Hi Simon,
Your Hamiltonian is already a k-space expression of a tight-binding
model, and you should create it directly. Discretizer will only work
on Hamiltonians that are polynomial in momentum space (yours has a
cosine).
Best,
Anton
On Thu, 23 Jan 2020 at 17:36, <simon.fl...@uzh.ch> wrote:
>
> Dear kwant users
> I was trying to implement the following Hamiltonian: H_j,j+1 = H_j+1,j = -t,
> H_j,j = -0.02*t*cos(k_y + 2pi (phi/W)*j)
> for a square lattice of size W*L with attached leads in y-direction.
> Unfortunately it doesn't work. Could anyone give me a hint
> how to do this the right way?
>
> Thank you for your answers in advance
>
> Best,
>
> Simon
>
> def make_system(a=1, L=60, W=30):
> offdiagmat = np.zeros((W, W))
> for i in range(W):
> for j in range(W):
> if i == j + 1 or j == i + 1:
> offdiagmat[i][j] = 1
>
>
> hamiltonian = "-1.0*offdiagmat - identity(4)*2*0.01*cos(k_y +
> (2*pi*phi/30)*x)"
>
> hamiltonian = kwant.continuum.sympify(hamiltonian,
> locals=dict(offdiagmat=offdiagmat))
>
> template = kwant.continuum.discretize(hamiltonian, grid=a)
>
> def shape(site):
> (x, y) = site.pos
> return (0 <= x < W and 0 <= y < L)
>
> def lead_shape(site):
> (x, y) = site.pos
> return (0 <= x < W)
>
> syst = kwant.Builder()
> syst.fill(template, shape, (0, 0))
>
> lead = kwant.Builder(kwant.TranslationalSymmetry([0, -a]))
> lead.fill(template, lead_shape, (0, 0))
>
> syst.attach_lead(lead)
> syst.attach_lead(lead.reversed())
>
> syst = syst.finalized()
> return syst
>
> def analyze_system():
> params = dict(phi=0.2)
> syst = make_system()
>
> kwant.plotter.bands(syst.leads[0], params=params,
> momenta=np.linspace(-pi, pi, 200), show=False)
>
> plt.grid(True)
> plt.xlim(-pi, pi)
> plt.xlabel('momentum [1/A]')
> plt.ylabel('energy [eV]')
> plt.show()
>
> def main():
> analyze_system()
>
>
> if __name__ == '__main__':
> main()
