``EDGE++''
============

Last update: 21.12.2016

Language: C++

Libraries: Eigen (required), MKL (optional)

Keywords: edge states; spectral function; self-energy; mixed boundary conditions;
          cylinders; Wannier functions; tight-binding Hamiltonian; wannier90;

What the code can do:
    1. Calculate band structures / DOS / A(w) / A(w,k) for a TB Hamiltonian in the wannier90 format 
    2. Calculate Z2 invariants (3D TB Ham.) and Chern numbers (2D TB Ham.)
    3. Calculate A(w) and A(w,k) for Hamiltonians supplemented with a self-energy
    4. Calculate edge A(w,k) for Hamiltonians supplemented with a self-energy

How to run the code:
    ./edge.o --goal <goal> config-file hr-file siw-file kpoints-file

    Possible goals are:
        'bs'    --- band structure
        'dos'   --- density of states
        'Aw'    --- spectral function
        'Awk'   --- k-resolved spectral function
            'Awkverbose' --- prints A(w,k) and atom/orbital/spin-resolved contributions
                             from the top and the bottom edge of the cylinder (for OBC).
            The goals 'Awkedge[T/B][U/D]' are deprecated, use 'Awkverbose' instead.
        'chern' --- Chern numbers 
                    // currently, only 2D Hamiltonians (in the kx-ky plane)
        'Z2'    --- Z2 invariants

    The program reads four input files: 

        1. `config-file` contains the following parameters:
            1.1 number of orbitals per cell
            1.2 number of cells per cylinder
            1.3 boundary conditions: 'p' for periodic, 'o' for open
            1.4 minimal frequency
            1.5 maximal frequency
            1.6 number of frequencies
            1.7 energy cutoff for H(i,j) matrix elements
            1.8 distance cutoff for H(i,j) matrix elements
            1.9 imaginary delta (needed if the self-energy is real)
            WARNING: The current version of the code reads the values from
                    the first 14 characters of each line.

	2. `hr-file` with the Hamiltonian in the wannier90 format (case_hr.dat),
           preceded by the lattice constants and the coordinates of Wannier centers.  
           WARNING: The current version of the code reads the values from
                    particular positions, i.e. it is sensitive to spaces.

	3. `siw-file` contains the real and imaginary parts of the self-energy
            for each frequency and each orbital:
                w Re(Sigma_1[w]) Im(Sigma_1[w]) Re(Sigma_2[w]) Im(Sigma_2[w]) ...
            WARNING: In the current version, this file has to be provided even if self-energy
                     is not used.  To generate this file, the script `create_zero_siw.py`
                     can be used.
            WARNING: Moreover, the number of columns in this file should be strictly
                     2*norb + 1, where `norb` is the number in the first line of the config file.

	4. `kpoints-file` contains the k-mesh in the wien2k format.  For Z2 or
	   Chern number calculations, the information on the neighboring
	   k-points is required.  Hence, each entry in the `kpoints-file` is
           supplemented with two additional columns (index of the right- and the
           top-neighbor for a given k-point).  These can be generated with:

                    create_2D_k_mesh_with_neighbors.py  (for Chern numbers)
                    create_k_mesh_with_neighbors.py (for Z2 invariants)

           WARNING: The current version of the code reads the values from
                    particular positions, i.e. it is sensitive to spaces.


Bugs and development:
	17.02.2016 --- Bug in the definition of self-energy
	15.04.2016 --- (j,i) instead of (i,j) when saving eigenvectors (chern)
	20.04.2016 --- complex-valued t_ij are now included (before it was only Re[t_ij])
	26.04.2016 --- printed eigenvalues: now increased precision
	29.04.2016 --- plot sites + couplings in the svg format
	31.05.2016 --- added "Awkedge[T/B][U/D]"
	02.06.2016 --- added "Awkverbose"
        06.09.2016 --- changed the Fourier transform to e^ik.R
        16.10.2016 --- added Z2 invariant calculation (2D, only)
        11.11.2016 --- fixed bug in the "create_2D_k_mesh_with_neighbors.py"
                       script (Ny neighbors for the Z2 case were wrong)
        21.12.2016 --- added a workaround for the case of non-orthogonal
                       basis vectors of the Brillouin zone.  Orthogonality
                       is enforced and the vectors are scaled by the parameter
                       given.  If the line is empty, the usual procedure is used.