Excitons in rolled up nanotubes of type-II semiconductor quantum wells: Theoretical study of a quasi-one-dimensional bosonic gas

The excitonic states and the quantum degenerate excitonic gas of spatially separated electron hole in an ideal rolled up nanotube of type-II semiconductor quantum wells with reverse bias configuration are studied theoretically. To illustrate the situation using the material constants appropriate to GaAs/AlAs type-II semiconductor, the exciton binding energy, its ground-state wave function, and the energies of the two low lying rotational states are calculated by numerical diagonalization of the single electron-hole Hamiltonian. By exploiting the ground-state wave function, the exciton-exciton interaction potential in the low-density limit is evaluated and found to be repulsive. It is then shown that a gas of such excitons at low temperature below the energies of the low lying rotational states behaves as a quasi-one-dimensional bosonic gas, which, at low density, is in the strong-coupling regime, and the excitons become fermions and the orthoexcitonic gas is paramagnetic.