Charging effects and Andreev reflection in a double-junction circuit: A model approach combining rate equations and Green’s functions

Schröter, Ursula; Scheer, Elke

doi:10.1103/physrevb.74.245301

Cited by 6 publications

(54 citation statements)

References 30 publications

(43 reference statements)

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“…Some care must be taken which one the argument ω refers to [11], but here this issue shall be restricted to the remark that making the argument the same for all T-functions in (25) is of advantage. Exploiting complex conjugate relations can save some effort in providing them [12]. Now using (24), (22) and (28) in (27) produces …”

Section: Calculating the T-functionmentioning

confidence: 99%

“…We assume a sufficiently small island between the two junctions, such that coherence can be maintained in transport across it, but large enough and bulk-like, such that a few excess charges do not alter the BCS density of states or the occupation given by the Fermi function. To actually calculate current-voltage characteristics, with the interest in whether Coulomb blockade suppresses MAR, the island's Fermi energy level needs to be changed with island charging as is done in [10,12]. However, in order to discuss unadulteratedly the recipe to establish the transfer Green's function, the island shall here be assumed to stay at fixed potential.…”

Section: Double Junction and Difficulties Getting Tmentioning

confidence: 99%

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Transfer Green's functions in two-fold interaction systems

Schröter

Scheer²

2008

J. Phys. A: Math. Theor.

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For systems governed by two kinds of interactions it is shown that these can be built successively into the Green's functions describing the system's response. Whereas for the ordinary Green's function the Dyson equation to solve has the same form in each step, we derive the non-trivial second-step equation for the transfer or coupling function, which on the one hand is closely related to the self-energy and on the other hand of practical relevance in transport calculations.

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Section: Calculating the T-functionmentioning

confidence: 99%

Section: Double Junction and Difficulties Getting Tmentioning

confidence: 99%

Transfer Green's functions in two-fold interaction systems

Schröter

Scheer²

2008

J. Phys. A: Math. Theor.

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“…After (6), σ I R + σ I R g RR T RR , however, to be contracted into T I R misses the term σ I L g LL T LR . This is therefore added and subtracted, and σ I L of the subtracted again brought to the end, where T RI g I I σ I L then simplifies to T RL (see also figure 2 (11) We now explain why (10) and similar expressions give the transport rates we need and how these get used in a master equation. Even with coherent transport through both junctions, the current (we skip factor e for unit charge) when evaluated as seen from the left side…”

Section: Charging Ratesmentioning

confidence: 99%

“…There are no additional terms like σ LI σ I R G +− RL , although G +− RL exists. Nevertheless, in contrast to the incoherent model [10] interaction to the Rreservoir is now contained in…”

Section: Charging Ratesmentioning

confidence: 99%

“…Here, with in order to model coherent interaction between the left and right junctions considering the whole system in the quantum-mechanical ansatz (1), (13) comes as a direct result of Ehrenfest's theorem. In the incoherent model [10] adding charging rates from both junctions for the island is done as part of setting up a classical rate equation. The result is formally identical to (13), the G +− however stemming from solving respective 2×2 Dyson equations for each junction separately.…”

Section: Charging Ratesmentioning

confidence: 99%

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Destructive interference in transfer rates by coherent coupling to a remote reservoir

Schröter¹,

Scheer²

2008

J. Phys. A: Math. Theor.

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Transport through two point-contacts in series, even with arbitrarily high transmissions, can be modeled with rate equations if the rates are deduced from the quantum mechanical current formula, which thus accounts for interferences on the wavefunction level. An expression using Green's functions giving the current through a single contact is valid for evaluating the charging rates of the enclosed island in the double-junction system, even in the case of coherent coupling all over the island from lead to lead. We demonstrate that these current rates for each junction can be rewritten as 2-products of the so-called transfer Green functions, maintaining formal analogy to the single-junction case. On the one hand this facilitates numerical calculations. On the other hand, the form of the rate terms reveals how besides direct coupling across one junction effective coupling between the involved and the remote lead contributes to transfers across the regarded junction and how coherent loss from the island across the other junction diminishes the rate. It is further explained that for the double junction in the case of coherent coupling between both contacts direct lead-to-lead transport adds current contributions; however, interferences are expected to reduce the net current as compared to incoherent mutual influence via the island charging only. Crossed Andreev reflection in the superconducting state-within the premises of our model-cannot surpass other transport processes such as to cause extra steps in current-voltage curves or negative differential conductance.

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Modelling partially coherent transport across an island - multiple Andreev reflection and charging effects

Schröter¹,

Scheer²

2009

J. Phys.: Conf. Ser.

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A Green's functions technique known to describe transport through a superconducting point contact with multiple Andreev reflection is merged with a rate equation scheme and thus extended to model transport through a series of two junctions enclosing an island between them. In the superconducting state such systems may show an interplay of multiple Andreev reflection and Coulomb blockade. Although not of unique shape calculated current-voltage characteristics exhibit more or less pronounced steps that can be associated to transport processes setting in because of the applied voltage becoming sufficient to overcome certain fractions of the superconductor gap or providing the required charging energy. The speciality of our model, however, lies in regarding all single-charge transfers out of every-order multiple reflection simultaneously instead of adding total rates for processes up to some order. The algorithm can treat series of junctions that are just incoherently coupled via the electrostatic charge on the island as well as transport maintaining coherence across the island. In the latter case we find direct lead-to-lead transport, but interestingly, Coulomb blockade never completely vanishes in our model. In principle, the scheme is also applicable to a mixed situation where interaction between the junctions is partly coherent and partly incoherent.

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Charging effects and Andreev reflection in a double-junction circuit: A model approach combining rate equations and Green’s functions

Cited by 6 publications

References 30 publications

Transfer Green's functions in two-fold interaction systems

Transfer Green's functions in two-fold interaction systems

Destructive interference in transfer rates by coherent coupling to a remote reservoir

Modelling partially coherent transport across an island - multiple Andreev reflection and charging effects

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