.. _sphx_glr_api_gallery_tight_binding:

Tight-Binding
-------------

The generic real-space and reciprocal-space machinery: the square
lattice, whose single band is simple enough to check by hand, as the
smallest complete illustration of Bloch's theorem; a graphene flake
diagonalized directly and its Bloch band structure along a k-path,
including Wallace's 1947 linear (Dirac) dispersion near the K point;
and :class:`tbkit.plot.Plot`'s lattice, spectrum, density-of-states, and
eigenstate-intensity plots.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A from-scratch walkthrough of tbkit&#x27;s two complementary ways of looking at a Tight-Binding model:">

.. only:: html

  .. image:: /api/gallery/tight_binding/images/thumb/sphx_glr_plot_graphene_bands_thumb.png
    :alt:

  :doc:`/api/gallery/tight_binding/plot_graphene_bands`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Graphene: Real-Space Flake and Reciprocal-Space Bands</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The smallest complete illustration of Bloch&#x27;s theorem: one orbital per unit cell on a square lattice, nearest-neighbor hopping only. With a single orbital the Bloch Hamiltonian H(\mathbf{k}) is a 1\times1 matrix, so &quot;diagonalizing&quot; it is nothing but reading it off, and the whole band structure is one closed-form expression,">

.. only:: html

  .. image:: /api/gallery/tight_binding/images/thumb/sphx_glr_plot_square_lattice_bands_thumb.png
    :alt:

  :doc:`/api/gallery/tight_binding/plot_square_lattice_bands`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Square Lattice: Bloch's Theorem in its Simplest Form</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Every other example in this gallery reaches straight for matplotlib to plot a spectrum or a band structure by hand. tbkit.plot.Plot instead wraps the handful of plots that come up for any real-space model, directly from a System instance: the lattice itself (with or without its hoppings drawn on), the spectrum (optionally colored by sublattice polarization), the density of states, and an eigenstate&#x27;s spatial intensity.">

.. only:: html

  .. image:: /api/gallery/tight_binding/images/thumb/sphx_glr_plot_visualizing_a_model_thumb.png
    :alt:

  :doc:`/api/gallery/tight_binding/plot_visualizing_a_model`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Visualizing a Model: tbkit.plot.Plot</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/tight_binding/plot_graphene_bands
   /api/gallery/tight_binding/plot_square_lattice_bands
   /api/gallery/tight_binding/plot_visualizing_a_model