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()
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.flury@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()
Ah I see Thank you very much :) -----"Anton Akhmerov" <anton.akhmerov+kd@gmail.com> schrieb: ----- An: simon.flury@uzh.ch Von: "Anton Akhmerov" <anton.akhmerov+kd@gmail.com> Datum: 23.01.2020 17:45 Kopie: "kwant-discuss" <kwant-discuss@kwant-project.org> Betreff: Re: [Kwant] tight-binding Hamiltonian 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.flury@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()
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Anton Akhmerov -
simon.flury＠uzh.ch