Dirac physics and charge localization due to quasiperiodic nonlinear capacitances

Superconducting circuits are an extremely versatile platform to realize quantum information hardware, and, as was recently realized, to emulate topological materials, such as Weyl semimetals or Chern insulators. We here show how a simple arrangement of capacitors and conventional SIS junctions can realize a nonlinear capacitive element with a surprising property: it can be quasiperiodic with respect to the quantized Cooper-pair charge. Integrating this element into a larger circuit opens the door towards the engineering of an even broader class of systems. First, we use it to simulate a protected Dirac material defined in the transport degrees of freedom. The presence of the Dirac points leads to a suppression of the classical part of the finite-frequency noise. Second, we exploit the quasiperiodicity to implement the Aubry-André model, and thereby emulate Anderson localization in charge space. Our setup implements a truly non-interacting version of the Aubry-André model, in which the macroscopic quantum mechanics of the circuit already incorporates microscopic interaction effects. We propose that measurements of the quantum fluctuations of the charge can be used to directly probe the localization effect.