/// <summary>
/// Calculate the charge density for this potential
/// NOTE!!! that the boundary potential is (essentially) set to infty by ringing the density with a set of zeros.
/// this prevents potential solvers from extrapolating any residual density at the edge of the eigenstate
/// solution out of the charge density calculation domain
/// </summary>
/// <param name="layers"></param>
/// <param name="charge_density"></param>
/// <param name="chem_pot"></param>
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
DoubleHermitianMatrix hamiltonian = Create_Hamiltonian(layers, dft_pot);
DoubleHermitianEigDecompServer eig_server = new DoubleHermitianEigDecompServer();
eig_server.ComputeEigenValueRange(dft_pot.mat.Min(), no_kb_T * Physics_Base.kB * temperature);
eig_server.ComputeVectors = true;
DoubleHermitianEigDecomp eig_decomp = eig_server.Factor(hamiltonian);
int max_wavefunction = 0;
if (eig_decomp.EigenValues.Length != 0)
{
double min_eigval = eig_decomp.EigenValues.Min();
max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
}
for (int i = 0; i < nx; i++)
{
for (int j = 0; j < ny; j++)
{
double dens_val = 0.0;
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
{
charge_density.Spin_Up.mat[i, j] = 0.0;
charge_density.Spin_Down.mat[i, j] = 0.0;
continue;
}
for (int k = 0; k < max_wavefunction; k++)
{
// and integrate the density of states at this position for this eigenvector from the minimum energy to
// (by default) 50 * k_b * T above mu = 0
dens_val += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_OneD_DoS(eig_decomp.EigenValue(k), no_kb_T);
}
// just share the densities (there is no spin polarisation)
charge_density.Spin_Up.mat[i, j] = 0.5 * dens_val;
charge_density.Spin_Down.mat[i, j] = 0.5 * dens_val;
}
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
DoubleHermitianEigDecomp Diagonalise_Hamiltonian(DoubleHermitianMatrix hamiltonian, out int max_wavefunction)
{
DoubleHermitianEigDecomp eig_decomp;
DoubleHermitianEigDecompServer eig_server = new DoubleHermitianEigDecompServer();
eig_server.ComputeEigenValueRange(E_min, no_kb_T * Physics_Base.kB * temperature);
eig_server.ComputeVectors = true;
eig_decomp = eig_server.Factor(hamiltonian);
max_wavefunction = 0;
if (eig_decomp.EigenValues.Length != 0)
{
double min_eigval = eig_decomp.EigenValues.Min();
max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
}
return(eig_decomp);
}
/// <summary>
/// Calculate the charge density for this potential
/// NOTE!!! that the boundary potential is (essentially) set to infty by ringing the density with a set of zeros.
/// this prevents potential solvers from extrapolating any residual density at the edge of the eigenstate
/// solution out of the charge density calculation domain
/// </summary>
/// <param name="layers"></param>
/// <param name="charge_density"></param>
/// <param name="chem_pot"></param>
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
DoubleHermitianMatrix hamiltonian = Create_Hamiltonian(layers, dft_pot);
DoubleHermitianEigDecompServer eig_server = new DoubleHermitianEigDecompServer();
eig_server.ComputeEigenValueRange(dft_pot.mat.Min(), no_kb_T * Physics_Base.kB * temperature);
eig_server.ComputeVectors = true;
DoubleHermitianEigDecomp eig_decomp = eig_server.Factor(hamiltonian);
int max_wavefunction = 0;
if (eig_decomp.EigenValues.Length != 0)
{
double min_eigval = eig_decomp.EigenValues.Min();
max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
}
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
double dens_val = 0.0;
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
{
charge_density.Spin_Up.mat[i, j] = 0.0;
charge_density.Spin_Down.mat[i, j] = 0.0;
continue;
}
for (int k = 0; k < max_wavefunction; k++)
{
// and integrate the density of states at this position for this eigenvector from the minimum energy to
// (by default) 50 * k_b * T above mu = 0
dens_val += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_OneD_DoS(eig_decomp.EigenValue(k), no_kb_T);
}
// just share the densities (there is no spin polarisation)
charge_density.Spin_Up.mat[i, j] = 0.5 * dens_val;
charge_density.Spin_Down.mat[i, j] = 0.5 * dens_val;
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
DoubleHermitianEigDecomp Diagonalise_Hamiltonian(DoubleHermitianMatrix hamiltonian, out int max_wavefunction)
{
DoubleHermitianEigDecomp eig_decomp;
DoubleHermitianEigDecompServer eig_server = new DoubleHermitianEigDecompServer();
eig_server.ComputeEigenValueRange(E_min, no_kb_T * Physics_Base.kB * temperature);
eig_server.ComputeVectors = true;
eig_decomp = eig_server.Factor(hamiltonian);
max_wavefunction = 0;
if (eig_decomp.EigenValues.Length != 0)
{
double min_eigval = eig_decomp.EigenValues.Min();
max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
}
return eig_decomp;
}