Effect of Energy-Dependent Proton Irradiation in Thin-Film YBa2Cu3O7-δ Superconductor

1. Introduction

The discovery of superconductivity in cuprate compounds in 1986 opened a new era of high-temperature superconductivity [1,2]. Due to their exceptional properties (high-$T_c$, $J_c$, and $H_{c2}$), they became important materials for novel technologies [3,4]. Among them, YBa₂Cu₃${\mathrm{O}}_{7-\delta }$ (YBCO) is one of the most studied compounds. While its Cooper pairing mechanism still remains under debate, it is widely accepted that the optimally-doped YBCO has $d_{x^2-y^2}$ wave pairing symmetry where the energy gap vanishes in nodal directions [5].

There are many different ways to investigate the pairing symmetry of a superconductor. One of the effective methods is to introduce artificial disorders into the crystal structure of the superconductor and study the response of its superconducting properties. According to Anderson’s theorem, non-magnetic disorders are not effective in suppressing superconductivity of isotropic s-wave superconductors [6]. However, magnetic disorders are effective in suppressing the superconductivity of s-wave superconductors (so-called the Abrikosov-Gor’kov theory, or AG theory) [7]. In an anisotropic d-wave superconductor such as YBCO, non-magnetic disorders are also effective in suppressing the superconductivity [8]. Openov et al. developed a generalized AG theory to explain the effect of non-magnetic disorders on the property of d-wave superconductors [9].

Experimental confirmations of the generalized AG theory have been conducted through high-energy particle irradiation. Different types of particles generate different forms of defects [10]. Electron irradiation has been known to be most effective in the generation of point-like atomic-scale defects due to its low rest mass, resulting in a rapid suppression of superconductivity [11,12,13,14]. Other particles, such as protons and heavy ions, have previously been shown to be effective in creating cascading or columnar defects which have been known to be significantly less effective in suppressing superconductivity [15,16,17,18]. However, neither of these results (electron or others) successfully reproduced the theoretical expectations (generalized d-wave AG theory). Some results have reproduced similar behavior, but rely on a more qualitative analysis rather than direct quantitative agreement. These results were explained in terms of different quality of each sample, different plasma frequencies [8,19], different ratio between in-plane and out-of-plane defects [20], and different electron correlation [21,22,23]. In our previous study, we conducted 0.6 MeV proton irradiation of a thin-film YBCO superconductor using Hope College’s particle accelerator (1.7 MV tandem Van de Graaff electrostatic accelerator) [24]. This experiment produced the results that are quantitatively closer to the theoretical expectation than any previous results. Therefore, we concluded that as the sample thickness approached the thin-film limit, the cascading defects produced by proton irradiation would become negligible, and the atomic point-like defects would dominate.

In this article, we conducted higher energy (1.7 MeV) proton irradiation in a YBCO thin-film superconductor and compared the result with the previous 0.6 MeV experiment. We found that in general, both 1.7 MeV and 0.6 MeV protons were equally effective in suppressing the superconductivity except for the most heavily irradiated cases (more than 80% $T_c$ suppression). For the most heavily irradiated cases, the 1.7 MeV proton was more effective in suppressing $T_c$ than the 0.6 MeV proton, indicating that the 0.6 MeV proton is more prone to create agglomeration of point defects than 1.7 MeV. Furthermore, we found that both results are consistent with the theoretical expectation when the larger London penetration depth value (${\lambda }_0$ = 215 nm) was assumed for thin-film YBCO superconductors.

2. Material and Methods

2.1. YBCO Thin-Film and Resistance Measurements

The YBCO thin-film (≈567 nm thick) was epitaxially grown on a lanthanum aluminate (LaAlO₃, or LAO) substrate. The sample was originally fabricated as resonators in commercial microwave filters for wireless base stations [25]. This thin-film sample shows $T_c$≈ 89.4 K, indicating that its superconducting property is close to the bulk single-crystalline sample of $T_c$≈ 93 K [2]. This sample is of the same batch as the previous study with 0.6 MeV proton irradiation [24].

