Giant proximity effect in single-crystalline MgB2 bilayers

Although giant proximity effect (GPE) can shed important information on understanding superconducting pairing mechanisms and superconducting electronics, reports on the GPE are few because the fabrication of the junctions with GPE is technologically difficult. Here, we report a GPE in the single-crystalline MgB2 bilayers (S′/S), where the S′ is the damaged MgB2 layer by cobalt (Co)-ion irradiation and the S is the undamaged MgB2 layer. Superconducting properties of the S′ is remarkably degraded by the irradiation, whereas those of the S is uninfluenced by the irradiation. The degraded superconductivity in the S′ is fully recovered by increasing the thickness of undamaged MgB2 layer S despite almost ten times larger thickness ~ 95 nm of S′ than the superconducting coherence length ξab(0) ~ 8.5 nm of the S, indicating a presence of GPE in the S′/S MgB2 bilayers. A diffusion of electrons in the S′ into the S can reduce a pair breaking scattering in the S′, and the similar electronic structures of S′ and S layers and a finite attractive electron-electron interaction in the S′ are thought to be origins of unpredicted GPE between the same superconducting materials. Both upper critical field (μ0Hc2) and in-field critical current density (Jc) of S′/S bilayers show a significant enhancement, representing a strong correlation between S′ and S. These discoveries provide the blue print to the design of the superconducting multilayers for fundamental researches on the mechanism of the GPE as well as their technological applications.


Results
(a) shows the mean projected range (δ = 95 nm) of the irradiated 140 keV Co ions into MgB 2 and damage events created by the irradiated energetic ions, simulated by the SRIM program 27 . If MgB 2 film is thick enough compared to the δ, it can be divided into two layers: damaged layer (S′) and undamaged layer (S). Superconducting (SC) properties of the S is expected to be same with that of the pristine state, while the SC properties of the S′ will be changed by the ion-irradiation conditions. In order to investigate the correlation between S′ and S, we considered two types of electrode configurations, i.e., 4-point contact method A and B, as described in the insets of Fig. 1(a). In contact method A, the 4 probes are directly connected to the S, whereas they are in contact with the S′ in contact method B.
The solid lines in Fig. 1(b) indicate the temperature dependences of electrical resistivity (ρ) for the pristine MB850 nm at magnetic fields of 2 and 4 T, where ρ(T) is normalized by the ρ value at T c onset, ρ n , at each magnetic field for comparison. After irradiation with a dose of 1 × 10 14 Co atoms/cm 2 in the MB850 nm, ρ(T) was measured again by using the 4-point contact method A and B. For the contact method B, the resistivity drop of the irradiated film at T c is sharper and more robust than that of the pristine: at 4 Tesla, the zero-resistance state is suppressed to 19.1 K for the irradiated film, while it is 4.8 K for the pristine. The ρ(T) curves measured by the contact method A, in contrast, show two SC transitions: the first SC transition is consistent with the SC transition of the S′ measured by the contact method B and the second SC transition is similar to the SC transition of the pristine sample. These results delineate that S′/S MgB 2 bilayer is fabricated via the ion irradiation method.
