Effect of large dielectric constant of SrTiO3 substrate on the characteristics of high T c dc superconducting quantum interference device

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Abstract
Effects of large dielectric constant of SrTiO3 substrate on the characteristics of high Tc dc superconducting quantum interference device (SQUID) are studied theoretically. It is shown that parasitic capacitance, which is caused by the substrate and distributes along an inductance of the SQUID, cannot be neglected when we use SrTiO3 substrate. Due to the distributed parasitic capacitance, the inductance can no longer be described as lumped element, but behaves like a transmission line when the length of the inductance becomes long. Taking into account the resonant characteristics of the transmission line, we have modified the conventional equivalent circuit of the SQUID, and presented a circuit model for this case. Using numerical simulation, we have clarified quantitatively how the SQUID characteristics are affected by the resonance due to the parasitic capacitance. The obtained results indicate the importance of taking into account the resonance when we use the SrTiO3 substrate, especially for the case of large junction resistance. Numerical simulation of the model cases shows the possibility that the transfer function can be much increased without degrading the flux noise when the SQUID is properly designed. The present theoretical results explain well the experimental results reported recently.