Continuously tunable charge in Andreev quantum dots

We show that a quantum dot connected via tunnel barriers to superconducting leads traps a continuously tunable and hence fractional charge. The fractional charge on the island is due to particle-hole symmetry breaking and can be tuned via a gate potential acting on the dot or via changes in the phase difference across the island. We determine the ground state, equilibrium, and excitation charges and show how to identify these quantities in an experiment.