The ρ(T) curve near T c for pristine MgB 2 films of MB130 nm, MB200 nm, MB410 nm, MB850 nm, and MB1300 nm is shown in Fig. 2(a), where ρ(T) is normalized by the ρ value at 41 K, ρ(41 K). With decreasing film thickness, T c of the pristine MgB 2 films slightly decreases and the SC transition remains sharp, except the thinnest MB130 nm (ref. 28 ) (see Fig. S1 in the Supplemental Information). On the other hand, T c of the S′/S MgB 2 bilayers is rapidly suppressed with decreasing the thickness (t′) of undamaged MgB 2 layer S, as shown in Fig. 2(b), where ρ(T) was measured by using the contact method A. The change in T c of the S′/S bilayers is linked to t′ because the same dose of Co ions with the same incident energy of 140 keV was irradiated. The large suppression of T c from 38.2 to 4.5 K in MB130 nm after the irradiation indicates that a dose of 1 × 10 14 Co atoms/cm 2 is enough to substantially degrade superconductivity of the MgB 2 . Interestingly, however, T c is rapidly restored back to the original value with increasing film thickness. Temperature dependences of dc magnetization (M) also showed similar results to the ρ(T) curve ( Fig. S2 in the Supplemental Information), indicating that the SC transition in the S′/S bilayers is not originated from filamentary nature. In addition, the fact that the thickness of damaged MgB 2 layer (S′) is much larger than the coherence length (ξ) of MgB 2 (ref. 26 ) indicates the emergence of giant proximity effect (GPE) in S′/S MgB 2 bilayers. We note that the GPE is often observed in S 1 /S 2 junctions, where S 1 and S 2 are superconducting layers with different T c (refs [11][12][13][14][15][16][17]. Figure 2(c) displays the SC transition temperature of the irradiated MgB 2 films (T c,irr. ), normalized by that of the pristine films (T c,pri. ), as a function of the reduced film thickness t′/δ, where t′ (=t − δ) represents the thickness of the undamaged layer (S) and δ corresponds to the thickness of the damaged layer (S′). Here, T c,pri. and T c,irr. are determined from the criterion of 50% resistivity drop from the resistivity value at 41 K. For comparison, T c,irr. /T c,pri. for S′/S bilayers with δ = 27 (stars) and 49 nm (circles) are also plotted in Fig. 2(c), where a beam energy of 35 (δ ~ 27.3 nm) and 70 keV (δ ~ 49.4 nm) was used with the same dose of 1 × 10 14 Co atoms/cm 2 . Inset of Fig. 2(c) shows T c,pri. and T c,irr. as a function of the t′/δ for pristine and irradiated MgB 2 films, respectively. T c,irr. that corresponds to the T c of S′/S bilayers is monotonically reduced with decreasing t′/δ and is completely suppressed to 0 K at the critical ratio t′/δ ~ 0.19, i.e. 19% of the thickness of S to that of S′. For δ = 95 nm, for instance, the critical thickness (T c,irr. = 0 K) of the S′/S MgB 2 bilayer is 113 nm.

Discussion
The thickness ratio (t′/δ) dependence of the SC transition temperature for the S′/S bilayers is expressed by the Werthamer theory considered the spatial variation of electron-electron interaction 6 , even though the thicknesses of the S and S′ are much thicker than coherence length of MgB 2 . In the BCS theory, T c of a normal metal (N) and superconductor (S) bilayer can simply be expressed by the relation T c = 1.14Θ D exp[−1/(N 0 V 0 ) eff ], where Θ D is Debye temperature, N 0 is the electronic density of states at the Fermi energy, and V 0 is strength of attractive electron-electron interaction, and (N 0 V 0 ) eff is the effective BCS interaction parameter 2,6,29 . For N/S bilayer, N 0 V 0 www.nature.com/scientificreports www.nature.com/scientificreports/ in the S layer is an important parameter to determine T c of the bilayer, because V 0 = 0 in the N layer. On the other hand, a finite V 0 in the N layer could induce the long range of the PE due to the slow decay of SC pair amplitude in the N layer 16,18,24 , which is probably one of the primary reasons for GPE in the S′/S MgB 2 bilayer.
The electronic density of states at the Fermi energy (N 0 ) is also important to determine T c , and the large reduction of T c in MgB 2 by the irradiation is believed to be due to the decreased N 0 and enhanced interband scattering [30][31][32][33][34] . Considering a significant decrease of T c of MB130 nm from 38.2 to 4.5 K by Co-ion irradiation, the T c variation in the S′/S MgB 2 bilayers is expressed by the decrease in the N 0 (refs 29,35,36 ). Figure 2(d) shows that the inverse of T c difference between the pristine and irradiated films, 1/ΔT c (=T c,pri. − T c,irr. ), is linearly proportional to the thickness ratio between the undamaged (t′) and damaged MgB 2 layers (δ), t′/δ, indicating that the T c suppression by the Co-ion irradiation is closely related with the decrease in the electronic density of states N 0 of the damaged layer S′ (refs 29,35,36 ). The initial slope of T c (∝|dT c (d n = 0)/dd n |) in S/N bilayer is proportional to the ratio of density of states between the two layers (N n /N s ) because  www.nature.com/scientificreports www.nature.com/scientificreports/ density of states at the Fermi energy for the normal and superconducting layer, respectively, and d n is a thickness of the normal layer 29,35,36 . Our results on the T c reduction with respect to the thickness ratio t′/δ is consistent with the decrease in the density of states of the S′ caused by the irradiation-induced disorder [30][31][32][33][34] .
