Hi, I appreciate the reply. I was impressed by the details you have given considering that you have to read the paper that I referenced to and you cross referenced some literatures in your response to help me understand better.
Kudos and I am looking forward to keep in touch with this group in the future Oliver On 12/8/16, Abbout Adel <[email protected]> wrote: > 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 < > [email protected]> 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 > -- 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
