⇦Chinese Physics Letters, 2022, Vol. 39, No. 7, Article code 077402 High-Temperature Superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ Josephson Junction Fabricated with a Focused Helium Ion Beam Ziwen Chen (陈紫雯)1,2,3, Yulong Li (李宇龙)1,2,3, Rui Zhu (朱瑞)4, Jun Xu (徐军)4, Tiequan Xu (徐铁权)1,2,3, Dali Yin (殷大利)1,2,3, Xinwei Cai (蔡欣炜)1,2,3, Yue Wang (王越)1,2,3, Jianming Lu (路建明)1,2,3, Yan Zhang (张焱)1,2,3*, and Ping Ma (马平)1,2,3* Affiliations 1Applied Superconductivity Research Center, Peking University, Beijing 100871, China 2State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Peking University, Beijing 100871, China 3School of Physics, Peking University, Beijing 100871, China 4Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China Received 22 April 2022; accepted manuscript online 6 June 2022; published online 18 June 2022 *Corresponding authors. Email: maping@pku.edu.cn; zhang_yan@pku.edu.cn Citation Text: Chen Z W, Li Y L, Zhu R et al. 2022 Chin. Phys. Lett. 39 077402    Abstract As a newly developed method for fabricating Josephson junctions, a focused helium ion beam has the advantage of producing reliable and reproducible junctions. We fabricated Josephson junctions with a focused helium ion beam on our 50 nm YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) thin films. We focused on the junction with irradiation doses ranging from 100 to 300 ions/nm and demonstrated that the junction barrier can be modulated by the ion dose and that within this dose range, the junctions behave like superconductor–normal-conductor–superconductor junctions. The measurements of the $I$–$V$ characteristics, Fraunhofer diffraction pattern, and Shapiro steps of the junctions clearly show AC and DC Josephson effects. Our findings demonstrate high reproducibility of junction fabrication using a focused helium ion beam and suggest that commercial devices based on this nanotechnology could operate at liquid nitrogen temperatures.
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 DOI:10.1088/0256-307X/39/7/077402 © 2022 Chinese Physics Society Article Text Highly reproducible and high-quality Josephson junctions are core elements of various superconducting electronics, such as rapid single flux quantum,[1] quantum bits,[2] and superconducting quantum interference device (SQUID) magnetometers.[3] Such devices with high densities of Josephson junctions are well established in low critical temperature superconducting (LTS) electronics, whereas typical nanofabrication processes in high critical temperature superconducting (HTS) devices, which can be operated with liquid nitrogen with lower power requirements, are too difficult. Although LTS Josephson junctions with high reproducibility have been widely used in commercial cases for weak magnetic signal detection since the 1970s, such as in magnetoencephalography (MEG), magnetocardiography, and nondestructive evaluation (NDE), the price of liquid helium is 50 times higher than that of liquid nitrogen. Moreover, a liquid helium cryostat with a large thermal insulating layer decreases the system's mobility, which restricts the practical applications of LTS devices. As a result, considerable effort has been devoted to HTS junction-based devices since the discovery of the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO).[4–6] Researchers have developed methods for fabricating various types of YBCO Josephson junctions over the years. Multilayer $c$-axis sandwich junctions have demonstrated difficulties in fabricating the nanoscale intermediate layer, which reduces the yield and limits practical applications.[7] The most commonly used grain boundary junctions, such as bicrystal and step edge junctions, which have shown excellent properties in the application of HTS devices,[8] have also suffered from poor yield and reproducibility because the junction properties are highly dependent on the quality of the bicrystal boundary and the step edge on the substrate, and any microscopic imperfectly uniform boundary or defect may lead to the inhomogeneous distribution of junction parameters. Besides these types of junctions, the directly written junctions using ion implantation should be free of the problems mentioned above. Historically, researchers have used high-energy ion irradiation to pattern HTS Josephson junctions with electron-beam lithography masks. The first HTS DC SQUIDs were created using an ion implantation Josephson junction.[9] Although the high aspect ratio trenches in the mask for irradiation are limited to 25 nm, the actual lateral area of junctions made by oxygen and gallium implantation straggles up to about 100 nm due to frequent large-angle scattering events from collisions.