:orphan:

.. status publishable
.. product Fermi Surface
.. sectionauthor Volker
.. SME Volker
.. PR Mikael
.. TW Ken
.. date 2018

.. keywords: Fermi surface

.. _FermiDTS:

|medea| *Fermi Surface* - Living on the Edge
--------------------------------------------

.. admonition:: **At-a-Glance**

   |medea|\ :sup:`®`\ [#TM]_ *Fermi Surface* displays isosurfaces
   of electronic energies of metals, semiconductors, and insulators
   in k-space, and lists the effective masses of all bands at
   arbitrary k-points.

   **Key Benefits**

   * Straightforward setup of the calculation
   * Automated distribution over a large number of tasks enables quick
     calculation
   * Easy selection of isosurface energy and isosurface sheets for display
   * Access to effective masses of all bands at any k-point


Allan Mackintosh's suggestion to define a metal as 'a solid with a Fermi
surface' underlines the importance of this quantity for a deeper
understanding of materials’ properties [#Mackintosh]_. It reflects
the outstanding contribution electrons at (and within an energy range of
k\ :sub:`B`\ T of) the Fermi surface make to a materials transport
properties. In addition, the Fermi surface plays a paramount role
in determining electronic system’s response to external
perturbations and in indicating instabilities arising from interaction
with the electrons' spins or the vibrational degrees of freedom.

|medea| *Fermi Surface* thus provides ample insight into the 'life on the
edge' [#Dugdale]_. Since this 'edge' can be shifted, even the isosurfaces
at the full spectrum of metals and semiconductors are accessible with
|medea| *Fermi Surface*.

As a simple example, the Fermi surface of Cu as shown in the below figure closely
resembles the perfect spherical Fermi surface of a free electron band,
but shows distinct deviations in the form of necks opening along the
<111> directions. This is due to band distortions at the Brillouin-zone boundaries,
caused by the real crystal potential. In general, calculated Fermi surfaces
have a very high predictive power, and while confirming experimentally
determined Fermi surfaces, *e.g.*, by de Haas-van Alphen measurements or
angle-resolved photoemission spectroscopy, facilitate interpretation of
these data [#Straub]_.

.. figure:: /Datasheets/images/Electronics-Cu-FermiSurface.png
   :align: center

   Fermi surface of Cu as calculated using |medea| Electronics.

:myquote:`The Fermi surface is the stage on which the 'drama of the
life of the electron' is played out.`

:myquotee:`M. I. Kaganov and I. M. Lifshits,
"Electron theory of metals and geometry",
Sov. Phys. Usp. 22, 904 (1979)`


Key Features
^^^^^^^^^^^^

* An intuitive user interface allows completely automated setup, execution,
  and processing of the background jobs required to calculate isosurfaces
  of the electronic energies and the corresponding effective masses
* Compute electronic eigenvalues with |medea| VASP
* Apart from the calculational parameters of the underlying |medea| VASP
  calculation, |medea| Fermi Surface requires only specification of the
  fineness of the **k**-point grid used to display the isoenergy surfaces
* Take advantage of the full integration in to the |medea| |menvironment| and
  the robust insfrastructure of the |medea| |mjobservertaskserver|.
* Efficiently manage calculations in line with the computational
  resources
* Automatically detect and use space-group symmetry

.. figure:: /Datasheets/images/Electronics-Fermi-GUI.png
   :align: center

   |medea| Fermi Surface Screenshot: Graphical user interface controlling
   setup of the calculation


.. add for a column break, adjust where needed
.. raw:: latex

   \newpage

Properties
^^^^^^^^^^

* Three-dimensional isosurfaces of electronic energies (Fermi surfaces)
  in **k**-space
* Interactive analysis of effective masses for each band at any point
  in **k**-space
* Interpolated electronic band structure displayed for orientation

.. figure:: /Datasheets/images/Electronics-Fermi-Analysis-GUI.png
   :align: center

   |medea| Fermi Surface Screenshot: Graphical user interfaces for the
   display and analysis of calculated Fermi surfaces and effective
   masses


Required Modules
~~~~~~~~~~~~~~~~

* |medea| |menvironment|
* |medea| |mvasp|
* |medea| |electronics|


Find Out More
^^^^^^^^^^^^^

Check out the closely related datasheet on |datasheetelectronictransport|.


.. [#TM] |regTMinfo|

.. [#Mackintosh] A. R. Mackintosh,
   *Sci. Am.* **209**, 110 (1963)
   (`DOI <https://doi.org/10.1038/scientificamerican0763-110>`__)

.. [#Dugdale] S. B. Dugdale,
   *Phys. Scr.* **91**, 053009 (2016)
   (`DOI <https://doi.org/10.1088/0031-8949/91/5/053009>`__)

.. full author list: Th. Straub, R. Claessen, P. Steiner, S. Hüfner,
   V. Eyert, K. Friemelt, and E. Bucher
.. [#Straub] Th. Straub *et al.*,
   *Phys. Rev. B* **55**, 13473 (1997)
   (`DOI <https://doi.org/10.1103/PhysRevB.55.13473>`__)


.. only:: html

   :download: :download:`pdf </Datasheets/Datasheet-Fermi.pdf>`


.. :myquote:`The Fermi surface is the stage on which the "drama of the
.. life of the electron" is played out. And in the same way in which the life
.. of mountain people is essentially different from people living in the
.. valleys, the properties of electrons in lead, which has an exceedingly
.. complicated Fermi surface, do not resemble the properties of electrons in
.. sodium, whose Fermi surface is a sphere that is much smoother than a
.. billiard ball. However, both have something in common with the electrons
.. in the degenerate Fermi gas.`