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;
}
public bool GetPlaneST(Vector3 kpt, out double s, out double t)
{
Vector3 v = new Vector3();
// expand to cartesian coordinates
for (int i = 0; i < 3; i++)
{
v += (kpt[i] - origin[i]) * G[i];
}
s = v.DotProduct(sdir);
t = v.DotProduct(tdir);
double norm = (kpt - origin).DotProduct(sdir.CrossProduct(tdir));
if (Math.Abs(norm) > 1e-7)
return false;
else
return true;
}