Quantum materials on a lattice
In a lattice composed of superconducting islands connected via tunnel barriers (which could be an insulator or even a semiconductor), two energy scales compete: the charging energy, Ec, of each superconducting island and the Josephson energy, EJ, of the tunnel junctions. In this two-dimensional array of Josephson junctions, the ratio Ec/EJ determines the fate of the array upon cooling to near zero temperature. The possible ground states of the array include an insulating phase, where each island is isolated from its neighbors through an enormous charging energy, or the opposite regime where the islands are connected via Cooper pair tunneling through the barrier, allowing the array to develop global superconducting phase coherence. Intermediate between these two extremes, complex phases may arise such as the anomalous metal phase, whose origin is still not understood. Within such an array one might pick a different material, a different tunnel barrier or even subject it to small magnetic fields and induce vortices into the array. Vortices will now reside in the potential landscape formed by the superconducting islands and localize themselves onto energetically favorable pinning sites within the array. At exactly integer (or fractional) numbers of vortices per plaquette, a unique state emerges within the array where all vortices are collectively frozen into a so-called commensurate state. As the barriers weaken, and vortices can overcome their pinning potentials within the array, they can become free to move and interact with nearby vortices.
Quantum materials on a lattice offer a versatile platform to study quantum phase transitions, anomalous phases, and to explore the dynamics of interacting vortices pinned in the potential landscape of superconducting islands. Further, with direct control over the pinning potential and vortex interactions, we aim to develop new platforms to simulate complex phases that emerge in highly correlated materials.