Abstract
Recent experiments have demonstrated that the numbern of additional electrons on a small metallic island is a staircase function of a continuous external chargen x for temperaturesT small compared to the single electron charging energyU. We show that the finite conductanceg of the tunnel barrier connecting the island to the external gate gives rise to quantum fluctuations inn which lead to a smearing of the staircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductanceg≪1 the slope ∂<n>/∂n x at the turning point between two plateaus saturates at a finite value of order 1/g asT→0 instead of diverging likeU/T as predicted with thermal fluctuations only. The experimentally observed broadening however is still much larger which is probably due to extrinsic effects.
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References
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It is an interesting problem to investigate to which extent the two state approximation nearn x =m+1/2 which effectively reduces theXY symmetry to an Ising one can be justified quantitively and how it breaks down with decreasingU or increasingg. In fact in the limitg≫1 one expects that\(\left\langle {\hat n} \right\rangle \approx n_x \) for arbitraryU even atT=0