  Geometric frustration emerges when local interaction energies in an ordered
lattice structure cannot be simultaneously minimized, resulting in a large
number of degenerate states. The numerous degenerate configurations may lead to
practical applications in microelectronics, such as data storage, memory and
logic. However, it is difficult to achieve extensive degeneracy, especially in
a two-dimensional system. Here, we showcase in-situ controllable geometric
frustration with massive degeneracy in a two-dimensional flux quantum system.
We create this in a superconducting thin film placed underneath a
reconfigurable artificial-spin-ice structure. The tunable magnetic charges in
the artificial-spin-ice strongly interact with the flux quanta in the
superconductor, enabling the switching between frustrated and crystallized flux
quanta states. The different states have measurable effects on the
superconducting critical current profile, which can be reconfigured by precise
selection of the spin ice magnetic state through application of an external
magnetic field. We demonstrate the applicability of these effects by realizing
a reprogrammable flux quanta diode. The tailoring of the energy landscape of
interacting 'particles' using artificial-spin-ices provides a new paradigm for
the design of geometric frustration, which allows us to control new
functionalities in other material systems, such as magnetic skyrmions,
electrons/holes in two-dimensional materials and topological insulators, as
well as colloids in soft materials.
