Introduction

The superconducting proximity effect (PE), a leak of Cooper pairs from a superconductor (S) into a normal metal (N) when they are in contact with each other, is a fascinating phenomenon that is critical to the design of superconducting electronic devices, such as superconducting quantum interface device (SQUID) and quantum information device1,2,3,4. Superconducting coherence length (ξ) and electronic mean free path (l) in the normal metal are important parameters to determine the leaking distance of Cooper pairs in S/N junctions, which have been intensively studied and well understood based on conventional theories2,3,5,6,7,8,9,10.

Recently, unpredicted large PE was observed when superconductor S1 is connected with another superconductor S2 instead of normal metal, which is known as the giant proximity effect (GPE)11,12,13,14,15,16,17. Here, superconducting transition temperature (Tc) of S2 is lower than that of S1. The Cooper-pair leaking distance in S1/S2 junctions is almost ten times larger than the coherence length ξ, and Josephson critical current could be much improved in the superconducting multilayers composed of the optimally doped and under doped high-Tc cuprates, such as LSCO (La2-xSrxCuO4)/LCO (La2CuO4+δ)/LSCO trilayer13,14,15. The spatially long-ranged propagation of Cooper pairs between two different conventional superconductors, such as few-layer lead (Pb) island and Pb monolayer, was also visualized by using scanning tunnelling spectroscopy (STS) and scanning tunnelling microscopy (STM)16,17. The Cooper pairs’ leaking distance is influenced by the Tc of S2, which is considered due to its finite attractive interactions/phase fluctuations or an additional superconductivity between the interface of S1 and S2. However, the origin of GPE has yet to be clarified12,13,14,15,18.

GPE is expected to provide a significant technological advantage for the applications of superconducting electronics because thicker barrier can make it much easier to achieve uniform Josephson junctions. GPE observed in the cuprates-based Josephson junctions, however, has shown inconsistent results partly because of the surface roughness between layers and secondary phases13,15. Fabrication of the uniform multilayers in such complex compounds has proven to be difficult so far.

Ion irradiations have been often used to fabricate S/N/S Josephson junctions because local crystal disorders or defects can easily be controlled by an irradiating ion source or its dose19,20,21,22,23, and long range PE has been also observed in the junctions fabricated by ion irradiations23. Similar electronic structures between S and N layers and a finite SC pairing interaction in the N layer are considered as sources for the enhanced proximity effect13,14,16,24. Conventional superconductor MgB2 with relatively high Tc of 40 K is a good candidate for GPE realization via the ion irradiation technique because of its large superconducting coherence length, metallicity, and large superconducting energy gap25,26.

Here we report the giant proximity effect in the S′/S MgB2 bilayers. A dose of 1 × 1014 Co atoms/cm2 with the 140 keV beam energy (mean projected range δ = 95 nm), where δ is the average distance from the surface of the film at which the irradiated Co ions come to maximum concentration, is irradiated into single-crystalline MgB2 films with various thicknesses (t) of 130, 200, 410, 850, and 1,300 nm. Tc of the MgB2 film with t = 130 nm is considerably suppressed from 38.2 to 4.5 K after the Co-ion irradiation. Although, the thickness of damaged MgB2 layer (S′) by the irradiation is almost ten times longer than the coherence length, ξab(0) ~ 8.5 nm, of the undamaged MgB2 layer (S), the suppressed Tc of S′ by the irradiation is rapidly restored to that of the pristine state with an increase in the thickness of S. In addition, upper critical field (μ0Hc2) of the S′/S bilayers has two times larger value than that of the pristine films, and field performance of critical current density (Jc) of the bilayers is superior to that of the pristine MgB2 films. These results demonstrate that the existence of giant proximity effect in the S′/S MgB2 bilayers provides a blue print to fabricate superconducting MgB2 multilayers for their fundamental researches as well as technological applications.

Results

Figure 1(a) shows the mean projected range (δ = 95 nm) of the irradiated 140 keV Co ions into MgB2 and damage events created by the irradiated energetic ions, simulated by the SRIM program27. If MgB2 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.

