Hi Alex, The trick is to add the Peierls phase after you discretized your Hamiltonian, I do it in the following way: def apply_peierls_to_template(template, xyz_offset=(0, 0, 0)): template = deepcopy(template) # Needed because kwant.Builder is mutable x0, y0, z0 = xyz_offset lat = template.lattice a = np.max(lat.prim_vecs) # lattice contant def phase(site1, site2, B_x, B_y, B_z, orbital, e, hbar): x, y, z = site1.tag direction = site2.tag - site1.tag A = [B_y * (z - z0) - B_z * (y - y0), 0, B_x * (y - y0)] A = np.dot(A, direction) * a**2 * 1e-18 * e / hbar phase = np.exp(-1j * A) if lat.norbs == 2: # No PH degrees of freedom return phase elif lat.norbs == 4: return np.array([phase, phase.conj(), phase, phase.conj()], dtype='complex128') for (site1, site2), hop in template.hopping_value_pairs(): template[site1, site2] = combine(hop, phase, operator.mul, 2) return template You can apply this function to your template builder. In short, it does this combine(hop, phase, operator.mul, 2), which is creating a new function from the phase function and the hopping function and combining the arguments. You would probably need to adjust the form of the vector potential, the units (this is using nm) and change the form of the phase function. I have attached the combine.py script you will need to combine the functions. Please let me know whether it works or not. Best, Bas On Tue, Sep 19, 2017 at 11:26 PM, Alex Currie <alexjcurrie95@gmail.com> wrote:
Dear All,
I have a Hamaltonian (BHZ hamiltonian) and i'm trying to introduce a magnetic field. I believe I have to use the Peierls phase, however i'm not sure how to implement this after I have finalized the BHZ hamiltonian. Any assistance is appreciated. I will paste the code i have to generate my hamiltonian. You can find more information about the BHZ hamiltonian here: arxiv:0801.0901 <https://arxiv.org/abs/0801.0901>
""" import kwant import numpy as np import scipy.linalg as la import scipy.sparse.linalg as sla
import sympy
import matplotlib.pyplot as plt
from ipywidgets import interact
Gamma_so = [[0, 0, 0, -1], [0, 0, +1, 0], [0, +1, 0, 0], [-1, 0, 0, 0]]
hamiltonian = """ + M * kron(sigma_0, sigma_z) - B * (k_x**2 + k_y**2) * kron(sigma_0, sigma_z) - D * (k_x**2 + k_y**2) * kron(sigma_0, sigma_0) + A * k_x * kron(sigma_z, sigma_x) - A * k_y * kron(sigma_0, sigma_y) + Delta * Gamma_so """
params_bhz=dict(A=364.5, B=-686, D=-512, M=-10, Delta=1.6)
hamiltonian = kwant.continuum.sympify(hamiltonian, locals=dict(Gamma_so=Gamma_so)) hamiltonian
grid_spacing = 5 template = kwant.continuum.discretize(hamiltonian, grid_spacing=grid_spacing)
syst = kwant.wraparound.wraparound(template) syst = syst.finalized()
"""
Best,
Alex