity in layer compounds. The effect of pressure upon the physical properties is due to the reduction in interlayer spacing. The band structure calculations of the Fermi level for NbSe 2 at the middle of a narrow d sub-band situated between the unoccupied and primarily d bands of Nb and the fully occupied p bands of Se. Although differing in the details of the sub-band overlap with the p bands, both calculations highlight the importance of interband (hybridization) and interlayer interactions. These take the form of a nonzero empty site potential at the unoccupied interstitial positions between the Se layers due to wave function overlap in the modified muffin tin potential approach of Kasowski 47 . From earlier report, we inferred that neglecting a weak empty site potential broadens the sub-band and increases the overlap with the p bands. If the charge transfer occurs due to intercalation, shifts in the Fermi level towards the sloped region of the density of states curve and this can lead to a relatively a big change in density of states (N(ε F )) under pressure, and consequently, in T c . More detailed information about the electronic properties and superconductivity of the pure and intercalated NbSe 2 solid solution was obtained from specific heat 12 measurements.
The phonon mediated superconductors, the electron-phonon coupling constant have been estimated from McMilllan formula 48 using Debye temperature 49 and T c , where θ D is the Debye temperature, µ * is the screened pseudo-potential (characteristic for the electron repulsion) and assumed to be 0.15 suggested by McMilllan 48 for transition metallic superconductors and λ is the electron-phonon coupling constant and the parameters θ D , µ * and λ are all pressure dependent. The values of λ is 0.84 at ambient pressure suggest that strong coupling in superconductivity. With the Sommerfeld parameter (γ) and the electron-phonon coupling constant (λ), the electron density of states at the Fermi level (N(ε F )) can be obtained from ε γ π λ . The density of electronic states at the Fermi energy therefore clearly decreases when more metal ions intercalates into NbSe 2 . All the values of θ D and dθ D /dP for pure and intercalated samples are identical. The pressure dependence of Debye temperature θ D (P) can be obtained from the Gruneisen's formula 48 , where α is the thermal expansion coefficient, C v is the heat capacity and the value of dθ D /dP is one order of magnitude lower than the corresponding changes is T c with pressure. The large relative growth of T c can be qualitatively associated with the particularities of the NbSe 2 band structure, and corresponding changes of λ(P) 40 . Earlier it was shown that the intercalated Fe and Cu is located in the interlayer space, when the superconducting properties are affected by the interlaminar intercalant 12 . A redistribution of the interlayer . The last idea is supported by an increase of the width of the superconducting transition under pressure and more pronounced manifestation of its stepped form. This type of evolution in the superconducting state under high pressure 38,44,50 has been observed in layered structure superconductors with a small anisotropy parameter 23,33,34 .
It is known that T c is found to increase for NbSe 2 12,39 , Fe x NbSe 2 38 and Cr 0.0005 NbSe 2 compounds by applying high pressure. Figure 2(c) examines the normal-state resistivity of Cr 0.0005 NbSe 2 under hydrostatic pressure and its implication of electronic correlation. Low temperature region (7 ≤ T ≤ 50 K) of ρ(T) can be fitted using the Fermi liquid model, ρ = ρ 0 + AT 2 , where ρ 0 is residual resistivity and A is a scattering factor. Figure 2(c) shows good fitting for both data at ambient and high pressure and it supports the Fermi liquid model. The value of ρ 0 is 0.042 mΩ-cm: 0 GPa and 0.017 mΩ-cm (8 GPa) and the A [16.45 × 10 −6 mΩ-cm/K 2 (0 GPa) and 7.1 × 10 −6 mΩ-cm/K 2 : 8 GPa] value shows clear indication of electron-electron interaction exhibits in both ambient and high pressure in this sample. The nature ρ 0 and A under various hydrostatic pressure has been shown in Fig. 2(d) which suggests that Cr 0.0005 NbSe 2 is a weakly correlated system. Figure 3(a-c) [ Fig. S2] shows the temperature dependent of dc magnetization with various applied magnetic fields (H) with the constant P of 0, 0.5 and 1.02 GPa respectively. It is found that both T c and diamagnetic signal show decreasing trend and allows us to determine the upper critical field (H c2 ) of this material at various pressures. Taking the onset of transition in M(T) at various magnetic fields with constant pressure as the upper critical field point H c2 (T c ) and infer that almost all Cooper pairs are broken at this temperature and H. Further, the Meissner signal is suppressed with the application of various H at 0 GPa. However, the Meissner signal enhances at various H with constant pressure of 0.5 and 1 GPa, and it confirms that the pinning centers increase due to the application of pressure. Figure 3(d-f) shows the field dependent isothermal magnetization (MHL) scan in a low field region under various temperatures with applied pressure of 0, 0.5 and 1 GPa respectively. These results reveal that magnetic moment increases with the application of constant pressure, and confirms that when the occurrence of pinning increases as pressure increases in the sample.