[10] Consequently, the critical voltage $I_{\rm c}R_{\rm n}$ would be severely suppressed in this case since the large lateral area has led to a significantly reduced pair potential. Furthermore, the interaction volume of these traditionally implanted heavy ions with the target material is radial, resulting in a less uniform junction interface compared with lighter ions. Another disadvantage is the unavoidable chemical interaction of gallium with the HTS material YBCO. However, the advent and development of a commercial helium ion microscope (HIM) with lighter helium ions has enabled the fabrication of junctions with ultra-narrow lateral areas irradiated with lighter helium ions,[11] because HIM produces controllable atomic-resolution helium ion beams and the helium ion beam remains almost entirely forward-looking within the interaction volume.[12] Josephson junctions fabricated with HIM reported in recent works show great reproducibility and controllability compared with other HTS junctions. Furthermore, the potential applications of these nanoscale junctions have been investigated extensively, such as single flux quantum flip flop,[13] nano-SQUID arrays,[14] and THz spiral antenna.[15] Although relevant research is thriving, none of the research concerns working temperatures above 77 K, nor does it concentrate on HTS films thicker than 50 nm. On the one hand, it is supposed to fabricate the YBCO into generally used and economically friendly HTS devices working at liquid nitrogen temperatures, such as DC SQUIDs for MEG[8] and RF SQUIDs for mobile magnetic sensing.[16] However, the YBCO thicknesses reported in these HIM-fabricated junctions are mostly around 30 nm, limiting the corresponding devices' ability to operate at higher temperatures. A thinner film has a lower transition temperature and a wider transition range. In addition, the penetration depth $\lambda_{\bot}$ would be large and the kinetic inductance would be high. As a result, growing a thicker YBCO film would ensure a high enough $T_{\rm c}$, allowing the device to work at nitrogen temperatures. In this Letter, we report on the fabrication of high-quality Josephson junctions irradiated by Zeiss Orion Plus HIM and investigate the junction properties in detail. The YBCO film used for irradiation in this study is about 50 nm thick, which is thicker than those used in previous studies, which mostly used ultrathin films of around 25 nm[14] and 35 nm.[17] We explore the temperature dependence of junction resistance to investigate the Josephson coupling of junctions irradiated with different helium ion doses. Then, with a dose of 300 ions/nm, we focus on the junction and perform electric magnetic transport measurements, which provide us with information about the junction parameters. We also present the current-voltage characteristics of junctions (dose = 100, 200, 250, and 300 ions/nm) with and without microwave radiation. Methods—Sample Preparation and Measurement. The $c$-axis-oriented YBCO thin films were epitaxially grown on single-crystal (001)-oriented SrTiO$_{3}$ (STO) substrates ($5 \times 5$ mm$^{2}$) by pulsed laser deposition. These as-grown films were then coated with a bilayer of Ti/Ag (6 nm/100 nm) by DC magnetron sputtering through a metal mask to form the target patterns for electrical contacts and to protect the YBCO film from degradation. Following this, a microbridge for irradiation was created using UV lithography and Ar ion milling. The thickness of films was measured using a step-profiler. Subsequently, we used Zeiss Orion Plus HIM to write the junction over the microbridge with a line-scan mode and dose ranging from 100 to 800 ions/nm. To perform electromagnetic measurements on our irradiated junctions, a physical properties measurement system (PPMS, Quantum Design) and a standard four-probe method were used to characterize the junction parameters at different temperatures. Using BNC connectors, a custom-built “break-out box” was used to connect the cooled junction electrodes inside PPMS and the outside warm electronics. To control PPMS and the electrical measurement apparatus, homemade software was used. The magnetic field was provided by PPMS to characterize the electromagnetic properties of the irradiated junctions. Multiple warm-ups and slow cooling down cycles were performed to expel trapped flux during the measurements and compare the measurement results to avoid junction parameter fluctuation caused by electromagnetic interference or flux hopping.
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Fig. 1. (a) Schematic representation of a Zeiss Orion Plus HIM creating a junction in the YBCO bridge. (b) The microbridge used for irradiation under the image mode of HIM. (c) A zoom-in view of the central junction region irradiated with a dose of 300 ions/nm.