The in-plane resistance of the YBCO thin-film was measured using a standard four-probe technique as shown in Figure 1. The dimensions of the measured part of the sample are 1.835 (± 0.014) mm × 0.263 (± 0.0008) mm × 566.7 (± 1.9) nm. Four electrical contacts made of fine gold wires were adhered to the thin film using silver paste.

2.2. Energy Degrader and Homogeneous Proton Beam

The proton beam was produced by Hope College’s particle accelerator (1.7 MV tandem Van de Graaff electrostatic accelerator) which is capable of generating proton beams of up to 3.4 MeV kinetic energy. The irradiation was performed at $6\times {10}^{-8}$ torr at room temperature. This irradiation was conducted along the c-axis of the YBCO sample. 1.7 MeV proton beam was generated by using a 50 $\mu$m-thick aluminum energy degrader. Using SRIM calculation as shown in Figure 2, we confirmed that if a 2.85 MeV beam passes through a degrader of this thickness, the beam on our target would be 1.7 MeV. This degrader was held in place under the stainless-steel (SS) irradiation shield which shielded the entire sample from irradiation besides a 0.5 mm slit on the target area as seen in Figure 1(a-c). We tuned the beam to a 2 mm diameter beam spot on the Mylar strip atop the sample mount and the quadrupole magnets. We checked that this beam was homogeneous by capturing images of the beam spot and performing an intensity analysis. We tuned the beam until the intensity of the scintillator image was approximately 2 mm across with an even peak. We calibrated the image using the 2 mm by 2 mm square next to the Mylar scintillator as seen in Figure 1(b). This careful calibration was essential to ensuring a homogeneous proton beam. The irradiation was divided into 30-minute increments, during which we would measure the beam current and check the homogeneity of the beam. Using these current calculations, we estimated the fluences on target as shown in the results. The current on target was kept to about 10 nA to avoid sample heating. During irradiation, we experienced some charge buildup issue in the sample. This resulted in fractures occurring along the silver paste line in the YBCO, which destroys the sample. We avoided this effect by grounding four electrical contacts to the metallic sample holder during the irradiation, which eliminated the rapid charge buildup and discharging issue.

3. Results and Discussion

Five resistance measurements and four 1.7 MeV proton irradiations were alternatively conducted in the same YBCO thin-film. The measured resistance is plotted in Figure 3 (a) in comparison to the previous study of 0.6 MeV proton irradiations (Figure 3 (b)). All of these data show two superconducting transitions except for the pristine cases. These double transitions occur since only part of the area in which the resistance was measured was irradiated as described in Figure 1 (d). The $T_c$ of the unirradiated part does not change while the $T_c$ of the irradiated part decreases with increasing fluence. The normal state resistance above $T_c$ linearly increases upon irradiation following Matthiessen’s rule. This increase indicates that the number of defects in the irradiated part of the sample increases gradually upon irradiation. The rate of $T_c$ suppression with respect to the fluence is about three times larger for 0.6 MeV proton irradiation than for 1.7 MeV proton irradiation (Figure 4(b)). This is because as we increase the energy of the proton beam, we simultaneously increase the implantation depth. The greater implantation depth means the less energy per proton is deposited into our thin-film sample. As shown in Figure 2(b), it is evident that the number of defects created in the thin-film YBCO sample is about three times smaller for 1.7 MeV protons than for 0.6 MeV protons. This is consistent with the fact that 1.7 MeV proton irradiation needs about three times more fluence than 0.6 MeV proton irradiation to achieve the similar $T_c$ suppression as shown in Figure 4 (b). Figure 4(a) shows the broadening of superconducting transition upon irradiation. This broadening is caused by the spacing between aluminum energy degrader and the thin-film surface being about 0.5 - 0.7 mm. In the future, we plan to redesign the sample holder to decrease this spacing to 0.2 mm in order to minimize the broadening effect.