According to the Ginzburg-Landau (GL) theory, the absolute zero temperature upper critical field H c2 (0) can be estimated by using formula,  Table 1. H p (0) indicating that both orbital effect and Pauli spin paramagnetic effect (PSP) which gives an influence on the pair-breaking mechanism through the entire pressure region. However, we haven't excluded the effect of spin instability at low temperatures, which may very well play an important role in the occurrence of superconductivity. The absolute orbital upper critical field H (0)  are found to be higher at higher pressures than at ambient pressure. Further, the enhancement of critical field under pressure implies that the strong flux pinning exhibits in this sample. Since, Pauli limit superconductivity mechanism [ ] is exhibited by this sample, the calculated Maki parameter  Table 1.
The irreversible field (H irr ) is calculated from MHL using the criteria of the zero field current density [J c (H = 0)] and it occurs due to depinning of the magnetic fluxes in this sample. Figure 4(c) shows temperature dependent of H irr fitted with the equation, H irr (T) = H irr (0)(1 − (T/T c ) 2 ) 3/2 , pressure up to ~ 1.02 GPa. It reveals that enhancement of H irr with application of pressure and also provides evidence of the 3D nature of flux creep in the sample. This is an indication that H irr is mainly controlled by the flux pinning. H c1 is measured from MHL under various temperatures [ Fig. 3(a-c)] and plotted as a function of temperature with the parabolic function fitting as shown in Fig. 4(d). The precise determination of H c1 (0) from MHL possibly suffers from demagnetization effect. Further, H c1 (0) can also be deduced from the first penetration field ′ H (0) c1 , assuming that the magnetization M = −H c1 , when the first vortex enters into the sample. Thus, magnetic field has rescaled to H eff = H−NM , where N is a demagnetization factor and H is a magnetic field. It has been shown by Brandt 53 that a bar sample with a rectangle cross-section, the effective demagnetization factor = − . for approximate slab geometry 53 and these values of ′ H (0) c1 listed in Table 1. Using the H c1 (0), it is possible to estimate the penetration depth from the relation, λ Φ π κ = +.
′ . , where λ(0) is the penetration depth at 0 K. The ratio between the λ(0) and coherence length (ξ GL (0) gives GL parameter (κ) through the expression κ = λ(0)/ξ GL (0). The value of κ = 1/2 has been conventionally used to classify superconductors as type I or type II based on whether κ value is higher or lower than 1/2 . Our analysis predicts that κ value is very much higher than critical value and indicates Cr 0.0005 NbSe 2 as a type II superconductor. Similarly Cu x NbSe 2 12 and Zr 0.96 V 0.04 B 2 54 compounds were shown to be type-II superconductor, since κ value has been reported larger than the critical value.      These results indicate that application of pressure leads to an enhancement in J c and it is more significant at higher fields. The normalized J c as a function of temperature at 0 and 0.1 T for various pressures is shown in Fig. 7(b,c) and fitted with the scaling relation J c ∝ (1 − T/T c ) n where n is the critical exponent at each pressure. It is known that GL theory predicts distinct vortex pinning mechanisms in superconducting materials, with different values of exponent (n) at specific fields. The value of n = 1 and n >1.5 corresponds to non-interacting vortices and strong vortex core pinning mechanism respectively. The critical exponent is estimated from fitting the scaling relation in Fig. 7(b,c) for various magnetic fields at constant hydrostatic pressure. It reveals that the values of n are found to be 1.65 ≤ n ≤ 2.12(0 T) and 2.82 ≤ n ≤ 3.75 (0.1 T) under various hydrostatic pressure and shows higher value of n under pressure than at ambient pressure. Similar behaviour has been reported on J c (P), J c (T) and vortex dynamics properties in Fe x NbSe 2 38 and in pnictides 34 . The core pinning mechanism is examined in the framework of collective pinning theory in this sample. Generally, core pinning comprises that pinning mechanism related to the spatial variation in the charge carrier mean free path (l), called δl pinning and pinning due to randomly distributed spatial variation in T c , called δT c pinning, which is mostly due to crystal defects 60 . We analyzed the pinning mechanism as reported by Griessen et al. 60 using the relation J c /J 0 ∝ (1 − t 2 ) 5/2 /(1 + t 2 ) 1/2 for δl pinning mechanism, while J c /J 0 ∝ (1 − t 2 ) 7/6 /(1 + t 2 ) 5/6 applies to δT c pinning, where t = T/T c . Figure 8(a-f) shows almost perfect matching of the experimentally obtained J c with the theoretically calculated values and favour δl pinning mechanism in the entire pressure region. Our analysis directly supports δl pinning mechanism whatever be the pressure, and it is responsible for increasing in T c Our results suggest that there is a single vortex pinning due to spatial variations in the charge-carrier mean free path. The coherence length is proportional to the mean free path of the carriers, and therefore, the application of pressure leads to enhancement of δl pinning mechanism. One can note that similar results have been reported in case of Fe x NbSe 2 6,38 , FeTe 0.7 Se 0.3 61 and pnictides 34 superconducting compounds. We have calculated