Results and Discussion. Figure 1(a) schematically shows the process of using HIM to create a Josephson junction in the YBCO bridge. As a result of ion irradiation, the implanting of He$^{+}$ into the YBCO film could result in oxygen loss within the YBCO lattice, degrading the superconductivity of the irradiated region and forming a nanoscale junction barrier. Researchers have shown that when a relatively high dose is applied, it can cause damage to the lattice structure.[18] Figure 1(b) shows a typical image of the microbridge in our experiment with a width of 4 µm prepared for He$^{+}$ irradiation, which was taken using the image mode of HIM. The irradiation region was indicated in the image by a red line crossing the microbridge. A close-up view of this region irradiated with a dose of 300 ions/nm is shown in Fig. 1(c). As shown in the figure, the lateral extended junction area with a width of 18 nm irradiated by the focused helium ion beam (He-FIB) can be clearly identified by its contrast from the YBCO film surface due to carbon deposition induced by He-FIB during the implanting process. The continuous YBCO film surface morphology with a typical grain matrix also suggests that the film is epitaxially grown in good quality with $c$-axis orientation, which is supported by our electrical measurement results presented in the following paragraph.
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Fig. 2. [(a), (b)] $R(T)$ dependence of YBCO Josephson junctions irradiated by different doses. (b) An enlargement of the resistance transitions of these junctions. [(c), (d)] Experimental data (green and blue lines) and numerical fitting results (red line) for dose equals to 100 ions/nm (c) and 300 ions/nm (d), respectively.
To investigate how the ion irradiation affects the properties of the junction with a thickness of 50 nm, we measured the resistance versus temperature ($R$–$T$) characteristics of the junctions with varying He$^{+}$ irradiation doses since it could be expected that changing the irradiation dose could modulate the junction barrier due to the mechanism mentioned above. Koelle et al. discussed the $R$–$T$ relationship of a junction with a thickness of 50 nm that was irradiated with a relatively high dose of 700 ions/nm,[18] whereas our work focuses on a relatively low dose with a YBCO film thickness of 50 nm. Figure 2(a) shows $R$–$T$ curves measured with a biased current of 10 µA without the magnetic field of YBCO Josephson junctions fabricated by HIM with doses of $D = 100,\, 200,\, 250,\, 300$, and 800 ions/nm. The ratio of resistance between 300 K and 100 K is about $3\!:\!1$. Each of these curves displays a sharp drop in the resistance starting from around $T = 89.5$ K with a transition width of less than 1.5 K, as is presented in the inset of Fig. 2(a). The enlarged scale in Fig. 2(b) shows a broad foot-structure resistance on these irradiated junctions after the superconducting transition. This plateau-like resistance presented over a considerable temperature range in our irradiated junctions, which have also been observed in high-temperature junctions made by other techniques, could be a consequence of the thermally activated phase slippage (TAPS) effect, as predicted by the Ambegaokar–Halperin (A-H) model.[19] According to the theory, such a plateau-like resistance could occur when the thermal energy $k_{\rm B}T$ is comparable with the Josephson coupling energy at a relatively high-temperature near the superconducting transition. This phenomenon could be qualitatively explained by a simple representation of the “tilted washboard potential”, as thermal fluctuation-induced phase slippage between potential minimums would result in a finite voltage due to the DC Josephson effect. In our experiments, the normal resistance $R_{\rm p}$, which denotes the resistance of junctions when the TAPS begins to appear after superconducting transition, shows a monotonous increase with the increase of $D$ and sustains a larger temperature range when a larger dose is applied. The inset of Fig. 2(b) depicts a linear increase of $R_{\rm p}$ with the increasing He$^{+}$ dose, and it is fitted by an experienced formula of $R_{\rm p}\propto \exp (D/2D_{0})$, where $D_{0}$ is a fitting parameter. A $D_{0}$ value of 156 ions/nm is obtained in our junctions fabricated with a film thickness of 50 nm, which is similar to the results obtained in a previous work.[18] This dependence is thought to be caused by an increase in the width of the amorphous track caused by irradiation as well as a decrease in the order parameter within the irradiated region as the dose increases, both of which result in a decrease in Josephson coupling energy and effectively increase the thermal fluctuation.