The increase in normal-state resistance is caused by the resistance increase in the irradiated part of the sample. Thus, we can convert the resistance increase to the resistivity increase by considering the volume of the irradiated part of the sample. Because the normal state resistance increases linearly across all temperature regions above the superconducting transition, the resistance value at 125 K was chosen to calculate the resistivity increase ($\Delta {\rho }_{125K}$).

According to Openov [19], the generalized AG theory for the case of the non-magnetic disorders in d-wave superconductors can be written as follows,

$$-ln\left(t_c\right)=\mathsf{\Psi }({\displaystyle \frac{1}{2}}+{\displaystyle \frac{g}{2t_c}})-\mathsf{\Psi }\left({\displaystyle \frac{1}{2}}\right),$$

(1)

where $t_c$ is $T_c$/$T_{c0}$, $T_{c0}$ is the initial $T_c$ before the disorders are added, and g is the dimensionless scattering rate. $t_c$ asymptotically goes to zero as g approaches 0.28. Using the Drude model [28,29], g can also be written in terms of the residual resistivity (${\rho }_0$) as follows,

$$g={\displaystyle \frac{\hslash {\rho }_0}{2\pi k_B{\mu }_0{T}_{c0}{\lambda }_0^2}},$$

(2)

where ${\rho }_0$ is the residual resistivity at T = 0 K of the irradiated part of the YBCO sample, $T_{c0}$ is the critical temperature of the pristine sample, and ${\lambda }_0$ is the zero-temperature London penetration depth of the pristine sample. Due to the high $T_c$ of the YBCO sample, it is difficult to estimate the exact residual resistivity. If the normal state residual resistivity is very small, ${\rho }_0$ in Eq. 2 can be replaced by $\Delta \rho$. Indeed, the linear approximation of normal state resistivity in our previous study [24] suggests very small residual resistivity at T = 0 K (≈ 8 $\mu \Omega cm$) and the current YBCO sample is almost identical to the previous sample as shown in Figure 7. By replacing ${\rho }_0$ in Eq. 2 with $\Delta \rho$, g can be rewritten as follows,

$$g\approx {\displaystyle \frac{\hslash \Delta {\rho }_{125K}}{2\pi k_B{\mu }_0{T}_{c0}{\lambda }_0^2}},$$

(3)

where $\Delta {\rho }_{125K}$ is the resistivity increase at T = 125 K of the irradiated part of the YBCO sample. This calculation requires a value for the London penetration depth, which we are not able to measure in our lab. Therefore, we surveyed experimental values of ${\lambda }_0$ from the previous studies, such as $1460\pm 150$ Å [30], 1550 Å [31], $1990\pm 200$ Å [32], and 2150 Å [33]. Among them, we used 2150 Å [33] for thin-film single-crystalline YBCO samples and $1405\pm 92$ Å [34] for bulk single-crystalline YBCO samples in Figure 6. The YBCO single-crystallined thin-films on LAO substrate are structurally less perfect than YBCO bulk single crystals. Therefore, strong scattering of the charge carriers, characterized by the mean-free path (l), is expected to extend the penetration depth in thin-film samples similar to that predicted by Tinkham [35] for “dirty" superconductors. Thus, large ${\lambda }_0$ of 215 nm is reasonable for thin-film samples. For the purpose of comparison, we used both London penetration depth values of 140.5 nm and 215 nm to plot our results in Figure 5. When ${\lambda }_0$ = 215 nm is used, both 1.7 MeV and 0.6 MeV results closely follow the theoretical expectation. However,the heavily irradiated results (more than 80%$T_c$ suppression) start deviating from the theoretical expectation. This indicates a development of extended defects where the nearby point defects agglomerate at high fluence as mentioned by Wu et al. [15]. For the most heavily irradiated cases, furthermore, $T_c$ suppression upon 0.6 MeV proton irradiation is not as effective as 1.7 MeV proton irradiation. It suggests that lower-energy protons are prone to create a cluster of point defects even in the thin-film limit than the higher-energy protons.

