public Matrix CalcHamiltonian(Vector3 kpt)
{
Matrix m = new Matrix(Orbitals.Count, Orbitals.Count);
kpt *= 2 * Math.PI;
for (int i = 0; i < Orbitals.Count; i++)
{
for (int j = 0; j < Orbitals.Count; j++)
{
HoppingPair p = Hoppings.FindOrThrow(i, j);
Complex val = new Complex();
for (int k = 0; k < p.Hoppings.Count; k++)
{
HoppingValue hop = p.Hoppings[k];
Vector3 R = hop.R;
Complex newval = hop.Value *
Complex.Exp(new Complex(0, kpt.DotProduct(R)));
val += newval;
}
m[i, j] = val;
}
}
if (m.IsHermitian == false)
{
throw new Exception("Hamiltonian at k = " + kpt.ToString() + " is not Hermitian.");
}
return(m);
}
/// <summary>
/// This function does not work with symmetries, so it is unused.
/// </summary>
/// <param name="inp"></param>
/// <param name="outputfile"></param>
void tet_DoDensityOfStates(TightBinding.TbInputFileReader inp)
{
KptList ks = KMesh;
StreamWriter outf = new StreamWriter(outputfile + ".dos");
double smearing = TemperatureMesh[0];
double smearNorm = 1 / smearing * Math.Pow(Math.PI, -0.5);
double oneOverSmearSquared = Math.Pow(smearing, -2);
double emin, emax;
Hoppings.EnergyScale(out emin, out emax);
emin -= smearing * 5;
emax += smearing * 5;
int epts = 2000;
double[] energyGrid = new double[epts];
double[,] dos = new double[epts, Orbitals.Count + 1];
smearNorm /= ks.Kpts.Count;
for (int i = 0; i < epts; i++)
{
energyGrid[i] = emin + (emax - emin) * i / (double)(epts - 1);
}
Output.WriteLine("Calculating DOS from {0} to {1} with tetrahedron method.",
emin, emax, smearing);
Output.WriteLine("Using {0} tetrahedrons.", ks.Tetrahedrons.Count);
for (int tetindex = 0; tetindex < ks.Tetrahedrons.Count; tetindex++)
{
Tetrahedron tet = ks.Tetrahedrons[tetindex];
if (tetindex % (ks.Tetrahedrons.Count / 10) == 0 && tetindex > 0)
{
Output.WriteLine("At {0}...", tetindex);
}
Matrix[] eigenvals = new Matrix[4];
for (int i = 0; i < 4; i++)
{
Matrix m = CalcHamiltonian(tet.Corners[i]);
Matrix vals, vecs;
m.EigenValsVecs(out vals, out vecs);
eigenvals[i] = vals;
}
for (int nband = 0; nband < eigenvals[0].Rows; nband++)
{
for (int i = 0; i < 4; i++)
{
tet.Values[i] = eigenvals[i][nband, 0].RealPart;
}
tet.SortCorners();
int estart = FindIndex(energyGrid, tet.Values[0]);
int eend = FindIndex(energyGrid, tet.Values[3]);
for (int ei = estart; ei < eend; ei++)
{
dos[ei, 0] += tet.IntegrateArea(energyGrid[ei]);
}
}
}
for (int i = 0; i < epts; i++)
{
dos[i, 0] /= ks.Tetrahedrons.Count;
}
for (int i = 0; i < epts; i++)
{
outf.Write("{0} ", energyGrid[i]);
for (int j = 0; j < Orbitals.Count + 1; j++)
{
outf.Write("{0} ", dos[i, j]);
}
outf.WriteLine();
}
outf.Close();
Output.WriteLine("Creating +coeff file.");
outf = new StreamWriter(Path.Combine(Path.GetDirectoryName(outputfile), "+coeff"));
outf.WriteLine("#\t1\t0\t" + ks.Kpts.Count.ToString());
outf.Write("# band index\te(k,n)\t");
for (int i = 0; i < Orbitals.Count; i++)
{
if (string.IsNullOrEmpty(Orbitals[i].Name))
{
outf.Write("TB{0}\t", i);
}
else
{
outf.Write("{0}\t", Orbitals[i].Name);
}
}
outf.WriteLine();
for (int kindex = 0; kindex < ks.Kpts.Count; kindex++)
{
Matrix m = CalcHamiltonian(ks.Kpts[kindex]);
Matrix vals, vecs;
m.EigenValsVecs(out vals, out vecs);
outf.WriteLine("# spin= 1 k={0}", ks.Kpts[kindex].Value);
for (int i = 0; i < vals.Rows; i++)
{
outf.Write("{0} {1} ", i + 1, vals[i, 0].RealPart);
for (int j = 0; j < vecs.Columns; j++)
{
outf.Write("{0} {1} ", vecs[i, j].RealPart, vecs[i, j].ImagPart);
}
outf.WriteLine();
}
}
}