Topology of Exciton in Artificial Structure


Masami Kumagai
Optical Science Laboratory

  Topology of an electron wavefunction in artificial structures is determined by the structural parameters if the disturbance of the electron can be neglected [1]. The topology of an exciton wavefunction, however, heavily depends on the delocalized feature of the relative motion of an electron-hole pair making an exciton as well as the structural parameters. We focused our eyes to this situation and investigate the topological aspects of the exciton in nanotube structures [2].
  It has been demonstrated that the exciton wavefunction shows variety of spatial distribution patterns depending on the structural parameters of the nanotube structure. We found that the origin of the change of the exciton wavefunction by controlling the tube circumference length comes from the topological transition. As shown in Fig. 1, the kinetic energy of the ground state exciton in nanotubes decreases monotonically when the circumference length decreased. This is somewhat curious because smaller confinement region yields larger confinement kinetic energy in conventional artificial structures. The exciton wavefunction is delocalized and it is connected in small circumference nanotubes, while the exciton wavefunction is localized in large circumference ones. The connected wavefunction has ring-like topology and it yields the flat wavefunction for a ground state electron and exciton reducing the confinement energy.
  We have also found that the topological transition can be controlled even by changing the barrier dielectric constant of the nanotubes. Figure 2 plots the ground state exciton wavefunctions on developments of two nanotubes with different barrier dielectric constants, 12 and 3. It can be clearly seen that the wavefunction of ε=12 case is delocalized in the direction of circumference (horizontal in the figure) and connected, while the wavefunction of ε=3 case is localized in a small area and disconnected. This implies that we can control the topology of the exciton wavefunction simply by changing the dielectric constant or other material parameters. We expect the control of the artificial structure to provide a novel guiding principle for creating functional devices through the topological control of excitons.

[1] M. Kumagai and T. Ohno, Solid State Commun. 83 (1992) 837.
[2] M. Kumagai, et al., Solid State Commun. 145 (2008) 154.

Fig. 1. Tube circumference dependence of the confinement energy.
Fig. 2. Topological control of exciton by changing dielectric constant.

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