Focused crossed Andreev reflection

Haugen, Håvard Jostein; Brataas, Arne; Waintal, Xavier; Bauer, G.

doi:10.1209/0295-5075/93/67005

Cited by 3 publications

(2 citation statements)

References 34 publications

(114 reference statements)

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“…Recently, the effects of disorder [3] and spin-orbit interaction [4][5][6][7][8] were investigated and focusing experiments in graphene were performed [9]. It was also discussed to study by coherent electron focusing the structure of graphene edges [10] as well as Andreev reflections in normal-superconductor systems [11][12][13]. Moreover, a 2DEG in a strong magnetic field shows the quantum Hall effect, which is explained by the transport through edge channels straight along the boundary of the system [14].…”

Section: Introductionmentioning

confidence: 99%

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

2013

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We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field B onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized four-point Hall resistance R x y as a function of B. In weak fields, R x y shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, R x y shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in B (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in R x y . In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust.

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Section: Introductionmentioning

confidence: 99%

Magnetotransport along a boundary: from coherent electron focusing to edge channel transport

2013

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“…Several schemes have been developed to make the recursive Green's function method suitable for multi-terminal systems. These include: An optimal block-tridiagonalization scheme [3,4], a scheme utilizing the reverse Cuthill-McKee algorithm for connected graphs [5], a decimation method [6,7], a circular slicing scheme for a simple four-terminal cross [8,9], and a "knitting" algorithm [10]; of which, the knitting algorithm has been particularly popular in the research community [11,12,13]. Our focus, however, will be on the circular slicing scheme.…”

Section: Introductionmentioning

confidence: 99%

Recursive Greenʼs function method for multi-terminal nanostructures

Thorgilsson

Viktorsson

Erlingsson

2014

Journal of Computational Physics

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We present and review an efficient method to calculate the retarded Green's function in multi-terminal nanostructures; which is needed in order to calculate the conductance through the system and the local particle densities within it. The method uses the recursive Green's function method after the discretized Hamilton matrix has been properly partitioned. We show that this method, the circular slicing scheme, can be modified to accommodate multi-terminal systems as well as the traditional two-terminal systems. Furthermore, we show that the performance and robustness of the circular slicing scheme is on par with other advanced methods and is well suited for large variety of multi-terminal geometries. We end by giving an example of how the method can be used to calculate transport in a non-trivial multi-terminal geometry.

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