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Fig. 3. Electric magnetic transport measurements for junction 4 fabricated with dose of 300 ions/nm. (a) $I$–$V$ characteristics at different temperatures were measured in a four-probe configuration. (b) Temperature dependence of $I_{\rm c}$, $R_{\rm n}$ and ${I}_{\rm c}R_{\rm n}$ of junction 4. (c) ${I}_{\rm c}(B)$ pattern.
Because of its various contributions to the structural disorder of the junction area, the variation of $R$–$T$ curves confirms that the junction barrier can be effectively tuned by varying the irradiation dose. However, when the dose is up to 800 ions/nm, the Josephson coupling energy is so low that the thermal fluctuation dominates the junction behavior, increasing the resistance as the temperature decreases after superconducting transition. In Figs. 2(c) and 2(d), a good agreement between experimental data and theory for this TAPS-induced resistance is shown using the A-H theory on junctions with $D = 100$ ions/nm and 300 ions/nm, respectively. As predicted by the A-H theory, the resistance $R$ as a function of temperature can be expressed as $$ \frac{R(T)}{R_{\rm p}}=\Big[I_{0}\Big(\frac{\gamma_{0}}{2}\Big)\Big]^{-2}. $$ Here $I_{0}$ is the modified Bessel function as a function of the thermal fluctuation parameter $\gamma_{0}=\hslash I_{\rm c}(T)/ek_{\rm B}T$ with respect to the Josephson coupling energy. $I_{\rm c}(T)$ is the critical current of the junction, which is assumed to be ${C(1-T/T_{\rm c})}^{n}$ in the absence of thermal fluctuation with $C$ being proportional to the zero-temperature critical current $I_{0}$. The parameter $n$ may provide useful information about the junction's behavior, such as whether it is a superconductor–normal-conductor–superconductor (SNS) or superconductor–insulator–superconductor (SIS) junction. The fitting yield coefficient $C$ of 6300 and 53 for junctions with $D = 100$ and 300 ions/nm, respectively, demonstrates a decrease in the Josephson coupling energy with increasing irradiation doses. The parameter $n$ of 2 and 1.6 is also obtained for $D = 100$ and 300 ions/nm, respectively. We can infer that the junction is SNS-like with a relatively low dose below 300 ions/nm, whereas the junction with $D = 300$ ions/nm should be more SNS-like rather than SIS-like. This will be demonstrated further in the following paragraph. In the following section, we present the transport measurement results of junction 4, which is fabricated with a dose of 300 ions/nm. Figure 3(a) shows the current–voltage ($I$–$V$) curves at several temperatures close to the superconducting transition from 67 K to 77 K with typical RSJ-like characteristics. At temperatures lower than 77 K, the ohmic portion of the $I$–$V$ curves extends to a nonzero current value at the $y$ axis, often referred to as excess current,[20] which suggests that the junction exhibits SNS-like junction behavior. This indicates non-equilibrium excess current distribution across the junction area of sample 4. Because the excess current portion is less sensitive to the applied magnetic field in practice, it may have an effect on device performance. We could also note that there are bumps near $I_{\rm c}$ in these curves, which can be explained by the quite common thermal fluctuation in HTS junctions. Sample 4 does not exhibit hysteresis in these measurements since it is in the overdamped limit and the Stewart–McCumber parameter $\beta_{\rm c}\ll 1$ $(\beta_{\rm c}=2\pi