Bound States in ``Majorana Box''*

We perform bias spectroscopy and observe Coulomb peak motion in InAs quantum dots with an epitaxial superconducting aluminum shell. Varying the length of the aluminum shell and applying a magnetic field, we are able to tune between regimes with 2e and 1e-periodic Coulomb oscillations. The doubling in periodicity reflects a transition from two-electron tunneling to single quasiparticle charging, attributable to a competition between the charging energy and the superconducting energy gap. At high fields below the superconducting-to-normal transition, we observe low-lying features in bias and 1e-periodic Coulomb peaks, both consistent with the presence of a zero-energy discrete state. We discuss these results in the context of proposed experimental signatures of Majorana fermions.