.. _sphx_glr_api_gallery_optics:

Optics
------

Linear and nonlinear optical response of Bloch bands: the Kubo-Greenwood
optical conductivity and the universal absorption of graphene, the Berry
curvature dipole behind the nonlinear Hall effect, and the shift current
of the bulk photovoltaic effect.


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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="A crystal without an inversion centre can turn light into a DC current with no junction: the bulk photovoltaic effect, seen in ferroelectrics since the 1970s (Glass, von der Linde and Negran 1974). Baltz and Kraut (1981), then Sipe and Shkrebtii (2000), traced its main part to a purely quantum-geometric mechanism: when light excites an electron from band n to band m, the electron&#x27;s centre of charge moves by the shift vector">

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  .. image:: /api/gallery/optics/images/thumb/sphx_glr_plot_bulk_photovoltaic_shift_current_thumb.png
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  :doc:`/api/gallery/optics/plot_bulk_photovoltaic_shift_current`

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      <div class="sphx-glr-thumbnail-title">The Bulk Photovoltaic Effect: the Shift Current of Gapped Graphene</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In 2008 Nair et al. held a suspended graphene membrane in front of a light source and found that one atomic layer absorbs \pi\alpha \approx 2.3\% of white light, with \alpha = e^2/4\pi\varepsilon_0\hbar c the fine-structure constant: no material parameter enters. The reason is graphene&#x27;s optical conductivity. Its massless Dirac electrons absorb at \hbar\omega through vertical transitions from -\hbar\omega/2 to +\hbar\omega/2, and the growing number of those transitions exactly compensates their weakening matrix elements, so">

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  .. image:: /api/gallery/optics/images/thumb/sphx_glr_plot_graphene_universal_absorption_thumb.png
    :alt:

  :doc:`/api/gallery/optics/plot_graphene_universal_absorption`

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      <div class="sphx-glr-thumbnail-title">The Universal Absorption of Graphene: Opacity Defined by the Fine-Structure Constant</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A linear Hall response needs broken time-reversal symmetry: the Berry curvature \Omega(\mathbf{k}) is odd in \mathbf{k} and its integral over the occupied states vanishes. Sodemann and Fu (2015) noticed that its first moment need not vanish. In a DC field (or at frequency \omega), the shifted Fermi sea carries the Hall current">

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  .. image:: /api/gallery/optics/images/thumb/sphx_glr_plot_nonlinear_hall_berry_curvature_dipole_thumb.png
    :alt:

  :doc:`/api/gallery/optics/plot_nonlinear_hall_berry_curvature_dipole`

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      <div class="sphx-glr-thumbnail-title">The Nonlinear Hall Effect: the Berry Curvature Dipole of a Tilted Dirac Cone</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/optics/plot_bulk_photovoltaic_shift_current
   /api/gallery/optics/plot_graphene_universal_absorption
   /api/gallery/optics/plot_nonlinear_hall_berry_curvature_dipole