R^{2}C/\varPhi_{0})$. The inset shows the differential resistance as a function of current bias of sample 4. We can clearly observe the strong Josephson coupling across the irradiated layer below $T = 75$ K. The critical current is calculated as the point at which the differential resistance exceeds the zero-bias current. The differential resistance of the $I$–$V$ curves after the sharp transition into the normal state is used to calculate the normal resistance. The temperature dependence of the critical current $I_{\rm c}$, normal resistance $R_{\rm n}$ and their product the characteristics voltage $I_{\rm c}R_{\rm n}$ are shown in Fig. 3(b). The resistance has no clear temperature dependence, and its values remain within a range of 0.24 $\Omega$ to 0.36 $\Omega$. According to Likharev's evaluation of SNS-type junctions, the temperature dependence of $I_{\rm c}R_{\rm n}$ in the dirty limit satisfies the expression as[20] $$ {I_{\rm c}R}_{\rm n}\mathrm{\propto (1-}{(T/T_{\rm c})}^{4})\Big(\frac{L\sqrt {T/T_{\rm c}}}{\xi_{\rm n}(T_{\rm c})}\Big)\exp\Big[-\frac{L\sqrt {T/T_{\rm c}}}{\xi_{\rm n}(T_{\rm c})}\Big], $$ where $L$ represents the lateral thickness of the barrier, which is directly determined to be 18 nm using the image mode of HIM in our case. The fitting using this formula gives the parameter $L/\xi_{\rm n}(T_{\rm c})$ a value of 15. Therefore, we can obtain the coherence length of YBCO $\xi_{\rm n}(T_{\rm c}) = 1.2$ nm. If this relation is within the clean limit, $\sqrt{T/T_{\rm c}}$ is replaced by $T/T_{\rm c}$ in the above expression, which gives $\xi_{\rm n}(T_{\rm c}) = 1.5$ nm. These theoretical calculation results are very close to the typical value of the coherence length of YBCO, demonstrating that the junction is SNS-like. Furthermore, we show the magnetic field dependence of the critical current $({I}_{\rm c}(B)$ pattern) of junction 4 at 60 K under the in-plane magnetic field. The observed peaks' magnetic field period is around 0.52 mT, and the minimum of each period is not exactly equal to zero. Because the film thickness is less than the magnetic penetration depth, sample 4 can be well treated with the Rosenthal theory, which gives equal magnitude magnetic periodicities and explains the absence of zeros.[21] The junction 4 we created is clearly a high-quality SNS junction, similar to the Josephson junction. However, the deviation from the ideal Fraunhofer diffraction pattern[22] in our case suggests that the junction is not perfectly uniform and that the current density distribution within the barrier may be inhomogeneous. This conclusion is also consistent with the electronic transport properties shown in Fig. 3(a). Furthermore, the skewed pattern with the first peak not exactly at zero magnetic fields could be caused by the geomagnetic field or residual field of PPMS.
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Fig. 4. Shapiro steps of junctions 1–4 (separately 100, 200, 250, 300 ions/nm). (a)–(d) The $I$–$V$ curves of Shapiro steps with and without microwave radiation. Microwaves are applied with a frequency of $f = 10$ GHz. (c) and (d) Heat maps of differential conductance $dI/dV$ ($\Omega ^{-1}$) as a function of bias current and RF power of junctions 1–4. The white dotted line is used to guide the eye; they are positions where the Shapiro steps show up. Numbers 1, 2, 3, and 4 on the top of each heat map represent the 1$^{\rm st}$, 2$^{\rm nd}$, 3$^{\rm rd}$, and 4$^{\rm th}$ step.
