# Gross-Pitaevskii equation with magnetism

We solve the 2D Gross-Pitaevskii equation with a magnetic field. This is similar to the previous example (Gross-Pitaevskii equation in one dimension), but with an extra term for the magnetic field.

using DFTK
using StaticArrays
using Plots

Unit cell. Having one of the lattice vectors as zero means a 2D system

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

Confining scalar potential, and magnetic vector potential

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...);

Parameters

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

Collect all the terms, build and run the model

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)