using DFTK
using StaticArrays
using Plots

a = 10
lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];

pot(x, y, z) = (x - a/2)^2 + (y - a/2)^2
Apot(x, y, z) = .2 * @SVector [y - a/2, -(x - a/2), 0]
Apot(X) = Apot(X...);

Ecut = 20  # Increase this for production
C = 500.0
α = 2
n_electrons = 1;  # Increase this for fun

terms = [Kinetic(),
         ExternalFromReal(X -> pot(X...)),
         PowerNonlinearity(C, α),
         Magnetic(Apot),
]
model = Model(lattice; n_electrons=n_electrons,
              terms=terms, spin_polarization=:spinless)  # "spinless electrons"
basis = PlaneWaveBasis(model, Ecut, kgrid=(1, 1, 1))
scfres = direct_minimization(basis, tol=1e-5)  # Reduce tol for production
heatmap(scfres.ρ.real[:, :, 1], c=:blues)