ABSTRACT
Figure 1.12 The first two band-to-band transitions for light polarized along the CNT axis (a) and perpendicular to the CNT axis (b). Adapted from [23]. 1.5.2 ExcitonsIn general, the optical properties of a certain material can be well described by the single particle picture and band-to-band transitions. However, for 1D material such as CNTs, the optical properties mainly determined by many-body effects. Exciton is the most significant feature of many-body effects. The exciton is usually defined as electron-hole pair bound by the Coulomb interaction. Figure 1.13 shows a conceptual picture of exciton formation. An electron is excited across the bandgap by the absorption of a photon, leaving behind a hole in valence band. A hydrogen-like bound state can be formed between the excited electron and the hole through the Coulomb interaction. In an exciton, the electron and hole are separated by the exciton radius. The attractive Coulomb interaction potential can induce quantization of energy. The exciton binding energy can be defined as the difference between the free electron energy and the quantized energy levels.