To demonstrate the potential of HIM junctions for integration on liquid nitrogen-based devices, we investigated the dose modulation on DC and AC Josephson effects of these junctions at 77 K, as shown in Fig. 4. Figures 4(a)–4(d) present the $I$–$V$ characteristics with and without the 10 GHz microwave radiation of the junctions with irradiation doses of 100, 200, 250, and 300 ions/nm. In the former case, increasing the irradiation dose suppressed the critical current of the junction, which is consistent with the TAPS results. In the latter case, one can also clearly see the emergence of Shapiro steps in all these junctions in Figs. 4(a)–4(d). The $n^{\rm th}$ steps of these junctions under a particular RF power appear at $V=nhf/2e$, where $n$ is an integer, $f$ stands for the frequency of the applied microwave, and $h/2e$ is a flux quantum.[23] To see the behavior of the steps, we show the heat map of differential conductance $dI/dV$ as a function of bias current and RF power in Figs. 4(e)–4(h), which are drawn from Figs. 4(a)–4(d). The steps are visible in the heatmap's brighter regions, and the width of each one represents the step height. The oscillations of the step height (the vanishing and reappearing of the steps), as indicated by the white dotted line, could be observed in these figures, whereas at a lower dose of 100 ions/nm, the step height could only be observed to increase monotonously with increasing power, and the oscillations should occur at higher RF power. The critical current of junction 4 with 300 ions/nm is almost suppressed at 77 K, and even at 67 K, the critical current is quickly suppressed with a microwave power of 16 dBm, as shown in Figs. 4(d) and 4(h). The periodic oscillation behavior of the 0$^{\rm th}$ and 1$^{\rm st}$ steps in Fig. 4(h) is shown in Fig. S1 in the Supplementary Material. The above results show that junctions with doses ranging from 100 ions/nm to 300 ions/nm can exhibit pronounced AC and DC Josephson effects at nitrogen temperatures, whereas junctions with doses greater than 300 ions/nm should exhibit comparable performance at lower temperatures. The junction parameters are obtained in the differential form of the $I$–$V$ curves, as shown in the Supplementary Material (Fig. S2). The $I_{\rm c}R_{\rm n}$ of the junctions at 77 K shows a reduction with increasing the irradiation dose, while the junction of 100 ions/nm shows the highest value of 251 µV. Furthermore, to demonstrate the reproducibility of HIM junctions fabricated with a focused helium ion beam, we present four junctions with a dose of 100 ions/nm on the same film in the Supplementary Material (Fig. S3), where a deviation of around 10% could be estimated on both the critical current and the normal resistance, which could be partially due to deviation of junction geometry, e.g., the junction width and film thickness, demonstrating the high reproducibility of HIM junctions. Conclusion and Outlook. In summary, we have successfully fabricated high quality Josephson junctions using the focused helium ion beam with a relative low irradiation dose of 100–300 ions/nm on our 50 nm YBCO films. The $R$–$T$ dependence of junctions with various doses have been studied. By using the A-H theory, we quantitatively investigate the dose modulation upon TAPS induced resistance which reflects the Josephson coupling of the junction. Furthermore, the measured current-voltage characteristics, magnetic field dependence of junction critical current, and observation of Shapiro steps under microwave radiation at 77 K provide clear evidence that the irradiation junctions we made within the dose range of 100–300 ions/nm are high-quality SNS-like Josephson junctions. Our findings indicate a high potential for using this highly reproducible nanotechnology to fabricate devices for practical use, such as RF SQUIDs, microwave mixers, and superconducting digital devices. With a good design, if a moderate dose of 100 ions/nm to 300 ions/nm is used, the devices based on such a Josephson junction may achieve a high operating performance above 77 K. Acknowledgments. The work was supported by the National Key Research and Development Program of China (Grant No. 2017YFC0601901) and