# Fully Superconducting Josephson Bolometers for Gigahertz Astronomy
## 4 Experimental Realization of JES and Nano-TES
### Bias Current Control of Resistance versus Temperature Characteristics  
The realization of a typical 1D-JJ is shown by the scanning electron micrograph displayed in Figure 5a. The 1D superconducting active region consists of the same Al/Cu bilayer presented in Section 4.2, that is \(t_{Al}=10.5\) nm and \(t_{Cu}=15\) nm. The width of \(A\) is \(w=100\) nm, while its length is \(l=1.5\)\(\upmu\)m. Finally, the lateral banks are composed of a 40-nm-thick aluminum film. The zero-temperature critical current of this 1D-JJ is \(I_{C,0}\simeq 575\) nA. The resistance \(R\) vs. temperature characteristics and of the Al banks were obtained by conventional four-wire low-frequency lock-in technique at 13.33 Hz in a filtered He\({}^{3}\)-He\({}^{4}\) dry dilution refrigerator. The current was generated by applying a voltage (\(V_{ac}\)) to a load resistor (\(R_{L}\)) of impedance larger than the device resistance (\(R_{L}=100\) k\(\Omega\gg R\)), as shown in Figure 5a. In particular, the device showed a normal state resistance \(R_{N}\simeq 77\)\(\Omega\). To prove that the Al/Cu bilayer can be considered a uniform superconductor, we need to demonstrate that it respects the Cooper limit [53; 54], that is the contact resistance between the two layers is negligible and the thickness of each component is lower than its coherence length. Since its large surface area, the Al/Cu interface can be considered fully transparent, i.e., its resistance is negligibly small with comparison to \(R_{N}\). Furthermore, the superconducting Al film fulfills \(\xi_{Al}=\sqrt{\hbar D_{Al}/\Delta_{Al}}\simeq 80\) nm \(\gg t_{Al}=10.5\) nm, where \(D_{Al}=2.25\times 10^{-3}\) m\({}^{2}\) s\({}^{-1}\) is the diffusion constant of Al thin films and \(\Delta_{Al}\simeq 200\)\(\upmu\)eV is its superconducting energy gap. Concurrently, the normal copper film respects \(\xi_{Cu}=\sqrt{\hbar D_{Cu}/(2\pi k_{B}T)}\simeq 255\) nm \(\gg t_{Cu}=15\) nm, with \(D_{Cu}=8\times 10^{-3}\) m\({}^{2}\) s\({}^{-1}\) the typical copper diffusion constant for thin films deposited in the same conditions (pressure and evaporation rate. We note that the temperature is chosen to the worst case scenario \(T=150\) mK. As a consequence, the Al/Cu bilayer lies within the Cooper limit and can be considered a single superconducting material. We now focus on the 1D nature of the fully superconducting nanowire Josephson junction. The superconducting coherence length in \(A\) is given by \(\xi_{A}=\sqrt{\hbar/\left[(t_{Al}N_{Al}+t_{Cu}N_{Cu})R_{N}e^{2}\Delta_{A,0} \right]}\simeq 220\) nm, where \(N_{Al}=2.15\times 10^{47}\) J\({}^{-1}\) m\({}^{-3}\) and \(N_{Cu}=1.56\times 10^{47}\) J\({}^{-1}\) m\({}^{-3}\) are the density of states at the Fermi level of Al and Cu, respectively. Therefore, the bilayer shows a constant pairing potential along the out-of-plane axis, since the Cooper pairs coherence length is much larger than its thickness (\(\xi_{a}\gg t=t_{Al}+t_{Cu}=25.5\) nm). Furthermore, \(\xi_{A}\gg w=100\) nm. Therefore, the active region is one dimensional with respect to the superconducting coherence length. In addition, the London penetration depth for the magnetic field of \(A\) can be calculated from \(\lambda_{L,A}=\sqrt{(\hbar wt_{A}R_{N})/(\pi\mu_{0}l\Delta_{A,0})}\simeq 970\) nm, where \(\mu_{0}\) is the magnetic permeability of vacuum. Since \(\lambda_{L,A}\gg t,w\), \(A\) is 1D with respect to the London penetration depth, too. The magnetic field generated at the wire surface by the maximum possible bias current is \(B_{l,max}=\mu_{0}I_{C,0}/(2\pi t)\simeq 5\)\(\upmu\)T. This value is orders of magnitude lower than the  
Figure 5: Experimental \(I\)-tuning of the transport properties of a 1D-JJ. **(a)** False-color scanning electron micrograph of a typical 1D-JJJ. The core of the device is made of an Al/Cu nanowire (purple) in contact with thick Al leads (blue). The nanosensor is AC current-biased (amplitude \(I\)), while the voltage drop across the wire (\(V_{out}\)) is measured through a lock-in amplifier. \(R_{L}\) is a load resistor (\(R_{L}\gg R_{N}\)).