Figure 1
figure 1

Schematic view of MgB2/MgB2 bilayers fabricated by cobalt ion irradiation. (a) SRIM simulation for the mean projected range (δ) and target vacancies resulted from damaged events of irradiated Co ions with an incident energy of 140 keV in MgB2, where the estimated δ is around 95 nm. Insets show two types of configurations for the four-probe point contacts: contact method A and B. Electrical resistivity (ρ) measured by the contact method A is influenced by both damaged layer (S′) and undamaged layer (S). On the other hand, the SC transition measured by the contact method B is determined by the S′. (b) Temperature dependences of the normalized resistivity, ρ(T)/ρn, for the pristine and irradiated MB850 nm at magnetic fields of 2 and 4 T, where ρn is the resistivity at Tc onset at each magnetic field. The kinks and the second SC transitions observed from the contact method A are due to the undamaged layer S, indicating the formation of the S′/S MgB2 bilayer via the Co-ion irradiation.

Full size image

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 Tc onset, ρn, at each magnetic field for comparison. After irradiation with a dose of 1 × 1014 Co atoms/cm2 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 Tc 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 MgB2 bilayer is fabricated via the ion irradiation method.

The ρ(T) curve near Tc for pristine MgB2 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, Tc of the pristine MgB2 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, Tc of the S′/S MgB2 bilayers is rapidly suppressed with decreasing the thickness (t′) of undamaged MgB2 layer S, as shown in Fig. 2(b), where ρ(T) was measured by using the contact method A. The change in Tc 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 Tc from 38.2 to 4.5 K in MB130 nm after the irradiation indicates that a dose of 1 × 1014 Co atoms/cm2 is enough to substantially degrade superconductivity of the MgB2. Interestingly, however, Tc 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 MgB2 layer (S′) is much larger than the coherence length (ξ) of MgB2 (ref.26) indicates the emergence of giant proximity effect (GPE) in S′/S MgB2 bilayers. We note that the GPE is often observed in S1/S2 junctions, where S1 and S2 are superconducting layers with different Tc (refs11,12,13,14,15,16,17).

Figure 2
figure 2

Thickness dependence of superconducting transition temperature for irradiated MgB2 films. ρ(T) curves near the SC transitions for (a) pristine and (b) Co-ion irradiated MB130 nm, MB200 nm, MB410 nm, MB850 nm, and MB1300 nm, where ρ(T) was normalized by the ρ at 41 K, ρ(41 K), for comparison. (c) The SC transition temperature of the irradiated films (Tc,irr.) as a function of t′/δ, where the Tc,irr. is normalized by Tc of the pristine films (Tc,pri.) and t′ (=t − δ) is the thickness of the S. Star, circle, and square symbols represent Tcs for different incident energies of 35 (δ ~ 27 nm), 70 (δ ~ 49 nm), and 140 keV (δ ~ 95 nm), respectively. Both Tc,pri. and Tc,irr. are determined from the midpoint of SC transition, ρ50%, 50% resistivity drop from the ρn. The red solid line is a fitting curve by using the Werthamer theory. Inset shows the Tc,pri. and Tc,irr. as a function of t′/δ. (d) The inverse of the Tc reduction, 1/ΔTc (=Tc,pri. − Tc,irr.), is plotted as a function of t′/δ.

