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Transport through two coupled, one-dimensional quantum wires
Katharina Eissing (LMU)
25.10.2012 at 12:30
When edge channels in a Quantum Point Contact in the Quantum Hall Regime are brought controllably together and are allowed to mix, one could observe an unexpected plateau in longitudinal resistance at 0.5 h/e^2. It is argued that this indicates that half of the current is backscattered while half is transmitted [1].
In order to explain this, Altland et al. [2] considered a system consisting of two luttinger liquids which are interacting over an extended scattering region and showed a conductance of G=1/2 e^2/h for this configuration. They conlude that their system becomes a (½, ½ ) beam splitter.
Motivated by these works, we try to find a model for this system that can be treated with functional Renormalization Group. We consider two configurations of two one-dimensional quantum wires modeled by tight-binding chains, which are coupled to each other over a certain region. The first system consists of two semi-infinite chains, whereas the second of two infinitely long chains. Using fRG1 we numerically compute the conductance.
In my talk, I'll motivate our work by shortly introducing those two papers, will give a brief diagrammatical derivation to the fRG equations and will explain our models and first results.
[1] Nakaharai et al., Phys Rev Lett 107, 036602 (2011)
[2] Atland et al., Phys Rev Lett 108,136401 (2012)
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