Hi,
I'm looking to perform numerical computations for topological materials,
including computations involving the Chern number. So, I came across
Z2Pack and it seemed intuitive enough for me to use. However, as I've been
going through examples and changing parameters/trying to replicate results
from the literature, I find myself a little confused about the Haldane
model example. I suspect it's some confusion with defining the reciprocal
lattice. In particular, in the Z2Pack example reads in a lattice of
k-values, then makes arrays for the nearest neighbor and next nearest
neighbor k_a and k_b values, then makes those directly the arguments of
cosines and sines to determine the Hamiltonian. However, a lot of the
literature simplifies the sums of those cosines and sines, where I am
performing those calculations to ensure I understand. However, if I
directly put in that Hamiltonian with the simplified expressions, (for
example assuming k=(kx,ky) and a vector from the honeycomb lattice being
(sqrt(3)/2, 1/2), then inner(k,a) = sqrt(3)/2*kx + 1/2*ky), I am unable to
get the Chern number to be correct when taking the lattice of k-values that
is the argument of the Hamiltonian in Z2Pack. So, where are the k_a and
k_b values coming from?
Any help would be much appreciated.
Thank you,
Michael Warnock