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Superconductivity is the transmission of current with no resistive losses, and is one of the most active areas of condensed matter physics research.

1 vote
1 answer
283 views

Eigenvectors of the BCS Hamiltonian

In introductory superconductivity one often studies the BCS Hamiltonian $$H= \begin{pmatrix} \xi & -\Delta \\ -\Delta & -\xi \end{pmatrix} $$ I can find the Eigenvalues and Eigenvectors by writing …
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4 votes
0 answers
82 views

Is there a violation in the Onsager-Kelvin relation in Normal metal - superconductor junctions?

I'm currently reading the paper https://journals.aps.org/prb/pdf/10.1103/PhysRevB.48.15198 It is about charge $I$ and heat $I_H$ currents in NS junctions due to temperature $(\Delta T)$ and voltage $ …
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0 votes
0 answers
309 views

Deriving Continuum BdG equation from Tight-Binding model for Graphene-Superconductor interface

Background My question concerns Beenakker's paper on "Specular Andreev Reflection in Graphene": cond-mat/0604594 (arxiv)/Phys.Rev.Lett. 97, 067007 (The same topic is also discussed in Rev. Mod. Phys. …
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Why is Andreev reflection in a NS junction retroreflective?

Solution The solution is actually quite simple. Let us for simplicity consider two dimensions $(x,y)$. The electron and hole dispersions are \begin{equation} \mathbf{k}^2 = \frac{2m}{\hbar}\left(\mu + …
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1 vote
1 answer
248 views

Why is Andreev reflection in a NS junction retroreflective?

Background Consider a normal metal (N) - superconductor (S) junction. Assume N is in the region $x<0$ and S is in the region $x>0$. In addition, let us assume that the system is invariant in the $y$ a …
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0 votes
1 answer
690 views

Electron and holes in tight binding Hamiltonian on two sublattices

Background Say that I have a tight binding Hamiltonian (with spinless fermions) of the form $$H = - 2t \sum_{ij} (c_i^{\dagger} c_j + h.c) - 2\mu \sum_i c^{\dagger}_i c_i$$ where we only sum over nea …
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