# Enhancing Precision in SQUID Sensors: Analyzing Washer Geometry Dependence at the Microscale
## 4 Results
### Screening Currents  
Screening currents, also known as supercurrents, circulate within the superconducting loop of the SQUID to uphold the quantization of magnetic flux inside the loop. When an external magnetic field is applied, these currents adapt to counteract the external flux within the superconductor, effectively shielding the superconducting loop from alterations in the external magnetic fields. The functionality of a SQUID hinges on the interference pattern generated by two superconducting paths containing Josephson junctions. These screening currents influence the phase difference between the superconducting wave functions along these paths, which, in turn, is highly sensitive to the magnetic flux. This sensitivity enables the SQUID to discern incredibly minute changes in magnetic flux, thereby translating them into measurable voltage changes across the Josephson junctions. Our examination of the current density distributions across three unique washer loop configurations unveils a prominent concentration of current density at the peripheries of the devices, while the inner regions exhibit negligible to zero current density, as evidenced by the coloration in the loop diagrams provided earlier. The subsequent graphs, depicting current density (\(|J|\)) in units of [mA/\(\upmu\)m] plotted against distance along the cut (\(\upmu\)m), further validate this observation. Notably, this distribution pattern is confined within the London penetration depth of the superconductor surface, with the Meissner effect fosters a high-density current near the boundary. Our simulations on the circulation of currents within SQUID washer loops (Figure 8) unveil an intriguing observation: the current magnitude across circular, octagonal, and square washers remains largely equivalent. However, upon comparative analysis at y = \(-150\)\(\upmu\)m, it becomes evident that the square washer loop manifests the lowest current density, particularly at its corners, indicating a significantly lower stability in current density compared to the circular washer loop. Conversely, the performance of the octagonal washer loop closely mirrors that of the circular one, displaying comparable efficacy and stability. Nonetheless, this inconsistency marks a slight dip in current density stability compared to their circular counterparts. Figure 7: Results of the Meissner effect simulations: (**a**) Meissner response for a square washer. (**b**) Meissner response for a circular washer. (**c**) Meissner response for an octagonal washer. The upper images depict the Meissner effect, while the graphs below detail the magnetic field response intensity at tangential positions. Different colors indicate the simulation results for different tangent positions. The simulation results of the applied circulating currents indicate that the magnitude of currents generated by the three types of washer loops is approximately equivalent. However, the comparative analysis at y = \(-150\)\(\upmu\)m highlights that the square washer loop displays the lowest current density, especially at its corners, indicating significantly lower stability in the current density compared to the circular washer loop. Conversely, the performance of the octagonal washer loop closely mirrors that of the circular one, exhibiting comparable efficacy and stability. The study on magnetic dipole simulation (Figure 9) further elucidates this point, demonstrating a clear tendency for vortex formation along the inner edges of the square washer. The magnetic fields emanated by magnetic dipoles culminate in the generation of flux vortices at the periphery of square washers. The dynamics and redistribution of these vortices instigate alterations in the local magnetic fields, necessitating the redistribution of superconducting currents within the vortices to uphold the conservation of the magnetic flux. This readjustment of the current, in tight coupling with the washer, engenders flux noise, significantly undermining the device's sensitivity and its capacity to discern weak signals.