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Graphene is a relatively new material (2004) made of atomic layers of carbon arranged in a honeycomb lattice. Josephson junction devices are made from graphene by depositing two parallel superconducting leads on a graphene flake. These devices have hysteretic current-voltage characteristics with a supercurrent branch and Shapiro steps appear when irradiated with microwaves. These properties motivate us to investigate the presence of quantum metastable states similar to those found in conventional current-biased Josephson junctions. We present work investigating the nature of these metastable states for ballistic graphene Josephson junctions. We model the effective Washboard potential for these devices and estimate parameters, such as energy level spacing and critical currents, to deduce the design needed to observe metastable states. We propose devices consisting of a parallel on-chip capacitor and suspended graphene. The capacitor is needed to lower the energy level spacing down to the experimentally accessible range of 1-20 GHz. The suspended graphene helps reduce the noise that may otherwise come from two-level states in the insulating oxide layer. Moreover, back-gate voltage control of its critical current introduces another knob for quantum control. We will also report on current experimental progress in the area of fabrication of this proposed device.

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Several theoretical analyses of the two superconducting energy gaps of magnesium diboride, ∆π and ∆σ, predict substructures within each energy gap, rather than two pure numbers. Recent experiments have revealed similar structures. We report tunneling conductance data providing additional experimental evidence for these features. The absence of these features in c-axis tunneling, and a sharp peak in the subgap (associated with the counterelectrode material), support the conclusion that these features are intrinsic to MgB2. By demonstrating the inadequacy of a simple two-gap model in fitting the data, we illustrate that some distinctions between theoretical models of energy gap substructures are experimentally accessible.