Dear Eric, Yes, you can use a 3D lattice and define a lead as you proposed, but you can also do that more easily and stay in the 2D space. The main idea is to add a self-energy to the potential of the site below the tip. I suppose that you want to use 1D lead to mimic the effect of tip so you need just to be careful about some details: 1) You need a shift in the potential of the supposed 1D lead because the conduction band for 1D and 2D are not the same. (you chose it in way your 1D lead is also conducting for the Fermi energy of the 2D system ) 2) Use the option 'check_hermiticity=False' when you call the scattering matrix because your Hamiltonian is not Hermitian anymore (it is an effective complex Hamiltonian due to the self-energy of the tip ) 3) The Current in the tip will be the sum of the currents coming from the left lead and the right lead. Each of them is deduced by M-R-T where M is the number of the conducting modes and R,T are the reflection and transmission respectively (see the script below) 4) You can use the exact form of the self-energy with the correct energy dependence and a special coupling if you wish. So, as you see, the self-energy will replace the effect of the lead and therefore no need to define it. An small example is provided below. Finally as a remark, you should notice that if the potential induced by the tip is real, you will have an SGM tip (scanning gate microscopy), where no current is passing through the tip and only a change in the whole conductance is induced. I hope that this helps. Adel import kwant from matplotlib import pyplot from numpy import * def make_system(a=1, t=1.0, W=10, L=30): lat = kwant.lattice.square(a) sys = kwant.Builder() #the self energy of a 1D lead with coupling tc def sigma(energy,V,tc): return (tc**2)/t *((energy-V)/(2*t)-1j*sqrt(1-((energy-V)/(2*t)**2)) ) #to the onsite potential add a self energy def Potential(site, tip_site,energy,V,tc): if site==tip_site: return 0.02+4*t+sigma(energy,V,tc) else: return 0.02+4*t #### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = Potential sys[lat.neighbors()] = -t #### Define and attach the leads. #### # Construct the left lead. lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = 4 * t lead[lat.neighbors()] = -t # Attach the left lead and its reversed copy. sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys def plot_conductance(sys,energy,V,tc): # Compute conductance data = [] for site in sys.sites: smatrix = kwant.smatrix(sys, energy,args=([site,energy,V,tc]),check_hermiticity=False) number_of_modes=(smatrix.data.shape[0])/2 #conducting modes T1=number_of_modes-smatrix.transmission(1, 0)-smatrix.transmission(0, 0) T2=number_of_modes-smatrix.transmission(0, 1)-smatrix.transmission(1, 1) transmission_to_the_tip= T1+T2 data.append(transmission_to_the_tip) pyplot.figure() kwant.plotter.map(sys,data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def main(): sys = make_system() kwant.plot(sys) sys = sys.finalized() plot_conductance(sys,energy=0.1,V=-2,tc=0.1) if __name__ == '__main__': main() On Sun, Jan 8, 2017 at 3:28 AM, Eric Mascot <emasco2@uic.edu> wrote:

Hello

I was wondering, is it possible to have a lead that hovers above a 2D system? I'm guessing that I have to use a 3D system where the system is in the XY plane and the lead has a translational symmetry in the Z direction.

Thanks, Eric

-- Abbout Adel