Dear Mohit, The Caroli et al formula gives the tunneling current in a system connected to electrodes (leads in our terminology). A lead is an infinite system which has the important characteristics that it exhibits a complex self energy with a negative imaginary part.
If you had constructed your leads normally, this imaginary part would have been present automatically in the conduction region (the bands). Since you put fictitious leads with a zero self energy, you will obtain no current. Change your self energy to something like: -1j* Gamma/2 where Gamma is a norbs x norbs definite positive matrix. It should work like this. I hope this helps, Adel On Wed, Jun 10, 2020 at 4:22 AM <mohit.gupta9...@gmail.com> wrote: > I have been trying to evaluate current through a josephson junction using > the green function formalism using the following formula: > I=2 (e Kb T)/hbar(sum over matsubara freq.)(H_ij G_ij-H_ji G_ji) > To calculate current I have mounted two virtual leads on the slabs where I > want to evaluate the current using the following code: > > def mount_vlead(sys, vlead_interface, norb): > dim = len(vlead_interface)*norb > zero_array = np.zeros((dim, dim), dtype=float) > def selfenergy_func(energy, args=()): > return zero_array > > vlead = kwant.builder.SelfEnergyLead(selfenergy_func, > vlead_interface,()) > sys.leads.append(vlead) > > where vlead_interace was supplied using the following code: > > v1=kwant.Builder() > v1[(lat(nx_1,i) for i in range(ny))]=(2*t-mu_n)*tau_z > v1[lat.neighbors()]=-t*tau_z > v2=kwant.Builder() > v2[(lat(nx_2,i) for i in range(ny))]=(2*t-mu_n)*tau_z > v2[lat.neighbors()]=-t*tau_z > mount_vlead(syst,v2.sites(),2) > > Here nx_1 and nx_2 are the two points where the points where I have > mounted virtual leads. Then I have used the greens_function solver in kwant > to evaluate green function for a given matsubara frequency. > The issue that i am facing is that I am getting identical diagonal > elements in green_function.submatrix(v1,v2) and > green_function.submatrix(v2,v1), thus when taking trace it gives me zero as > the hopping matrix is same. > -- Abbout Adel
