.. _sphx_glr_api_gallery_condensed_transport:

Electronic transport
--------------------

Drude's classical electron gas (DC and AC conductivity, the Hall effect)
and the Boltzmann equation with Fermi-Dirac statistics that corrected it
(the Wiedemann-Franz law and the thermopower of a degenerate metal).


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Three years after the discovery of the electron, Paul Drude (1900) treated the electrons of a metal as a classical gas, accelerated by fields and randomized by collisions every \tau on average. This gives Ohm&#x27;s law with \sigma_0 = nq^2\tau/m (~physicskit.condensed.transport.drude_conductivity), a Lorentzian AC response (~physicskit.condensed.transport.drude_ac_conductivity), and, in a magnetic field, a Hall resistivity \rho_{yx} = B/(nq) with no magnetoresistance (~physicskit.condensed.transport.drude_conductivity_tensor).">

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  .. image:: /api/gallery/condensed/transport/images/thumb/sphx_glr_plot_drude_model_thumb.png
    :alt:

  :doc:`/api/gallery/condensed/transport/plot_drude_model`

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      <div class="sphx-glr-thumbnail-title">The Drude model: conductivity and the Hall effect</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Drude&#x27;s classical gas got the conductivity right but the electronic heat capacity and thermopower wrong by factors of order k_BT/E_F. Sommerfeld (1927-1928) kept the kinetic picture but used Fermi-Dirac statistics. Only electrons within k_BT of the Fermi energy carry current or heat. The Boltzmann equation in the relaxation-time approximation (~physicskit.condensed.transport.boltzmann_transport) then gives, for any band, the Wiedemann-Franz law \kappa/\sigma T = \pi^2/3 (k_B = e = 1) and Mott&#x27;s formula for the Seebeck coefficient. This example checks both on a 2D tight-binding band sampled on a k-grid.">

.. only:: html

  .. image:: /api/gallery/condensed/transport/images/thumb/sphx_glr_plot_sommerfeld_boltzmann_transport_thumb.png
    :alt:

  :doc:`/api/gallery/condensed/transport/plot_sommerfeld_boltzmann_transport`

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      <div class="sphx-glr-thumbnail-title">Sommerfeld's electron gas: the Wiedemann-Franz law and thermopower</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/condensed/transport/plot_drude_model
   /api/gallery/condensed/transport/plot_sommerfeld_boltzmann_transport