Scattering in quantum wires and junctions of quantum wires with edge states of quantum spin Hall insulators

An integral part of scattering theory calculations in continuum quantum systems involves identifying appropriate boundary conditions addition to writing down the correct Hamiltonian. In simplest problem one dimensional lattice, due an on-site potential and unequal bond (in otherwise translationally invariant lattice) give different results for amplitudes. While problems lattice models can be mapped another potential, equivalent model is missing. We introduce a new parameter $c$ condition that on lattice. Further, we study junction between normal metal wire edge spin Hall insulator (QSHI) using $c$. case QSHI, identify permits maximum transmission. solve QSHI map it results. The transport four channels spinful two not well-defined. rectify this situation by formulating terms semi-infinite with infinite gapping out section Zeeman field applying at junction. calculate amplitudes analytically.