Full size image

Figure 2(c) displays the SC transition temperature of the irradiated MgB2 films (Tc,irr.), normalized by that of the pristine films (Tc,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, Tc,pri. and Tc,irr. are determined from the criterion of 50% resistivity drop from the resistivity value at 41 K. For comparison, Tc,irr./Tc,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 × 1014 Co atoms/cm2. Inset of Fig. 2(c) shows Tc,pri. and Tc,irr. as a function of the t′/δ for pristine and irradiated MgB2 films, respectively. Tc,irr. that corresponds to the Tc 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 (Tc,irr. = 0 K) of the S′/S MgB2 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 interaction6, even though the thicknesses of the S and S′ are much thicker than coherence length of MgB2. In the BCS theory, Tc of a normal metal (N) and superconductor (S) bilayer can simply be expressed by the relation Tc = 1.14ΘDexp[−1/(N0V0)eff], where ΘD is Debye temperature, N0 is the electronic density of states at the Fermi energy, and V0 is strength of attractive electron-electron interaction, and (N0V0)eff is the effective BCS interaction parameter2,6,29. For N/S bilayer, N0V0 in the S layer is an important parameter to determine Tc of the bilayer, because V0 = 0 in the N layer. On the other hand, a finite V0 in the N layer could induce the long range of the PE due to the slow decay of SC pair amplitude in the N layer16,18,24, which is probably one of the primary reasons for GPE in the S′/S MgB2 bilayer.

The electronic density of states at the Fermi energy (N0) is also important to determine Tc, and the large reduction of Tc in MgB2 by the irradiation is believed to be due to the decreased N0 and enhanced interband scattering30,31,32,33,34. Considering a significant decrease of Tc of MB130 nm from 38.2 to 4.5 K by Co-ion irradiation, the Tc variation in the S′/S MgB2 bilayers is expressed by the decrease in the N0 (refs29,35,36). Figure 2(d) shows that the inverse of Tc difference between the pristine and irradiated films, 1/ΔTc (=Tc,pri. − Tc,irr.), is linearly proportional to the thickness ratio between the undamaged (t′) and damaged MgB2 layers (δ), t′/δ, indicating that the Tc suppression by the Co-ion irradiation is closely related with the decrease in the electronic density of states N0 of the damaged layer S′ (refs29,35,36). The initial slope of Tc (∝|dTc(dn = 0)/ddn|) in S/N bilayer is proportional to the ratio of density of states between the two layers (Nn/Ns) because Tc = 1.14 ΘDexp[−1/(N0V0)], where Nn and Ns are the density of states at the Fermi energy for the normal and superconducting layer, respectively, and dn is a thickness of the normal layer29,35,36. Our results on the Tc 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 disorder30,31,32,33,34.

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 MgB2 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 (ρn) 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 (Tc2) is consistent with the SC transition temperature of pristine films (Tc,pri.), indicating that Tc2 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 Tc2 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′.

Figure 3
figure 3

Upper critical fields of MgB2/MgB2 bilayers. ρ(T) curves for (a) pristine and (b) Co-ion irradiated MB410 nm in magnetic fields, where ρ(T) was normalized by the ρn at each magnetic field. In (b), the open and solid symbols are obtained from the contact method A and B, respectively. Temperature dependence of upper critical field, μ0Hc2(T), for (c) MB410 nm and (d) MB850 nm. Criteria for Tc,pri., Tc,irr., Tc2, and Tk are indicated by arrows in (a,b). The red dashed lines are obtained from the two-band Ginzburg-Landau theory. The Tc2’s obtained from the second SC transition are consistent with Tc,pri., demonstrating that the irradiated films are composed of the S′/S bilayer: damaged MgB2 layer (S′) and undamaged MgB2 layer (S).

