Master-equation approach to macroscopic quantum tunneling of charge in ultrasmall single-electron-tunneling double junctions

It is known that classical Coulomb blockade effects of single-electron-tunneling (SET) devices are disturbed by higher-order tunneling effects denoted as macroscopic quantum tunneling of charge (q-MQT) or cotunneling. Starting from the von Neumann equation, a master-equation approximation of cotunneling is given for ultrasmall SET double junctions in the limit T=0. The influence of an external electromagnetic environment modeled by an additional impedance in the circuit is studied both in the low-impedance and high-impedance limits. General tunneling channels described by quasiparticle current amplitudes ImIq({ω}) are considered just as the Ohmic approximation which leads to some known results. The rates of cotunneling show in the high-impedance case the effect of a ``quantum'' Coulomb blockade. By regularizing the logarithmic singularities in the quantum rates using linewidth effects, the master-equation description (Markov property) is complete in the sense of the tunneling theory up to fourth order.