the pinning force (F p = J c H) as a function of magnetic field under various hydrostatic pressures and have investigated the magnetic field dependence of the pinning force density (F p ) in order to understand vortex pinning mechanisms in this sample. Field dependence of F p [ Fig. S4] for various temperatures in superconductors may be scaled into a unique curve if they are plotted as a function of reduced field, h = H/H irr . The scaling of normalized pinning force from the Dew-Hughes formula 62 , f p = h p (1 − h) q , where p and q are the parameters describing the pinning mechanism. Further, J c 0.5 H 0.25 is plotted as a function of magnetic field is known as Kramer plot 63 and it is used to determine H irr , where H irr is determined as the extrapolated to zero field from various isotherms of J c and the temperature dependent of H irr shows a linear behavior.  Figure 9(a-f ) shows normalized pinning force (f p = F p /F p (max) ) as a function of reduced critical field (h = H/H irr ) for various temperatures and constant P (0,0.5 and 1.02 GPa) [Fig. S5]. For the scaling of both point and surface pinning, we use the relation, f p = Ah p (1 − h) q , where p and q describes the nature of specific pinning mechanism 62 . It is known from Dew-Hughes model, when p = 1/2 and q = 2 and p = 1 and q = 2 describes the surface pinning and point pinning respectively as predicted by Kramer 63 . The best fit of the curves is obtained with f p (h) dependence given by,   is more dominant than surface pinning mechanism under high pressure [ Fig. S5]. The broadening of the pinning force with the application of pressure indicates that the pinning centers are enhanced with the application of pressure for this sample. Cr intercalation of into Se-Nb-Se layers of NbSe 2 single crystals leads to an increase of more pinning centers compared with the undoped NbSe 2 .

Conclusion
In summary, we have shown that hydrostatic pressure is a very effective means to significantly enhance T c , J c , H irr , and flux pinning in the Cr 0.0005 NbSe 2 superconductor. We demonstrate that hydrostatic pressure significantly increases T c from M(T) (dT c /dP = 0.91 K/GPa; 0 < P < 1 GPa) and ρ(T) (0.75 K/GPa; P < 1.5 GPa & 0.09 K/GPa; 1.5 < P < 8 GPa) measurements. The pressure introduces more point defects in sample and it is responsible for enhancement J c . We found that the hydrostatic pressure stabilizes a strong δl pinning mechanism. In addition, we found that the point pinning is more dominant than surface pinning under high pressure. The pressure enhanced the H c1 , H c2 , H irr and reduces both coherence length and penetration depth which are responsible for the pinning mechanism.

Experimental Techniques
Cr 0.0005 NbSe 2 single crystal has been synthesized using chemical vapour transport method. The essential commercially available high purity elemental metallic powders such as Nb (99.95%), Se (99.99%) and Cr (99.99%) procured from Alfa Aeser, which are mixed with suitable stoichiometric ratio and made of 6 mm (ϕ) pellet. The pellet kept in a sealed quartz tube with tiny amount of iodine in the presence of liquid nitrogen atmosphere. The sealed quartz tube is placed in a two-zone furnace with programmable temperature controller and the temperatures of charge and growth zone at 800 °C and 720 °C respectively for a period of seven days. The grown crystals are characterized structural phase and the elemental composition analyses are confirmed using x-ray diffraction and Energy dispersive X-ray Spectroscopy techniques respectively and further details about synthesis and characterization of these materials were recently reported by Rukshana Pervin et al. 64 . A cubic anvil pressure device, consisting of six tungsten carbide (WC) anvils, which have been used to produce homogeneous hydrostatic pressure up to 8 GPa for resistivity measurements 65 . The applied pressure is calibrated from the resistance changes of Bi with its phase transitions at room temperature such as Bi I-II (2.55 GPa), Bi II-III (2.77 GPa) Bi III'-V (7.68 GPa) and Daphne #7373 used as a pressure transmitting medium 66 . The temperature of sample inside the Teflon cell is monitored by measuring the resistivity of three calibrated Pt(Co) resistance thermometers attached to the neck of each anvil. The electrical contacts were made using gold wire of 20 µm ϕ and Ag paste is used to make contacts on the surface of the sample with the typical sample size is 0.8 × 0.5 × 0.5 mm 3 . The standard four probe method is used for doing resistivity measurements under ambient and high pressure upto 8 GPa and the anvils are through the gold foil. The magnetic properties (ZFC & FC) of Cr 0.0005 NbSe 2 single crystals were investigated under various magnetic fields at ambient and high pressures. The dc magnetization measurements under pressure were carried out using Physical Property Measurements System -Vibrating Sample Magnetometer (PPMS-VSM, Quantum Design, USA). The external pressure was generated up to ~1 GPa by a clamp type miniature hydrostatic pressure cell which is made of specially heat treated nonmagnetic Cu-Be alloy. The fluorinert FC #70 and FC #77 (1:1) mixture was used as a pressure transmitting medium and the in-situ pressure was estimated from the superconducting transition temperature of pure Sn which was loaded along with the sample in the capsule.