Quantum phase transitions in two layers of ultrasmall Josephson junctions, coupled capacitively with each other, are investigated. As the inter-layer capacitance is increased, the system at zero temperature is found to exhibit an insulator-to-superconductor transition. It is shown that, unlike in the case for one-dimensional arrays with a similar coupling configuration, the transition cannot be...

Exact analytical formulas are derived, by means of Keldysh Green functions, for currents and current correlation functions in a Cooper pair splitter modeled on double quantum dot system coherently coupled to superconductor two normal metallic electrodes. Confining the subspace with interdot singlet we show perfect entanglement split electrons separated crossed Andreev reflection processes. The ...

Based on the many-particle-number-state treatment for transport through a pair of Majorana zero modes (MZMs) which are coupled to leads via two quantum dots, we identify that reason cross correlation currents at uncoupling limit between MZMs is from degeneracy teleportation and Andreev process channels. We then propose scheme eliminate by introducing finite charging energy island allows coexist...