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);
double[,] xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
double beta = 1.0 / (Physics_Base.kB * temperature);
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density.Spin_Up.vol[k][i, j] *= g_2d * Math.Log(1.0 + Math.Exp(-1.0 * beta * xy_energy[i, j])) / beta;
charge_density.Spin_Down.vol[k][i, j] *= g_2d * Math.Log(1.0 + Math.Exp(-1.0 * beta * xy_energy[i, j])) / beta;
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
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);
DoubleHermitianEigDecomp eig_decomp = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
double[] dens_x = new double[nx];
// and generate a density for the y-direction
for (int i = 0; i < nx; i++)
for (int k = 0; k < max_wavefunction; k++)
dens_x[i] += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i]) * Get_OneD_DoS(energies[k], no_kb_T);
// multiply the z-densities by the y-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
// 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;
}
charge_density.Spin_Up.mat[i, j] *= dens_x[i];
charge_density.Spin_Down.mat[i, j] *= dens_x[i];
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
/// <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;
}
/// <summary>
/// returns the eigen-energies for the given potential and charge density
/// </summary>
public override DoubleVector Get_EnergyLevels(ILayer[] layers, Band_Data pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data band_pot = pot.DeepenThisCopy();
Get_Potential(ref band_pot, layers);
DoubleHermitianMatrix hamiltonian = Create_Hamiltonian(layers, band_pot);
DoubleHermitianEigDecomp eig_decomp = new DoubleHermitianEigDecomp(hamiltonian);
return eig_decomp.EigenValues;
}
/// <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_deriv"></param>
/// <param name="chem_pot"></param>
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, 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);
DoubleHermitianEigDecomp eig_decomp = new DoubleHermitianEigDecomp(hamiltonian);
double min_eigval = eig_decomp.EigenValues.Min();
int 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_deriv = 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_deriv.Spin_Up.mat[i, j] = 0.0;
charge_density_deriv.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_deriv += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_OneD_DoS_Deriv(eig_decomp.EigenValue(k), no_kb_T);
}
// just share the densities (there is no spin polarisation)
charge_density_deriv.Spin_Up.mat[i, j] = 0.5 * dens_val_deriv;
charge_density_deriv.Spin_Down.mat[i, j] = 0.5 * dens_val_deriv;
}
// and multiply the density derivative by e to get the charge density and by e to convert it to d/dphi (as increasing phi decreases the charge: dn/dphi*-e^2 )
charge_density_deriv = unit_charge * unit_charge * charge_density_deriv;
}
public override DoubleVector Get_EnergyLevels(ILayer[] layers, 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);
// diagonalise matrix for k = 0
int tmp = 0;
DoubleHermitianEigDecomp eig_decomp = Diagonalise_Hamiltonian(Create_Hamiltonian(dft_pot, 0.0), out tmp);
return eig_decomp.EigenValues;
}
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, Band_Data chem_pot)
{
Get_SOI_parameters(chem_pot);
// if (dV_x == null)
// throw new Exception("Error - Band structure derivatives are null! Have you initiated this type properly by calling Get_SOI_parameters(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);
// reset charge density
charge_density_deriv = 0.0 * charge_density_deriv;
// integrate up density from k = 0 to k = k_F
int count = 0;
double k = 0;
// create initial hamiltonian and eigendecomposition
int max_wavefunction_old_p, max_wavefunction_old_m;
DoubleHermitianMatrix hamiltonian_p = Create_H_Using_SOIP(dft_pot, k);
DoubleHermitianEigDecomp eig_decomp_old_p = Diagonalise_Hamiltonian(hamiltonian_p, out max_wavefunction_old_p);
DoubleHermitianEigDecomp eig_decomp_old_m = Diagonalise_Hamiltonian(hamiltonian_p, out max_wavefunction_old_m);
while (k < kmax)
{
// increment the wavevector
k += delta_k;
count += 1;
// create new decompositions for forwards and backwards analysis
int max_wavefunction_p, max_wavefunction_m;
DoubleHermitianEigDecomp eig_decomp_p = Diagonalise_Hamiltonian(Create_H_Using_SOIP(dft_pot, k), out max_wavefunction_p);
DoubleHermitianEigDecomp eig_decomp_m = Diagonalise_Hamiltonian(Create_H_Using_SOIP(dft_pot, -1.0 * k), out max_wavefunction_m);
SpinResolved_Data new_charge_deriv = new SpinResolved_Data(nx, ny);
// cycle over each of the positive bands
for (int i = 0; i < max_wavefunction_p; i++)
