TY - JOUR
T1 - Dimensional and correlation effects of charged excitons in low-dimensional semiconductors
AU - Rønnow, Troels Frimodt
AU - Pedersen, Thomas Garm
AU - Cornean, Horia
PY - 2010
Y1 - 2010
N2 - In this paper, we investigate the existence of bound trion states in fractional dimensional nanostructures, in terms of variational calculus. We start with trial states, then we refine the result with the help of the Hartree–Fock approximation and finally we use a partial basis expansion. We show that Hartree–Fock significantly underestimates the trion binding energy and that the correlation energy is comparable with the trion binding energy. Furthermore we calculate the binding energies of positive and negative trions restricted to a large subspace of functions, which we expect to span the low-lying eigenstates of the full Hamiltonian. We find that the difference between the positive and negative trion binding energies varies very little for the electron–hole mass fractions me/mh = σ [0.8; 1.0] and that the difference between the positive and negative trion energies grows as the dimension decreases. Finally, we compare a cylindrical effective-mass model of a typical carbon nanotube, with a fractional dimensional model with D = 1.71. We find very good agreement between the trion binding energies predicted by the two models.
AB - In this paper, we investigate the existence of bound trion states in fractional dimensional nanostructures, in terms of variational calculus. We start with trial states, then we refine the result with the help of the Hartree–Fock approximation and finally we use a partial basis expansion. We show that Hartree–Fock significantly underestimates the trion binding energy and that the correlation energy is comparable with the trion binding energy. Furthermore we calculate the binding energies of positive and negative trions restricted to a large subspace of functions, which we expect to span the low-lying eigenstates of the full Hamiltonian. We find that the difference between the positive and negative trion binding energies varies very little for the electron–hole mass fractions me/mh = σ [0.8; 1.0] and that the difference between the positive and negative trion energies grows as the dimension decreases. Finally, we compare a cylindrical effective-mass model of a typical carbon nanotube, with a fractional dimensional model with D = 1.71. We find very good agreement between the trion binding energies predicted by the two models.
U2 - 10.1088/1751-8113/43/47/474031
DO - 10.1088/1751-8113/43/47/474031
M3 - Journal article
SN - 1751-8113
VL - 43
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 47
ER -