Hi Johnny, To obtain a tight-binding Hamiltonian from a momentum space Hamitlonian we need to calculate a tight-binding description of the momentum operator. This is done using discretization, as shown e.g. here: https://kwant-project.org/doc/1/tutorial/tutorial1#discretization-of-a-schro... or here: http://mybinder.org/repo/kwant-project/kwant-tutorial-2016/notebooks/2.1.Dis... Best, Anton On Tue, Nov 1, 2016 at 9:45 AM, T.C. Wu <tcwu@connect.ust.hk> wrote:

Dear Kwant users,

I recently reading the course materials about topological insulator at http://topocondmat.org/w7_defects/ti_majoranas.html. However, the Kwant code which simulates the majoranas on the quantum spin-Hall edge is not quite transparent to me. In particular, the hoppings defined in Kwant are

def onsite(site, p): (x, y) = site.pos return (p.M - 4 * p.B) * s0szsz - 4 * p.D * s0s0sz + p.gaps(x, y)[1] * mysz + p.gaps(x, y)[0] * s0s0sx

def hopx(site1, site2, p): return p.B * s0szsz + p.D * s0s0sz + 0.5j * p.A * szsxsz

def hopy(site1, site2, p): return p.B * s0szsz + p.D * s0s0sz - 0.5j * p.A * s0sysz

I got a bit lost since I don't quite understand why should hopx and hopy be defined in this way. Maybe a silly question, but how should one obtain the hoppings by looking at the momentum space BdG Hamiltonian?

Thanks for your help.

Best, Johnny