Realizing Topological Order in Synthetic Quantum Materials

Realizing and probing topological order in solid-state materials remains a major challenge in condensed matter physics. As an alternative, we propose their realization in synthetic materials: networks of superconducting wires and quantum dots in the presence of magnetic flux. We show that the interplay of transport interference, electron co-tunneling, and Andreev reflection processes can give rise to rich phases, as topological superconductors or quantum spin liquids depending on the network geometry. This offers a concrete path toward experimentally realizing topological phases in controllable superconducting meta-materials.