.. lieb_tb documentation master file, created by
    sphinx-quickstart on Sat Apr 18 18:56:08 2015.
    You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive.

.. toctree::
    :titlesonly:

About
=====

This is the primary site for the distribution of the python package **graphene_flake**, from Charles Poli at Lancaster University.


Motivations
-----------

The **graphene_flake** package models a tight-binding graphene flake submited to inhomogeneous triaxial linear strain [Sch13]_, [Pol14]_.

The lattice is defined by two sublattices labeled A and B, and three hoppings: :math:`t_1`, :math:`t_2`, :math:`t_3`, and three bond vectors : :math:`\rho_1`, :math:`\rho_2`, :math:`\rho_3`.

        .. image:: figs/graphene_sublattices.png
            :width:  30%
            :align: center

In presence of the triaxial linear train, the hoppings are given by:

.. math::

    t_l = t [1 + (\beta/2)\boldsymbol{\rho}_l . \mathbf{r}_l]\, , \quad \text{with}, l=1,2, 3.

The resulting strain-induced hopping pattern:

        .. image:: figs/strained_induced_pattern.png
            :width:  80%
            :align: center

The class **graphene_flake** can

    * obtain the spectrum (eigenenergies of the tight-binding Hamiltonian) and the probability densities of the states of the system (modulus squared eigenvectors of the Hamiltonian).
    * select states by introducing a condition on the eigenenergies.
    * Analyze the degeneracy and the wavefunction support of the pLLs.
    * Analyze the evolution of the eigenenergies depending on the strength of the strain (analogous to the Hofstadter's butterfly).
    * Analyze the vortex-induced localized states appearing between pLLs.


References
----------

.. [Sch13] H. Schomerus, *Parity Anomaly and Landau-Level Lasing in Strained Photonic Honeycomb Lattices*.
    Phys. Rev. Lett. **110**, 013903 (2013)

.. [Pol14] C. Poli, J. Arkinstall, and H. Schomerus, *Degeneracy doubling and sublattice polarization in strain-induced pseudo-Landau levels*.
    Phys. Rev. B **90**, 155418 (2014).



Feedback
--------

Please send comments or suggestions for improvement to cpoli83 at hotmail dot fr