The effects of mutual inductances in two-dimensional arrays of Josephson junctions

The quantum interference effects of one-dimensional (1D) parallel arrays of high-temperature superconducting (HTS) SQUIDs were investigated experimentally and theoretically via the voltagemagnetic field responses for 4-81 Josephson junctions. The sensitivity of the arrays generally decreased as the number of junctions (and SQUIDs) in parallel increased, contrary to the predictions of models in the low (zero) inductance limit. A full theoretical description was developed to describe 1D parallel HTS SQUID arrays with finite inductances in an applied magnetic field, by extending the model for a single DC SQUID to multiple loops in parallel and including the flux generated by currents circulating through all loops in the array. Calculations were extended from SQUID arrays with equal loop areas to arrays with a distribution of loop areas, otherwise known as superconducting quantum interference filters. The model uses parameters relevant to HTS arrays, including typical variations (up to 30%) in HTS Josephson junction parameters, such as critical current and normal resistance. The effect of the location of the current biasing leads was also explored through the calculations. This model shows good agreement with experimentally measured 1D arrays of different lengths and highlights the importance of the geometry of the current biasing leads to the arrays when optimizing the array response.

Section: Schultze Et Almentioning

confidence: 96%

Quantum interference effects in 1D parallel high-T _c SQUID arrays with finite inductance

Mitchell

Müller

Purches

et al. 2019

“…Less data is available for large 2D arrays, like #A1. However Cybart et al [35] showed and modelling [36], confirmed that as the mutual inductance decreased (by successively removing parallel connections in the arrays) the voltage modulation increased for large 2D arrays.…”

Section: 000 Junction Equal-area Loop Array (Design #1)mentioning

confidence: 99%

2D SQIF arrays using 20 000 YBCO highR_nJosephson junctions

Mitchell

Hannam

Lazar

et al. 2016

Superconducting quantum interference filters (SQIFs) have been created using two dimensional arrays of YBCO step-edge Josephson junctions connected together in series and parallel configurations via superconducting loops with a range of loop areas and loop inductances. A SQIF response, as evidenced by a single large anti-peak at zero applied flux, is reported at 77 K for step-edge junction arrays with the junction number N = 1 000 up to 20 000. The SQIF sensitivity (slope of peak) increased linearly with N up to a maximum of 1530 V T−1. Array parameters related to geometry and average junction characteristics are investigated in order to understand and improve the SQIF performance in high temperature superconducting arrays. Initial investigations also focus on the effect of the SQUID inductance factor on the SQIF sensitivity by varying both the mean critical current and the mean inductance of the loops in the array. The RF response to a 30 MHz signal is demonstrated.

“…Initial studies relied on assumptions such as the absence of thermal noise or a negligible screening parameter [6,13,17,18]. More recent models included inductance effects but thermal noise was still omitted [19]. These methods are sufficient when describing trends in low temperature superconducting (LTS) arrays, but they are insufficient when trying to replicate experimental data for high-temperature superconducting (HTS) arrays.…”

Section: Introductionmentioning

confidence: 99%

The effect of bias current configuration on the performance of SQUID arrays

Galí Labarias,

Müller,

Mitchell

2023

Designing superconducting electronic devices involves a careful study of all the elements in the circuit, including the superconducting bias leads. In this work, we introduce a theoretical model for two-dimensional superconducting quantum interference device (SQUID) arrays capable of simulating the voltage-to-magnetic flux response of devices with different bias current configurations. First, we compare uniformly biased and centre biased SQUID arrays by investigating the voltage versus magnetic flux response, maximum transfer function and voltage modulation depth. Then, we calculate the time-averaged fluxoid distributions for 1D and 2D centre biased arrays. Finally, we study the performance of the two bias current configurations depending on array size, screening parameter, thermal noise strength and kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D parallel SQUID arrays present an unusual voltage response caused by the asymmetric fluxoid distribution; (ii) the optimal transfer function of centre biased arrays strongly depends on the number of junctions in parallel; (iii) the performance of centre biased arrays approaches the uniform biased ones when the number of junctions in series exceeds those in parallel; (iv) while the screening parameter and the thermal noise strength clearly affect the device performance, the kinetic to self-inductance fraction seems to play only a secondary role.