Figure 5. Normalized $T_c$ ($\Delta t_c=(T_c-T_{c0})/T_{c0}$) as a function of g (dimensionless scattering rate) upon 1.7 MeV and 0.6 MeV proton irradiation. Since g depends on the London penetration depth (${\lambda }_0$), we used two values commonly used for bulk single-crystalline (140.5 nm) and thin-film YBCO (214 nm). When ${\lambda }_0$ = 215 nm is used, both 1.7 and 0.6 MeV proton irradiation results closely follow the theoretical expectation. For the heavily irradiated cases (more than 60 % $T_c$ suppression), both results start deviating from the theoretical expectation. Particularly for the most heavily irradiated cases (more than 80 % $T_c$ suppression) there is a clear difference between 1.7 MeV and 0.6 MeV irradiation.

Figure 5. Normalized $T_c$ ($\Delta t_c=(T_c-T_{c0})/T_{c0}$) as a function of g (dimensionless scattering rate) upon 1.7 MeV and 0.6 MeV proton irradiation. Since g depends on the London penetration depth (${\lambda }_0$), we used two values commonly used for bulk single-crystalline (140.5 nm) and thin-film YBCO (214 nm). When ${\lambda }_0$ = 215 nm is used, both 1.7 and 0.6 MeV proton irradiation results closely follow the theoretical expectation. For the heavily irradiated cases (more than 60 % $T_c$ suppression), both results start deviating from the theoretical expectation. Particularly for the most heavily irradiated cases (more than 80 % $T_c$ suppression) there is a clear difference between 1.7 MeV and 0.6 MeV irradiation.

It is evident that the agglomeration is more significant in 0.6 MeV proton irradiation than 1.7 MeV proton irradiation.

Figure 6. Normalized $T_c$ ($\Delta t_c=(T_c-T_{c0})/T_{c0}$) as a function of g (dimensionless scattering rate) for previous studies and current 1.7 MeV proton irradiation study [10,11,12,15,24].

Figure 6. Normalized $T_c$ ($\Delta t_c=(T_c-T_{c0})/T_{c0}$) as a function of g (dimensionless scattering rate) for previous studies and current 1.7 MeV proton irradiation study [10,11,12,15,24].

Figure 6 compares the relation between $T_c$ and g of the current study with previous irradiation studies [10,11,12,15,24] and theoretical expectation [19]. Note that different penetration depth values are used for bulk single crystals and thin-film single crystals. The current proton irradiation study is the one that most agrees with the theoretical expectation. In particular, it is surprising that the current proton irradiation is more effective in suppressing superconductivity than the electron irradiation. This can be partially understood that the dominant form of defects caused by proton irradiations shifts from cascade defects to atomic-size point-defects as the sample thickness reaches the thin-film limit; i.e., the implantation depth of the proton becomes much longer relative to the sample thickness. However, further investigation is needed to fully understand it.

Figure 7. The pristine resistivity of the 0.6 MeV and 1.7 MeV samples. There is little to no difference in the sample resistivity indicating the samples are nearly identical. Normal state resistivity is higher in the current YBCO study than previous studies.

Figure 7. The pristine resistivity of the 0.6 MeV and 1.7 MeV samples. There is little to no difference in the sample resistivity indicating the samples are nearly identical. Normal state resistivity is higher in the current YBCO study than previous studies.

4. Conclusions

We conducted 1.7 MeV proton irradiation in a YBCO thin film and compared the result with the previous study (0.6 MeV proton irradiation). We found that both 1.7 MeV and 0.6 MeV irradiations were effective in suppressing superconductivity. For the most heavily irradiated cases (more than 80 % $T_c$ suppression), 0.6 MeV irradiation was less effective in suppressing the superconductivity than 1.7 MeV. This indicates that 0.6 MeV irradiation produced more agglomeration of point-defects for the heavily irradiated cases. Furthermore, when ${\lambda }_0$ = 215 nm is assumed, both 1.7 MeV and 0.6 MeV results were consistent with the theoretical expectation except for the most heavily irradiated cases.