Dear Olivier, I see two options: 1) you can mix the two examples [1] [2] of kwant tutorial and work with a quasi 1D system. In this case, you need to choose an energy for which you will have only one conducting mode in the leads. You need also a spin orbit coupling small enough to have a precession length much larger than the width of your lead to avoid the non-parabolicity [3] in your dispersion relation (ie: in order to obtain results close to the exact 1D system ). So as you see, with this system, you can only study the non-adiabatic situation of the article by Trushin and Chudnovskiy. a small program is included below.
2) You can work with an exact 1D system (ie with a line ) . In this case, you need to handle the circular part of your system.(kwant does not have a lattice suitable for the cylindrical discritization ) The tip is to do the discritization of your Hamiltonian in the cylindrical coordinates[4][5], then, you need to know that your discrete system is a graph, and the position of the sites is not important anymore: only the potential on the sites and the hoppings between them are pertinent. So you will put the sites of your ring in a straight line and put the hoppings you obtain from the discritization (the hoppings will be site dependent ) and therefore you will finally get a simple 1D system that can be studied by kwant. You will need to use a hopping of the form : $-i\alpha \frac{\sigma_r}{R}$ with $\sigma_r= \sigma_x \cos(\theta)+\sigma_y \sin(\theta)$ [5] (appendix) ######################### from cmath import exp from math import pi import kwant # For plotting from matplotlib import pyplot %matplotlib inline import tinyarray # define Pauli-matrices for convenience sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) def make_system(a=1, t=1.0, W=10, r1=10, r2=20 ,alpha=0.5): lat = kwant.lattice.square(a) sys = kwant.Builder() def ring(pos): (x, y) = pos rsq = x ** 2 + y ** 2 return (r1 ** 2 < rsq < r2 ** 2) and x>=0 sys[lat.shape(ring, (0, r1 + 1))] = 4 * t * sigma_0 sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x sym_lead = kwant.TranslationalSymmetry((-a, 0)) def lead_shape(pos): (x, y) = pos return (r1 < abs(y) < r2) def createLead(r): lead=kwant.Builder(sym_lead) lead[lat.shape(lead_shape, (0, r))] = 4 * t * sigma_0 lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x return lead lead1=createLead(r1+1) lead2=createLead(-r1-1) #### Attach the leads and return the system. #### sys.attach_lead(lead1) sys.attach_lead(lead2) return sys def main(): sys = make_system(alpha=.2) # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() data=[] energies=[0.001*i for i in range(400)] for energy in energies: smatrix=kwant.smatrix(sys,energy) data.append(smatrix.transmission(0,1)) pyplot.plot(energies,data) if __name__ == '__main__': main() [1] nontrival shapes (kwant tutorial) [2] Matrix structure of on-site and hopping elements Nontrivial shapes (kwant tutorial ) [3]https://arxiv.org/pdf/0907.4122v1.pdf [4]http://journals.aps.org/prb/abstract/10.1103/PhysRevB.70.195346 [5]http://skemman.is/stream/get/1946/10141/25310/1/ThesisMSc-CsabaD.pdf -- I hope that this helps. Adel On Wed, Dec 7, 2016 at 6:22 PM, Oliver Generalao < oliver.b.genera...@gmail.com> wrote: > HI, > > I was trying to implement the paper > http://link.springer.com/article/10.1134%2FS0021364006080042 in kwant, > however I have trouble creating the geometry of the wire. I tried some > tutorials, I got confused since I am a novice to kwant. > It is a 3D setup with the wire(ideally close to a 1-D quantum wire) on > xy-plane and the external field's direction is upward(in the direction > of positive z-axis). The lead input is from x=-infinity to x=0(in the > negative y-axis) ,then from x=0 the wire starts to curve(in a perfect > semicircle manner) with radius R towards the positive y-axis, and the > output lead starts from x=0 to x=-infinity. > > Herein is the figure attached as well. > > Any guidance and help in creating the code will be greatly > appreciated. Thank you. > > > > > -- > Oliver B. Generalao > > M.S. Physics student > Structure and Dynamics Group > National Institue of Physics > University of the Philippines > Diliman, Quezon City > Trunkline: +63-2-981-8500 > Mobile: +63-927-4033966 > -- Abbout Adel