Connecting the macroscopic phase of a Bardeen-Cooper-Schrieffer condensate to static electric fields

The possibility of tuning the properties of BCS metallic superconductors via conventional gating has been excluded for almost a century. Surprisingly, strong static electric fields have been recently shown to modulate the supercurrent down to full suppression and even to induce a superconductor-to-normal phase transition in metallic wires and Josephson junctions (JJs) without affecting their normal-state behavior. Yet, these results did not find a microscopic theoretical explanation so far. Here, we lay down a fundamental brick for both the insight and the technological application of this unorthodox field-effect by realizing a titanium-based monolithic superconducting quantum interference device which can be tuned by applying a gate bias to both JJs independently. We first show modulation of the amplitude and the position of the interference pattern of the switching current by acting with an external electric field on a single junction of the interferometer. Notably, this phenomenology cannot be explained by a simple squeezing of the critical current of the junction induced by the electric field. Consequently, a local electric field acts on a global scale influencing the properties of both JJs. Since the superconducting phases of the two JJs are non-locally connected by fluxoid quantization, we deduce that the electric field must act both on the critical current amplitude and couple to the superconducting phase across the single junction. The overall interferometer phase can shift from -0.4pi to 0.2pi depending on the used gate electrode and on the strength of the gate bias. Furthermore, the effect persists up to ~80% of the superconducting critical temperature. Fully-metallic field-effect controllable Josephson interferometers could lay the first stone of novel superconducting architectures suitable for classical and quantum computing, and for ultrasensitive tunable magnetometry.