Quasiclassical theory for the superconducting proximity effect in Dirac materials

We derive the quasiclassical nonequilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking p·σ¯, as relevant for topological insulators. We discuss in detail several of the key te...

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Bibliographic Details
Published in:Physical review. B 2017-06, Vol.95 (23), Article 235403
Main Authors: Hugdal, Henning G., Linder, Jacob, Jacobsen, Sol H.
Format: Article
Language:English
Subjects:
Bilayers
Charge density
Dependence
Electron spin
Equilibrium equations
Exchanging
Fermi surfaces
Josephson junctions
Mathematical analysis
Parameterization
Proximity effect (electricity)
Quantum theory
Resistance
Superconductivity
Topological insulators
Transport
Wave attenuation
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Summary:We derive the quasiclassical nonequilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking p·σ¯, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wave function inside the F. Fields parallel to the transport direction lead to phase shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias and determine the dependence on the length of the N and F regions and the exchange field.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.95.235403