Dear Alexander and PWSCF users, I have two questions about complex band code based on the Choi and Ihm paper(PRB 59,2167,(1999)) 1. At the expressions where we have to use non local potential W((k+G)_{\perp},tau-z-d), i can see the code only uses W((k+G)_{\perp},tau-z). I guess this is because of periodicity of nonlocal potential in the z direction. Am i right? 2. This question is about determining the coefficients of the wavefunctions. As we can see from equations (17) for the local part of the potential it has N*2*N_2d number of unknown cofficients. Now using the boundary conditions, that the wavefunction and its derivative should be continuous between the slabs, we can determine (N-1)*2*N_2d unknownns, which leaves 2*N_2d no. of coefficients to be determined later. The same thing applies for the solutions of nonlocal part of the potential in equation (24). Thus the number of linearly independent solution for the nonlocal part is 2*N_2d. we use Bloch's condition to determine these unknown coeffiecints. This is where my question is. When we are trying to construct the general solution as in equation (39), the local part has number of unknown coeffieints 2*N_2d, which is fine. But the nonlocal part has C_{\alpha,l,m} number of unknown coefficients, which is not equal to 2*N_2d. My question is why? Are we somehow combining the coefficients of local part with nonlocal part? Any help will be appreciated. Happy Holidays!
Manoj Srivastava Graduate Student Department of Physics University of Florida, Gainesville, Fl 32601