QUANTUM FLUCTUATIONS IN A SINGLE-ELECTRON BOX

Recent experiments have demonstrated that the number n of additional e lectrons on a small metallic island is a staircase function of a conti nuous external charge n(x) for temperatures T small compared to the si ngle electron charging energy U. We show that the finite conductance g of the tunnel barrier connecting the island to the external gate give s rise to quantum fluctuations in n which lead to a smearing of the st aircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductance g much less th an 1 the slope partial derivative(n)/partial derivative n(x) at the tu rning point between two plateaus saturates at a finite value of order l/g as T-->O instead of diverging like U/T as predicted with thermal f luctuations only. The experimentally observed broadening however is st ill much larger which is probably due to extrinsic effects.