About
=====

.. _features:

Features
--------

The main features of TBPLaS include:

* Capabilities
    * Modeling
        * Models with arbitrary dimension, shape and boundary conditions
        * Model replicating, reshaping, merging and splitting
        * Clusters, nano-tubes, slabs and crystals
        * Defects, impurities and disorders
        * Hetero-structures, quasi-crystals, fractals
        * Built-in support for Slater-Koster formulation and spin-orbital coupling
        * Shipped with materials database (Graphene, phosphorene, antimonene, TMDC)
        * Interfaces to Wannier90, LAMMPS, DeepH-pack and DeePTB
        * Tools for fitting on-site energies and hopping integrals
        * Support for analytical Hamiltonian
    * Fields and strains
        * Homogeneous magnetic field via Peierls substitution
        * User-defined electric field
        * Arbitrary deformation with strain and stress
    * Exact-diagonalization
        * Band structure, density of states (DOS), wave functions
        * Berry curvature, phase and topological invariants
        * Spin texture
        * Polarizability, dielectric function, optical (AC) conductivity
        * Full diagonalization and selective diagonalization within specific energy range
        * Non-orthogonal basis set
    * Tight-binding propagation method (TBPM)
        * DOS, LDOS and carrier density
        * Optical (AC) conductivity and absorption spectrum
        * Electronic (DC) conductivity and time-dependent diffusion coefficient
        * Carrier velocity, mobility, elastic mean free path, Anderson localization length 
        * Polarization function, response function, dielectric function, energy loss function
        * Plasmon dispersion, plasmon lifetime and damping rate
        * Quasi-eigenstate and real-space charge density
        * Propagation of time-dependent wave function
    * Kernel polynomial method
        * Electronic (DC) and Hall Conductivity  
    * Recursive Green's function method
        * Local density of states (LDOS)
* Efficiency
    * Compatible Python/C++ modeling tools
    * C++ core for performance-critical parts
    * Hybrid parallelism based on MPI and OpenMP
    * GPU computation based on CUDA
    * Sparse matrices for reducing memory cost
    * Lazy-evaluation technique to reduce unnecessary operations
    * Interface to Netlib LAPACK, OpenBLAS, AMD AOCL and Intel MKL
* User friendliness
    * Intuitive object-oriented user APIs in both Python and C++
    * Simple workflow with a lot of handy tools
    * Transparent code architecture with detailed documentation
* Security
    * Detailed checking on input arguments with precise error message
    * Top-down and bottom-up techniques for keeping data consistency

.. _gallery:

Gallery
-------

.. rubric:: Modeling

.. figure:: images/fractal.png
    :alt: sierpinski carpet
    :align: center
    :scale: 45%

    Fractal

.. figure:: images/distortion.png
    :alt: distortion
    :align: center
    :scale: 45%

    Deformation

.. figure:: images/tbg.png
    :alt: tbg
    :align: center
    :scale: 60%

    Twisted bilayer graphene (TBG)

.. figure:: images/quasi_crystal.png
    :alt: quasi-crystal
    :align: center
    :scale: 45%

    Quasi-crystal

.. rubric:: Properties calculation

.. figure:: images/bands.png
    :alt: bands
    :align: center
    :scale: 45%

    Band structure of TBG from diagonalization (left) and TBPM (right)

.. figure:: images/dos.png
    :alt: dos
    :align: center
    :scale: 25%

    Density of states of graphene from diagonalization and TBPM

.. figure:: images/ac_cond.png
    :alt: ac_cond
    :align: center
    :scale: 25%

    Optical conductivity of graphene from diagonalization and TBPM
.. figure:: images/dos_mag.png
    :alt: dos_mag
    :align: center
    :scale: 25%

    Landau levels in graphene under magnetic field

.. figure:: images/z2.png
    :alt: z2
    :align: center
    :scale: 25%

    :math:`\mathbb{Z}_2` topological invariant of bilayer bismuth

.. figure:: images/param_fit.png
    :alt: param_fit
    :align: center
    :scale: 25%

    Refitting of on-site energies and hopping terms from Wannier90 output

.. figure:: images/plasmon.png
    :alt: plasmon
    :align: center
    :scale: 35%

    Plasmon modes in twisted bilayer MoS2 `Phys. Rev. B 105, 245415 (2022) <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.245415>`_ 

.. figure:: images/bubble.png
    :alt: bubble
    :align: center
    :scale: 50%

    Local DOS in graphene nanobubbles `Phys. Rev. B 109, 115420 (2024) <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.115420>`_ 

.. figure:: ../tutorial/prim_cell/images/spin_texture/spin_texture.png
    :alt: spin_texture
    :align: center
    :scale: 30%

    Spin texture of Kane-Mele model

.. figure:: ../tutorial/prim_cell/images/spin_texture/spin_bands.png
    :alt: spin_bands
    :align: center
    :scale: 100%

    Spin-resolved band structure of Kane-Mele model

.. figure:: images/berry_curvature.png
    :alt: berry_curvature
    :align: center
    :scale: 45%

    Berry curvature of Haldane model

.. figure:: ../tutorial/advanced/images/strain_fields/wfc.png
    :alt: wfc
    :align: center
    :scale: 20%

    Wave function propagation in graphene under deformation (f-j), scattering potential (k-o) and magnetic field (p-t)

.. figure:: ../tutorial/advanced/images/plot_wfc3d/h_chain.png
    :align: center
    :scale: 50%

    Export of 3D wave functions of hydrogen atomic chain

Citation
--------

.. include:: citing.rst

License
-------

TBPLaS is release under the BSD license 2.0, the complete content of which is as following:

.. include:: license.rst