We consider the diffusion of electrons inside the damaged S′ into the undamaged S as well as the diffusion of Cooper pairs from the S to S′. Those diffusion processes by the electrons and the Cooper pairs can lead the extension of the proximity region in terms of the strong correlation between S and S′. In particular, when the thickness of S is large, there can be enough space for the diffusion of electrons from the S′ into S. This interpretation is supported by the study on the lower and upper critical fields and critical current density for S′/S MgB 2 bilayers, which will be discussed below. Figure 3(a,b) show the ρ(T) curves in magnetic fields for the pristine and Co-ion irradiated MB410 nm, respectively, where the ρ(T) is normalized by the resistivity value in the normal state (ρ n ) for each magnetic field. In stark contrast to the pristine film, two-step SC transitions appear in the ρ(T,H) measured by the 4-probe contact method A for the Co-ion irradiated MB410 nm. The second SC transition temperature (T c2 ) is consistent with the SC transition temperature of pristine films (T c,pri. ), indicating that T c2 emerged at high magnetic fields is originated from superconductivity in the S. When the contact method B was used, on the other hand, there is no trace of T c2 in ρ(T,H) curves because the 4 probes of the contact method B are not directly in contact with the undamaged layer and the supercurrent flows mainly through the damaged layer S′.
Temperature dependences of the upper critical field (μ 0 H c2 ) for the pristine and irradiated MB410 nm and MB850 nm are presented in Fig. 3(c,d), respectively, where the magnetic field is applied perpendicular to the film's ab plane (H ⊥ ab). The criteria for T c,pri. and T c,irr. are 50% resistivity drop for the pristine and irradiated films, respectively, while T c2 , and T k are assigned as the 50% resistivity drop of the second SC transition and a kink temperature of the first SC transition, respectively (see the arrows in Fig. 3(a,b)). The magnetic field dependence of the kink temperature (T k ) for the MB410 nm suggests that T k is associated with T c of the undamaged layer S. One the other hand, there is no kink (T k ) in the irradiated MB850 nm because superconductivity of the damaged layer S′ is completely restored to that of the pristine state, i.e., T c,pri. ≈ T c,irr. . The fact that μ 0 H c2 (T)s determined by T c2 are consistent with those estimated from the T c,pri. underscores that the MgB 2 /MgB 2 bilayer is formed by the Co-ion irradiation. Upper critical field of the bilayers is enhanced by two times to the pristine films: μ 0 H c2 (0) = 5.29 → 9.75 T for MB410 nm and μ 0 H c2 (0) = 4.52 → 9.50 T for MB850 nm, which can be accounted for by additional www.nature.com/scientificreports www.nature.com/scientificreports/ defects introduced via the Co-ion irradiation 37 . The SC coherence length, ξ ab (0), obtained from the μ 0 H c2 (0) [=φ 0 /2πξ 2 ab (0)] is reduced from 7.89 to 5.81 nm and from 8.54 to 5.89 nm for MB410 nm and MB850 nm after the irradiation, respectively.
Temperature dependence of μ 0 H c2 is reasonably explained by the two-band Ginzburg-Landau theory, indicated by the red dashed lines in Fig. 3(c,d). According to Takahashi-Tachiki model in S 1 /S 2 superlattices, an upturn behavior in H c2 (T) can be observed near T c due to different spatial variations in the density of states, the diffusion constant, and the electron-electron attractive interaction potential between S 1 and S 2 (refs 38,39 ). The enhanced upturn feature of μ 0 H c2 (T) in the MgB 2 bilayer (MB850 nm) compared to that in the pristine film may be closely associated with the different diffusion constant between S and S′ layers because T c,pri. ≈ T c,irr. in the MB850 nm. The Cooper pairs in the damaged layer may be more effective in penetrating into the undamaged layer, inverse proximity effect 16,23 , than the reversal process because of a larger diffusion constant in the S than S′ layer, leading to the large upturn feature in μ 0 H c2 (T) near T c . On the other hand, Ferrando et al. suggested that a large upward behavior of H c2 (T) near T c in MgB 2 thin films is associated with a large resistive surface layer of MgB 2 due to the contamination in air rather than the multiband effect of MgB 2 (refs 40,41 ). In order to confirm this mechanism, however, further measurements for μ 0 H c2 (T) in high magnetic field parallel to the ab plane (H//ab) will be needed because this upturn behavior or sudden change of μ 0 H c2 (T) in S′/S is more prominent for H//ab (refs 38,39 ).
