Hi Steffen,
If I want a 1D lattice with a bi-atomic unit cell, is the following a correct way of defining the lattice? I am wondering, because I originally wanted to define my lattice vectors as [2,0] in order to not land on my second site when constructing the lattice, but it didn't let me (commensurate error).
When creating a polyatomic lattice Kwant doesn't care where you put the sites of the lattice basis, so putting a site at (0, 0) and one at (1, 0) with a lattice vector of (1, 0) is perfectly valid; the sites will belong to different site families, so Kwant will not confuse the two. It will, however, be confusing for *you* when plotting, as site 'a(1)' will be at the same realspace position as site 'b(0)'. If you use (0, 0) and (1, 0) for your basis, and have a lattice vector of (2, 0), then the translational symmetry vector must also be (-2, 0) in order to be commensurate with the symmetry of the lattice. You could also choose a basis of (0, 0) and (0.5, 0) and keep the translational symmetry vector as (-1, 0).
The next error where it hangs 'Matrices are not aligned' are again inherently python, but I think the reason for the error is rooted in my layout of the 1D lattice.
The error occurs when trying to use the HoppingKind with: ((0, 0), a, b) The problem is actually that you have supplied the 'delta' argument as a tuple with 2 elements, whereas your site families (sublattices) are 1D, and therefore only require a tuple with a single element. You should therefore define your long and short hoppings like:
LongBond = [((0,), a, b)] ShortBond = [((-1,), a, b)]
When the hoppings were defined in the graphene tutorial they also included the hopping like ((0,0),a,b) - does this refer to a hopping inside the unit cell itself between the two sublattices, I would have initially gone like (((1,0),a,b)?
This question is related to the above; the documentation of HoppingKind explains this. The 'delta' argument to HoppingKind specifies the difference between the tags, i.e. 'HoppingKind(delta, a, b)' matches hoppings of the form '(a(x + delta), b(x))' where 'x' is any tag and '+' should be taken to mean vector addition (and not to mean "append", which is the Python semantics for '+' with lists and tuples -- 'delta' is internally converted into an array first). We can therefore see that providing '((0,), a, b)' means '(a(0), b(0))', '(a(1), b(1))' and so on. In the context of your example this means hoppings between the two sublattices in the same unit cell. '((1,), a, b)' means '(a(1), b(0))', '(a(2), b(1))' and so on, so in your example this is hoppings between different sublattices in neighboring unit cells. This should hopefully also explain why providing '((0, 0), a, b)' (i.e. with a 2-element 'delta') did not work; the shape is not compatible with the tag of the 'a' and 'b' lattices. The error message is pretty poor in this case, and can be improved. I have opened an issue [1] on the Kwant bug tracker about this. Thanks for helping us make Kwant better! Happy Kwanting, Joe [1]: https://gitlab.kwant-project.org/kwant/kwant/issues/147