kwant.continuum.discretize_landau

kwant.continuum.discretize_landau(hamiltonian, N, momenta=None, grid_spacing=1)[source]

Discretize a Hamiltonian in a basis of Landau levels.

Parameters
hamiltonianstr or sympy expression
Npositive integer

The number of Landau levels in the basis.

momentasequence of str (optional)

The momenta defining the plane perpendicular to the magnetic field. If not provided, “k_x” and “k_y” are used.

grid_spacingfloat, default: 1

The grid spacing to use when discretizing the normal direction (parallel to the magnetic field).

Returns
builderBuilder

‘hamiltonian’ discretized in a basis of Landau levels in the plane defined by ‘momenta’. If a third coordinate is present in ‘hamiltonian’, then this also has a translational symmetry in that coordinate direction. The builder has a parameter ‘B’ in addition to any other parameters present in the provided ‘hamiltonian’.

Notes

The units of magnetic field are \(ϕ₀ / 2 π a²\) with \(ϕ₀ = h/e\) the magnetic flux quantum and \(a\) the unit length.

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