Dear Yuhao, To expand Joe's answer: I have created a demo notebook for graphene with 3NN hoppings: http://nbviewer.jupyter.org/urls/owncloud.lorentz.leidenuniv.nl/index.php/s/... (also in attachment). Tricky part here is that you need to select correct unit cell, so that periodic boundary condition hopping, created by wraparound, does not compete with hoppings in system and is not overwritten. There are some examples how to deal with it. Also: for my experience, wraparound works not always nicely with non-square lattices, I hope we have catched all the bugs there, but please always check consistency of you results with some common sence. On Mon, Apr 02, 2018 at 05:42:53PM -0400, yuhao kang wrote:

Hello,

I want to create a graphene-like system with periodic BC at transverse direction. I'm following

the discussion at https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00036.html.

For nearest-neighbor hopping, it works. There is hopping between the upper and lower side.

But when I add NNN hopping using:

A,B=graphene.sublattices

sys[A.neighbors()]=hopp_qsvh

sys[B.neighbors()]=hopp_qsvh

The NNN hopping doesn't exist between the upper and lower side.

Is there any way to solve it?

Thank you,

Yuhao

Attached is the code:

import numpy as np

import kwant

X,Y = 4, 4

s0=np.identity(2)

sz=np.array([[1,0],[0,-1]])

graphene = kwant.lattice.honeycomb(1,'b')

A,B=graphene.sublattices

def rectangle(pos):

x, y = pos

return -X/2 < x < X/2

def onsite_qsvh(site):

x,y=site.pos

if y<0:

onsite_a = .4*s0

onsite_b = -.4*s0

return onsite_a if site.family == A else onsite_b

else:

return np.zeros([2,2])

def hopp_qsvh(site1,site2):

x1,y1=site1.pos

x2,y2=site2.pos

hop_a = .4*1j*sz

hop_b = -.4*1j*sz

if (y1+0.1)*(y2+0.1)>0 and y1+0.1>0:

return hop_a if site1.family == A else hop_b

else:

return np.zeros([2,2])

sym = kwant.TranslationalSymmetry(graphene.vec((-Y/2,Y)))

anc = kwant.Builder(sym)

anc[graphene.shape(rectangle,(0, 0))] = None

anc[graphene.neighbors()] = None

sys = kwant.Builder()

sys[anc.sites()] = onsite_qsvh

sys[((a, sym.to_fd(b)) for a, b in anc.hoppings())] = -s0

sys[A.neighbors()]=hopp_qsvh

sys[B.neighbors()]=hopp_qsvh

sys = sys.finalized()

kwant.plot(sys,fig_size=(20, 10))

-- With best regards, Viacheslav Ostroukh Leiden University, Instituut-Lorentz Niels Bohrweg 2, Office 259 2333 CA Leiden, Netherlands +31 6 44 49 68 12 +380 99 721 76 06