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.