the National Natural Science Foundation of China (Grant No. 61571019). References RSFQ logic/memory family: a new Josephson-junction technology for sub-terahertz-clock-frequency digital systemsExtending the lifetime of a quantum bit with error correction in superconducting circuits122-channel squid instrument for investigating the magnetic signals from the human brainSensitive Single-Level Magnetometers of High Tc dc SQUIDsYBa2 Cu3 O7 Bicrystal Josephson Junctions and dc SQUIDsAnalysis of Step Etching on SrTiO3 Substrates for the Step-Edge YBCO Josephson JunctionsTunneling measurements on superconductor/insulator/superconductor junctions using single‐crystal YBa2 Cu3 O 7− x thin filmsHigh-$T_{\rm c}$ DC SQUIDs for MagnetoencephalographyQuantum interference devices made from superconducting oxide thin filmsPlanar thin film YBa2Cu3O7−δ Josephson junction pairs and arrays via nanolithography and ion damageNano Josephson superconducting tunnel junctions in YBa2Cu3O7–δ directly patterned with a focused helium ion beamYBa$_{2}$Cu$_{3}$O$_{7-\delta }$Single Flux Quantum Flip Flop Directly Written With a Focused Helium Ion BeamMicrometer Scale Y–Ba–Cu–O SQUID Arrays Fabricated With a Focused Helium Ion BeamTuning Y–Ba–Cu–O Focused Helium Ion Beam Josephson Junctions for Use as THz MixersA high- Tc flip-chip SQUID gradiometer for mobile underwater magnetic sensingLarge-Scale Focused Helium Ion Beam LithographyJosephson Junctions and SQUIDs Created by Focused Helium-Ion-Beam Irradiation of Y Ba 2 Cu 3 O 7 Voltage Due to Thermal Noise in the dc Josephson EffectSuperconducting weak linksFlux focusing effects in planar thin‐film grain‐boundary Josephson junctionsJosephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations
[1] Likharev K K and Semenov V K 1991 IEEE Trans. Appl. Supercond. 1 3
[2] Ofek N, Petrenko A, Heeres R, Reinhold P, Leghtas Z, Vlastakis B, Liu Y H, Frunzio L, Girvin S M, Jiang L, Mirrahimi M, Devoret M H, and Schoelkopf R J 2016 Nature 536 441
[3] Ahonen A I, Hamalainen M S, Kajola M J, Knuutila J E T, Laine P P, Lounasmaa O V, Parkkonen L T, Simola J T, and Tesche C D 1993 Phys. Scr. T49A 198
[4] Wang S G, Dai Y D, Zeng X H, Zheng P H, Wang S H, Xiong G C, Lian G J, and Gan Z H 1995 Chin. Phys. Lett. 12 229
[5] Kislinskii Y V, Zhao B R, Wu P J, Peng Z Q, Chen Y F, Yang T, Chen L, Sun J J, Xu B, Wu F, Zhou Y L, Li L, Zhao Z X, and Stepantsov E A 1996 Chin. Phys. Lett. 13 390
[6] Chen G H, Wang J, Zhao S P, Han B, Xu F Z, and Yang Q S 2001 Chin. Phys. Lett. 18 106
[7] Hirata K, Yamamoto K, Iijima K, Takada J, Terashima T, Bando Y, and Mazaki H 1990 Appl. Phys. Lett. 56 683
[8] Faley M I, Poppe U, Dunin-Borkowski R E, Schiek M, Boers F, Chocholacs H, Dammers J, Eich E, Shah N J, Ermakov A B, Slobodchikov V Y, Maslennikov Y V, and Koshelets V P 2013 IEEE Trans. Appl. Supercond. 23 1600705
[9] Koch R H, Umbach C P, Clark G J, Chaudhari P, and Laibowitz R B 1987 Appl. Phys. Lett. 51 200
[10] Chen K, Cybart S A, and Dynes R C 2004 Appl. Phys. Lett. 85 2863
[11] Cybart S A, Cho E Y, Wong T J, Wehlin B H, Ma M K, Huynh C, and Dynes R C 2015 Nat. Nanotechnol. 10 598
[12]Hlawacek G and Gölzhäuser A 2016 Helium Ion Microscopy (Cham: Springer International Publishing AG)
[13] Cai H, Li H, Cho E Y, LeFebvre J C, and Cybart S A 2021 IEEE Trans. Appl. Supercond. 31 7200205
[14] Cho E Y, LeFebvre J C, Dynes R C, and Cybart S A 2020 IEEE Trans. Appl. Supercond. 30 1100403
[15] Cortez A T, Cho E Y, Li H, Cunnane D, Karasik B, and Cybart S A 2019 IEEE Trans. Appl. Supercond. 29 1102305
[16] Keenan S T, Young J A, Foley C P, and Du J 2010 Supercond. Sci. Technol. 23 025029
[17] LeFebvre J C and Cybart S A 2021 IEEE Trans. Appl. Supercond. 31 1100404
[18] Müller B, Karrer M, Limberger F, Becker M, Schroppel B, Burkhardt C J, Kleiner R, Goldobin E, and Koelle D 2019 Phys. Rev. Appl. 11 044082
[19] Ambegaokar V and Halperin B I 1969 Phys. Rev. Lett. 22 1364
[20] Likharev K K 1979 Rev. Mod. Phys. 51 101
[21] Rosenthal P A, Beasley M R, Char K, Colclough M S, and Zaharchuk G 1991 Appl. Phys. Lett. 59 3482
[22]Barone A and Paterno G 1982 Physics and Applications of the Josephson Effect (New York: Wiley)
[23] Shapiro S 1963 Phys. Rev. Lett. 11 80