Transport in metallic multi-island Coulomb blockade systems: A systematic perturbative expansion in the junction transparency

Abstract

We study electronic transport through metallic multi-island Coulomb-blockade systems. Based on a diagrammatic real-time approach, we develop a computer algorithm that generates and calculates all transport contributions up to second order in the tunnel-coupling strengths for arbitrary multi-island systems. This comprises sequential and cotunneling, as well as terms corresponding to a renormalization of charging energies and tunneling conductances. Multi-island cotunneling processes with energy transfer between different island are taken into account. To illustrate our approach we analyze the current through an island in Coulomb blockade, that is electrostatically coupled to a second island through which a large current is flowing. In this regime both cotunneling processes involving one island only as well as multi-island processes are important. The latter can be understood as photon-assisted sequential tunneling in the blockaded island, where the photons are provided by potential fluctuations due to sequential tunneling in the second island. We compare results of our approach to a P(E)-theory for photon-assisted tunneling in the weak coupling limit.

Quantum-fluctuation effects on the thermopower of a single-electron transistor

“…10 For a quantitative analysis of these quantum-fluctuation effects, a systematic second-order perturbation expansion within a diagrammatic real-time technique has been performed 11,12 and used to study different singleelectron systems. 13,14,15 In particular, a logarithmic reduction ∼ α 0 ln β E C of the maximum conductance, indicating a renormalization of the tunnel conductance, has been found, in quantitative agreement with experimental observations. 16,17 In electron transport, the transfer of charge and heat are connected to each other.…”

Effect of decoherence on resonant Cooper-pair tunneling in a voltage-biased single-Cooper-pair transistor

“…Here we give rules for calculating the generalized transition rates between the SCPT's density matrix entries due to the coupling with the EE or CF. The derivation of the diagram rules is based on a series expansion of the system's time evolution operator in the interaction picture 18,32,33 . We also analyze the renormalization, translation invariance and validity of the higher-order calculation.…”

“…These decoherence sources are accompanied by quasiparticle tunneling across the JJs. We include the interaction with the relevant baths by using a real-time Keldysh diagrammatic technique 18,32,33 . This leads to a master equation for the SCPT's density matrix as the environment is traced out of the equations by using the assumption of unperturbed reservoirs.…”

Transport Out of Locally Broken Detailed Balance

“…A physical mesoscopic blowtorch can be defined that modulates the temperature of the system locally. This can be done either by introducing time dependent drivings [40,41,42], or by using either on-chip refrigerators [43,44,45,46,47,48] or the noise generated in a coupled conductor [49,29]. In the first case, the frequency of the driving must be much larger than the energy relaxation rate such that electrons have an increased effective temperature in the island.…”