Magnetic field dependences of critical current density (J c ) for the pristine and irradiated MgB 2 films at 5 and 20 K are shown in Fig. 4(a,b), respectively, where the magnetic field is applied perpendicular to the film's ab plane. The large J c at zero field and its rapid suppression in magnetic fields indicate that the pristine MgB 2 films used in this study is clean 42,43 . After Co-ion irradiation, in-field J c is significantly improved except for the thinnest MB130 nm film because of the large suppression of T c . The suppression of zero-field J c for the irradiated MB410 nm is also related with the suppressed T c by the irradiation. On the other hand, in-field J c for both MB850 nm and MB1300 nm is remarkably enhanced without the suppression of the zero-filed J c after Co-ion irradiation, suggesting that the proximity effect (PE) in the S′/S bilayers is not confined near the interface [11][12][13] , but is long ranged over the whole thickness of the irradiated layer S′ when the thickness of the S is sufficiently larger than that of the S′. In addition, the large in-field J c in S′/S MgB 2 bilayers manifests the strong correlation between S′ and S layers. www.nature.com/scientificreports www.nature.com/scientificreports/

Conclusion
In conclusion, we reported fabrication of MgB 2 /MgB 2 bilayers, where a dose of 1 × 10 14 Co atoms/cm 2 with a beam energy of 140 keV is irradiated into single-crystalline MgB 2 films and created the damaged layer (S′) interfaced with the undamaged layer (S). Superconductivity of MgB 2 in the damaged layer is significantly weakened: T c is suppressed from 38.2 to 4.5 K for the irradiated MB130 nm film. The suppressed superconductivity, however, was restored to the original SC state when the thickness of the undamaged MgB 2 layer (S) is sufficiently larger than that of the damaged MgB 2 layer (S′). Although the coherence length of the undamaged layer S (~8.5 nm) is more than ten times shorter than the damaged layer S′ (~95 nm), the proximity effect occurs over the whole thickness of the S′. This anomalously long-ranged proximity effect in S′/S MgB 2 bilayers is thought to be originated from the similar electronic structures of S′ and S layers and a finite SC pairing interaction in the S′ layer. The discovery of giant proximity effect (GPE) in the MgB 2 /MgB 2 bilayers is expected to provide a blue print to the design of superconducting MgB 2 multilayers for their fundamental researches as well as technological applications. www.nature.com/scientificreports www.nature.com/scientificreports/

Methods
Hybrid physical-chemical vapour deposition (HPCVD) method was used for the growth of single-crystalline MgB 2 films on the c-cut Al 2 O 3 substrates, and the details of the growth technique and the film's single-crystal quality are described elsewhere 43,44 . The MgB 2 films with various thicknesses (t) of 130 (MB130 nm), 200 (MB200 nm), 410 (MB410 nm), 850 (MB850 nm), and 1,300 nm (MB1300 nm) were fabricated for ion irradiations, and the same amount of dose of 1 × 10 14 Co atoms/cm 2 with 140 keV beam energy at room temperature was irradiated into the prepared MgB 2 films in Korea Multi-purpose Accelerator Complex (KOMAC). The mean projected range (δ) of irradiated Co ions is around 95 nm, which is simulated by the Monte Carlo simulation program SRIM (The Stopping and Range of Ions in Matter) 27 .
The formation of S′/S MgB 2 bilayers by the Co-ion irradiation was confirmed by simultaneously measuring electrical resistivity (ρ) of the damaged and undamaged MgB 2 layers in Physical Property Measurement System (PPMS 9 T, Quantum Design). The standard 4-probe method was used for electrical resistivity measurements, and the 4-point contact regions were protected from the irradiation by using gold (Au) coating and silver (Ag) epoxy in order to measure the resistivity of the undamaged layer after the irradiation. In order to estimate the critical current density (J c ), magnetization hysteresis (M -H) loops were measured by using a Magnetic Property Measurement System (MPMS 5 T, Quantum Design) before and after the Co-ion irradiations (see Fig. S3 in the Supplemental Information).