  We study how nonhelical spin textures affect the proximity-induced
superconductivity of topological insulator (TI)-superconductor (SC) interface
states. In particular we calculate the conductance of lateral heterojunctions
which comprise a TI surface that is only partially covered by a superconducting
material. Interface potentials at the TI-SC interface may lead to a Fermi
velocity and spin texture mismatch between the two regions of the lateral
heterojunction. By enforcing the hermiticity of the total Hamiltonian, we
derive the boundary conditions and calculate the conductance of the structure
in both the normal and superconducting state. The total Andreev conductance is
calculated for both $s$-wave and spin-triplet parent SCs, and for several
examples of nonhelical spin textures which lead to different Fermi surface
mismatches between the two planar regions of the heterojunction. We find that
for spin-triplet SCs, nonzero conductance signatures only appear for certain
combinations of nonhelical spin textures and parent superconducting material.
