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Conductance of a Finite Kitaev Chain
Mesoscale and Nanoscale Physics · Submitted 21 Aug 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We study the dependence of the conductance on the number of sites in the chain and find that only for sufficiently long chains and in the regime that the chain is a topological superconducter the conductance at both ends tends to the universal value $2e^2/h$, as expected on the basis of the contact resistance of a single conducting channel provided by the Majorana zero mode.
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The abstract, sentence by sentence
We present a stochastic formulation of the Keldysh theory to calculate the conductance of a finite Kitaev chain coupled to two electron reservoirs. We study the dependence of the conductance on the number of sites in the chain and find that only for sufficiently long chains and in the regime that the chain is a topological superconducter the conductance at both ends tends to the universal value $2e^2/h$, as expected on the basis of the contact resistance of a single conducting channel provided by the Majorana zero mode. In this topologically nontrivial case we find an exponential decay of the current inside the chain and a simple analytical expression for the decay length. Finally, we also study the differential conductance at nonzero bias and the full current-voltage curves. We find a nonmonotonic behavior of the maximal current through the Kitaev chain as a function of the coupling strength with the reservoirs.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a stochastic formulation of the Keldysh theory to calculate the conductance of a finite Kitaev chain coupled to two electron reservoirs. | method 0.68 | 0.93 | 0.05 | asserted 0.96 |
| s1 | We study the dependence of the conductance on the number of sites in the chain and find that only for sufficiently long chains and in the regime that the chain is a topological superconducter the conductance at both ends tends to the universal value $2e^2/h$, as expected on the basis of the contact resistance of a single conducting channel provided by the Majorana zero mode. | result 0.96 | 0.94 | 0.76 | asserted 1.00 |
| s2 | In this topologically nontrivial case we find an exponential decay of the current inside the chain and a simple analytical expression for the decay length. | result 1.00 | 0.96 | 0.13 | asserted 1.00 |
| s3 | Finally, we also study the differential conductance at nonzero bias and the full current-voltage curves. | contribution 0.99 | 0.90 | 0.04 | asserted 0.75 |
| s4 | We find a nonmonotonic behavior of the maximal current through the Kitaev chain as a function of the coupling strength with the reservoirs. | result 1.00 | 0.96 | 0.10 | asserted 1.00 |
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The paper
Original abstract
We present a stochastic formulation of the Keldysh theory to calculate the conductance of a finite Kitaev chain coupled to two electron reservoirs. We study the dependence of the conductance on the number of sites in the chain and find that only for sufficiently long chains and in the regime that the chain is a topological superconducter the conductance at both ends tends to the universal value $2e^2/h$, as expected on the basis of the contact resistance of a single conducting channel provided by the Majorana zero mode. In this topologically nontrivial case we find an exponential decay of the current inside the chain and a simple analytical expression for the decay length. Finally, we also study the differential conductance at nonzero bias and the full current-voltage curves. We find a nonmonotonic behavior of the maximal current through the Kitaev chain as a function of the coupling strength with the reservoirs.
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What this paper does with the arXiv papers it cites
Papers whose main result relates to this one's
States a conflicting result 1 paper
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We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of $e^2/h$ (for symmetric coupling to the leads),which is a half of the popular result of the zero-bias-peak, or, the so-called Majorana quantized conductance ($2e^2/h$).
What it cites
Cites as background 2 papers
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Note that we do not explicitly consider the effect of disorder, which is for instance the topic of recent work in Refs. [ref] .
Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains · Introduction · 0.96
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Note that we do not explicitly consider the effect of disorder, which is for instance the topic of recent work in Refs. [ref] .
Tunneling transport in NSN junctions made of Majorana nanowires across the topological quantum phase transition · Introduction · 0.96
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