Full size image

Temperature dependences of the upper critical field (μ0Hc2) 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 Tc,pri. and Tc,irr. are 50% resistivity drop for the pristine and irradiated films, respectively, while Tc2, and Tk 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 (Tk) for the MB410 nm suggests that Tk is associated with Tc of the undamaged layer S. One the other hand, there is no kink (Tk) in the irradiated MB850 nm because superconductivity of the damaged layer S′ is completely restored to that of the pristine state, i.e., Tc,pri. ≈ Tc,irr.. The fact that μ0Hc2(T)s determined by Tc2 are consistent with those estimated from the Tc,pri. underscores that the MgB2/MgB2 bilayer is formed by the Co-ion irradiation. Upper critical field of the bilayers is enhanced by two times to the pristine films: μ0Hc2(0) = 5.29 → 9.75 T for MB410 nm and μ0Hc2(0) = 4.52 → 9.50 T for MB850 nm, which can be accounted for by additional defects introduced via the Co-ion irradiation37. The SC coherence length, ξab(0), obtained from the μ0Hc2(0) [=ϕ0/2πξ2ab(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 μ0Hc2 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 S1/S2 superlattices, an upturn behavior in Hc2(T) can be observed near Tc due to different spatial variations in the density of states, the diffusion constant, and the electron-electron attractive interaction potential between S1 and S2 (refs38,39). The enhanced upturn feature of μ0Hc2(T) in the MgB2 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 Tc,pri. ≈ Tc,irr. in the MB850 nm. The Cooper pairs in the damaged layer may be more effective in penetrating into the undamaged layer, inverse proximity effect16,23, than the reversal process because of a larger diffusion constant in the S than S′ layer, leading to the large upturn feature in μ0Hc2(T) near Tc. On the other hand, Ferrando et al. suggested that a large upward behavior of Hc2(T) near Tc in MgB2 thin films is associated with a large resistive surface layer of MgB2 due to the contamination in air rather than the multiband effect of MgB2 (refs40,41). In order to confirm this mechanism, however, further measurements for μ0Hc2(T) in high magnetic field parallel to the ab plane (H//ab) will be needed because this upturn behavior or sudden change of μ0Hc2(T) in S′/S is more prominent for H//ab (refs38,39).

Magnetic field dependences of critical current density (Jc) for the pristine and irradiated MgB2 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 Jc at zero field and its rapid suppression in magnetic fields indicate that the pristine MgB2 films used in this study is clean42,43. After Co-ion irradiation, in-field Jc is significantly improved except for the thinnest MB130 nm film because of the large suppression of Tc. The suppression of zero-field Jc for the irradiated MB410 nm is also related with the suppressed Tc by the irradiation. On the other hand, in-field Jc for both MB850 nm and MB1300 nm is remarkably enhanced without the suppression of the zero-filed Jc after Co-ion irradiation, suggesting that the proximity effect (PE) in the S′/S bilayers is not confined near the interface11,12,13, 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 Jc in S′/S MgB2 bilayers manifests the strong correlation between S′ and S layers.

Figure 4
figure 4

Critical current density, Jc, of MgB2/MgB2 bilayer. Magnetic field dependences of the critical current density (Jc) at (a) 5 and (b) 20 K for the pristine and Co-ion irradiated MB130 nm, MB410 nm, MB850 nm, and MB1300 nm. Jc for all pristine films shows a similar field performance, and a rapid decrease of Jc in magnetic fields indicates that the MgB2 films used in this study is of high quality. A significant enhancement of in-field Jc after irradiation is observed except for the MB130 nm. There is no data for the Jc of the irradiated MB130 nm due to a substantially suppressed Tc and SC volume fraction.

Full size image

Conclusion

In conclusion, we reported fabrication of MgB2/MgB2 bilayers, where a dose of 1 × 1014 Co atoms/cm2 with a beam energy of 140 keV is irradiated into single-crystalline MgB2 films and created the damaged layer (S′) interfaced with the undamaged layer (S). Superconductivity of MgB2 in the damaged layer is significantly weakened: Tc 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 MgB2 layer (S) is sufficiently larger than that of the damaged MgB2 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 MgB2 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 MgB2/MgB2 bilayers is expected to provide a blue print to the design of superconducting MgB2 multilayers for their fundamental researches as well as technological applications.

Methods

Hybrid physical-chemical vapour deposition (HPCVD) method was used for the growth of single-crystalline MgB2 films on the c-cut Al2O3 substrates, and the details of the growth technique and the film’s single-crystal quality are described elsewhere43,44. The MgB2 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 × 1014 Co atoms/cm2 with 140 keV beam energy at room temperature was irradiated into the prepared MgB2 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 MgB2 bilayers by the Co-ion irradiation was confirmed by simultaneously measuring electrical resistivity (ρ) of the damaged and undamaged MgB2 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 (Jc), 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).