.. _sphx_glr_api_gallery_three_dimensions:

Three dimensions
----------------

Lattices in 3D space: the Anderson metal-insulator transition, which
exists only in three dimensions, and Weyl semimetals, whose band
touchings (located, with their chiralities, by a Weyl point finder) are
monopoles of Berry curvature with Fermi-arc surface states.


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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="Abrahams, Anderson, Licciardello and Ramakrishnan (1979) argued that the conductance of a disordered sample flows, as its size L grows, according to a single scaling function of the conductance itself. The consequence: in one and two dimensions every state is localized by any disorder, but in three dimensions a genuine metal-insulator transition survives, at a critical disorder -- W_c \approx 16.5\,t for the Anderson model on the cubic lattice, with onsite energies uniform in [-W/2, W/2].">

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  .. image:: /api/gallery/three_dimensions/images/thumb/sphx_glr_plot_anderson_transition_thumb.png
    :alt:

  :doc:`/api/gallery/three_dimensions/plot_anderson_transition`

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      <div class="sphx-glr-thumbnail-title">The Scaling Theory of Localization: the 3D Anderson Transition</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A 3D band touching where two bands meet linearly in every direction, H \approx \mathbf{v}\cdot\mathbf{q}\,\boldsymbol\sigma, is a Weyl point: a source or sink of Berry curvature, of charge \pm1. Wan, Turner, Vishwanath and Savrasov (2011) predicted Weyl semimetals in real materials, and in 2015 Xu et al. and Lv et al. observed them in TaAs by photoemission -- through their unmistakable surface signature, open Fermi arcs.">

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  .. image:: /api/gallery/three_dimensions/images/thumb/sphx_glr_plot_weyl_semimetal_thumb.png
    :alt:

  :doc:`/api/gallery/three_dimensions/plot_weyl_semimetal`

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      <div class="sphx-glr-thumbnail-title">Weyl Semimetals: Monopoles of Berry Curvature and Fermi Arcs</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/three_dimensions/plot_anderson_transition
   /api/gallery/three_dimensions/plot_weyl_semimetal