Wannier exciton bound states for electron and hole spatially separated in adjacent 2D quantum layers

We analyze the lowest bound states of a Wannier-Mott exciton in which the e lectron is constrained to move freely in a 2D quantum layer (2DL) and the h ole moves in another parallel 2DL. We assume that in the confinement direct ion z both electron and hole are in their respective ground state of a harm onic potential which yields a general multipolar expansion of the electron- hole Coulomb potential in terms of Legendre polynomials. The resulting Schr odinger equation can be solved by perturbing 2D exciton states for which bo th electron and hole are in the same 2DL.