Strong Electron Tunneling through Mesoscopic Metallic Grains

Abstract

We describe electron transport through small metallic grains with Coulomb blockade effects beyond the perturbative regime. For this purpose we study the real-time evolution of the reduced density matrix of the system. In the first part of the paper we present a diagrammatic expansion for not too high junction conductance, $h/4\pi^2e^2 R_t \lesssim 1$, in a basis of charge states. Quantum fluctuations renormalize system parameters and lead to finite lifetime broadening in the gate-voltage dependent differential conductance. We derive analytic results for the spectral density and the conductance in the limit where only two charge states play a role. In the second part of the paper we consider junctions with large conductance, $h/4e^2 R_t \gtrsim 1$. In this case contributions from all charge states, which broaden and overlap, become important. We analyze the problem in a quasiclassical approximation. The two complementary approaches cover the essential features of electron tunneling for all parameters.