.. _sphx_glr_api_gallery_superconductivity:

Superconductivity
-----------------

Superconductors in the Bogoliubov-de Gennes formalism: particle-hole
symmetric spectra and Andreev bound states in junctions, and the
Majorana zero modes at the ends of Kitaev's p-wave chain, with its
Pfaffian bulk invariant, the Majorana number, and of a Rashba nanowire
in a Zeeman field. The self-consistent BCS gap equation in real space,
with its universal ratio Delta(0)/T_c = 1.764 and the proximity effect.
Andreev reflection at a normal-superconductor junction and the BTK
conductance, from the scattering matrix resolved into electrons and
holes.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="An electron from a normal metal, with an energy inside the superconducting gap \Delta, cannot enter the superconductor alone. Andreev (1964) showed that it is retro-reflected as a hole while a Cooper pair enters the condensate, which carries a charge 2e across the interface. Blonder, Tinkham and Klapwijk (BTK, 1982) turned this into the conductance of a normal-superconductor (NS) junction with a barrier of strength Z,">

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  .. image:: /api/gallery/superconductivity/images/thumb/sphx_glr_plot_andreev_reflection_thumb.png
    :alt:

  :doc:`/api/gallery/superconductivity/plot_andreev_reflection`

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      <div class="sphx-glr-thumbnail-title">Andreev Reflection: the BTK Conductance of a Normal-Superconductor Junction</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="J. Bardeen, L. Cooper and J. R. Schrieffer (1957) explained superconductivity by the pairing of electrons with opposite momenta and spins into a condensate, whose gap \Delta solves the self-consistent gap equation">

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  .. image:: /api/gallery/superconductivity/images/thumb/sphx_glr_plot_bcs_gap_equation_thumb.png
    :alt:

  :doc:`/api/gallery/superconductivity/plot_bcs_gap_equation`

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      <div class="sphx-glr-thumbnail-title">The BCS Gap Equation: Delta(T) and the Universal Ratio Delta(0)/T_c = 1.764</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="P.-G. de Gennes (1966) wrote the BCS mean field site by site: a quasiparticle is a two-component wave function (u_i, v_i), an electron and a hole, solving">

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  .. image:: /api/gallery/superconductivity/images/thumb/sphx_glr_plot_bogoliubov_de_gennes_equations_thumb.png
    :alt:

  :doc:`/api/gallery/superconductivity/plot_bogoliubov_de_gennes_equations`

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      <div class="sphx-glr-thumbnail-title">The Bogoliubov-de Gennes Equations: Andreev Bound States</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A. Kitaev (2001) wrote down the simplest topological superconductor: a chain of spinless fermions with nearest-neighbour hopping t and p-wave pairing \Delta,">

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  .. image:: /api/gallery/superconductivity/images/thumb/sphx_glr_plot_kitaev_chain_thumb.png
    :alt:

  :doc:`/api/gallery/superconductivity/plot_kitaev_chain`

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      <div class="sphx-glr-thumbnail-title">The Kitaev Chain: Majorana Zero Modes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Kitaev&#x27;s chain needs spinless fermions with p-wave pairing, which no material offers. In 2010 R. Lutchyn, J. Sau and S. Das Sarma, and independently Y. Oreg, G. Refael and F. von Oppen, built one from ordinary parts: a semiconductor nanowire with strong Rashba spin-orbit coupling \alpha, a Zeeman field V_Z perpendicular to the spin-orbit field, and s-wave pairing \Delta induced by a superconductor nearby,">

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  .. image:: /api/gallery/superconductivity/images/thumb/sphx_glr_plot_majorana_nanowire_thumb.png
    :alt:

  :doc:`/api/gallery/superconductivity/plot_majorana_nanowire`

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      <div class="sphx-glr-thumbnail-title">Majorana Nanowires: Rashba, Zeeman and s-Wave Pairing</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/superconductivity/plot_andreev_reflection
   /api/gallery/superconductivity/plot_bcs_gap_equation
   /api/gallery/superconductivity/plot_bogoliubov_de_gennes_equations
   /api/gallery/superconductivity/plot_kitaev_chain
   /api/gallery/superconductivity/plot_majorana_nanowire