.. _sphx_glr_api_gallery_higher_order:

Higher-Order Topology
---------------------

Topological phases beyond dipoles: Wannier sectors, nested Wilson loops,
the quantized quadrupole moment of the Benalcazar-Bernevig-Hughes model,
and the zero-energy corner states and fractional corner charges it binds.


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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="In 2017 W. Benalcazar, B. A. Bernevig and T. L. Hughes showed that a crystal can carry a quantized electric quadrupole moment while having no dipole moment at all. Their model (BBH) has four orbitals per square cell, intra-cell hoppings \gamma, inter-cell hoppings \lambda, and a \pi flux through every plaquette. For |\gamma| &lt; |\lambda|:">

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  .. image:: /api/gallery/higher_order/images/thumb/sphx_glr_plot_quadrupole_insulator_thumb.png
    :alt:

  :doc:`/api/gallery/higher_order/plot_quadrupole_insulator`

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      <div class="sphx-glr-thumbnail-title">Quantized Electric Quadrupole Insulators: the Benalcazar-Bernevig-Hughes Model</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/higher_order/plot_quadrupole_insulator