new_charge_deriv += Calculate_Density_Derivative(eig_decomp_old_p, eig_decomp_p, i);
// and negative bands
for (int i = 0; i < max_wavefunction_m; i++)
new_charge_deriv += Calculate_Density_Derivative(eig_decomp_old_m, eig_decomp_m, i);
// set new eigenvalue decompositions and max_wavefunctions to the old ones
eig_decomp_old_m = eig_decomp_m; eig_decomp_old_p = eig_decomp_p;
max_wavefunction_old_m = max_wavefunction_m; max_wavefunction_old_p = max_wavefunction_p;
// and finally, add the charge density calculated
charge_density_deriv += new_charge_deriv;
}
}
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, 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);
double[,] xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density_deriv);
double beta = 1.0 / (Physics_Base.kB * temperature);
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density_deriv.Spin_Up.vol[k][i, j] *= g_2d * Get_Fermi_Function(xy_energy[i, j]);
charge_density_deriv.Spin_Down.vol[k][i, j] *= g_2d * Get_Fermi_Function(xy_energy[i, j]);
}
// and multiply the density derivative by e to get the charge density and by e to convert it to d/dphi (as increasing phi decreases the charge: dn/dphi*-e^2 )
charge_density_deriv = unit_charge * unit_charge * charge_density_deriv;
}
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);
double[,] xy_energy = new double[nx, ny];
xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
/*int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
double[,] dens_xy = new double[nx, ny];
// and generate a density for the y-direction
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < max_wavefunction; k++)
dens_xy[i, j] += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_Fermi_Function(energies[k]);
*/
IExperiment exp_green;
exp_green = new Iterative_Greens_Function_Test.Experiment();
Iterative_Greens_Function_Test.Iterative_Greens_Function iter = new Iterative_Greens_Function_Test.Iterative_Greens_Function(exp_green, xy_energy);
double[,] dens_xy = new double[nx, ny];
double max_energy = Physics_Base.kB * temperature * no_kb_T;
DoubleMatrix xy_energy_mat = new DoubleMatrix(xy_energy);
double min_energy = xy_energy_mat.Min();
double dE = 0.1;
//double min_energy = -1.0 * max_energy;
int n_slices = (int)((max_energy - min_energy) / dE);
for (int n = 1; n < n_slices-1; n++)
{
double energy = min_energy + n * dE;
double[,] dens_per_E = iter.GetDoS(energy);
double fermi_func = Get_Fermi_Function(energy);
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
dens_xy[i, j] += dens_per_E[i,j] * fermi_func;
}
}
//double fermi_fact_max = Math.Exp(max_energy / (Physics_Base.kB * temperature)) + 1;
//double fermi_fact_min = 2.0;
double[,] dens_per_E_max = iter.GetDoS(max_energy);
double[,] dens_per_E_min = iter.GetDoS(min_energy);
double fermi_func_max = Get_Fermi_Function(max_energy);
double fermi_func_min = Get_Fermi_Function(min_energy);
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
dens_xy[i, j] += 0.5*(dens_per_E_max[i, j] * fermi_func_max + dens_per_E_min[i,j] * fermi_func_min);
}
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density.Spin_Up.vol[k][i, j] *= dens_xy[i, j];
charge_density.Spin_Down.vol[k][i, j] *= dens_xy[i, j];
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
public Band_Data Get_KS_KE(ILayer[] layers, 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);
// create temporary density for input into...
DoubleMatrix dens_up = new DoubleMatrix(nx, ny, 0.0);
DoubleMatrix dens_down = new DoubleMatrix(nx, ny, 0.0);
SpinResolved_Data dens = new SpinResolved_Data(new Band_Data(dens_up), new Band_Data(dens_down));
// calculate eigenvectors
DoubleHermitianEigDecomp eig_decomp = Solve_Eigenvector_Problem(dft_pot, ref dens);
int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
// generate kinetic energy data
Band_Data ke = new Band_Data(nx, ny, 0.0);
Band_Data dens_tot = dens.Spin_Summed_Data;
double ke_prefactor = -0.5 * Physics_Base.hbar * Physics_Base.hbar / mass;
for (int i = 1; i < nx - 1; i++)
for (int j = 1; j < ny - 1; j++)
for (int k = 0; k < max_wavefunction; k++)
{
double dy2psi = (dens_tot.mat[i, j + 1] + dens_tot.mat[i, j - 1] - 2.0 * dens_tot.mat[i, j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i]);
double dx2psi = DoubleComplex.Norm(eig_decomp.EigenVector(k)[i + 1] + eig_decomp.EigenVector(k)[i - 1] - 2.0 * eig_decomp.EigenVector(k)[i]) * dens_tot.mat[i, j];
double psi_div2psi = (dens_tot.mat[i, j] * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i])) * (dx2psi + dy2psi);
ke.mat[i, j] += ke_prefactor * psi_div2psi * Get_OneD_DoS(eig_decomp.EigenValue(k), no_kb_T);
}
return ke;
}