Time-dependent currents of a single-electron transistor in dissipative environments

Abstract

Currents of the single-electron transistors driven by time-dependent fields via external dissipative circuits are investigated theoretically. By expressing the external circuit in terms of driven harmonic oscillators and using the reduced-density operator method, we derive time-and environmentdependent tunneling rates in the regime of sequential tunneling and present expressions for both displacement and tunneling currents with these tunneling rates. It is found that the dissipative environments affect tunneling currents in two ways; the determination of driving voltages at tunneling junctions and the depletion of particle-hole distribution functions. Considering a simple dissipative circuit, we discuss the effects of the environment on tunneling currents in both static and time-dependent cases.

Green's function approach to transport through a gate-all-around Si nanowire under impurity scattering

“…This type of the reduction for the transmission coefficient is also encountered in problems of tunneling in dissipative environments. [18,19] According to the theories, when environments of the device become more dissipative, carriers are harder to tunnel the barriers because more energies should be transferred to the environment.…”

Current and noise expressions for radio-frequency single-electron transistors

“…[23]. Then, the total Hamiltonian may be written as the sum of the unperturbed part and the tunneling part H ′ T ;…”

“…In thermal equilibrium, the timecorrelation functions are easily evaluated by exploiting the fluctuation-dissipation theorem, and results are, [3,23] (19) where Z ℓℓ ′ (ω) is related to each component of the impedance matrix Z(ω) in such a way of Z DD = Z 11 , Z DS = Z 12 , etc.…”

“…Our work is a generalization of several earlier works which address the effects partially, neglecting time-dependent perturbation, [10] higher-order co-tunneling, [21,23] and electron-electron interaction. [27,28] However, since we use a two-chargedstate model in a metallic island assuming large charging energy, along this aspect, our work is more restricted than Ref.…”

“…In the classical regime (or adiabatic regime) energies excited by timedependent perturbation appear to be continuous while in the quantum regime (we will also refer to this as nonadiabatic regime) discrete photon energies become observable and particles can emit or absorb photons when they tunnel from an initial state on one side of the barrier to a final state on the opposite side, called as photonassisted tunneling. [20,21,22,23] So, in order to understand transport properties of rf SETs, one may need generic theoretical considerations including higher-order co-tunneling processes as well as sequential tunneling, even in the quantum regime of timedependent perturbations. Actually, according to the recent experiments of rf SETs, [13,15,16,17,18] tunneling resistances range from α 0 = 10 −5 to 3 × 10 −2 , implying feasible co-tunneling processes for large values of α 0 .…”