Large radius excitons in single-walled carbon nanotubes

Abstract

The spectrum of large radius exciton in an individual semiconducting single-walled carbon nanotube (SWCNT) is described within the framework of elementary potential model, in which exciton is modeled as bound state of two oppositely charged quasi-particles confined on the tube surface. Due to the parity of the interaction potential the exciton states split into the odd and even series. It is shown that for the bare and screened Coulomb electron-hole (e-h) potentials the binding energy of even excitons in the ground state well exceeds the energy gap. The factors preventing the collapse of single-electron states in isolated semiconducting SWCNTs are discussed.

Environment Effects on Excitons in Semiconducting Carbon Nanotubes

“…[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] Environmental effects were theoretically discussed by assuming a dielectric constant 25,26,29,30,56) or using more elaborate models. [57][58][59][60][61] In this paper, we study environmental effects based on a k Á p scheme by exactly taking account of the image effect within a continuum model. The paper is organized as follows: In §2 a brief review is given on the k Á p description of electronic states, the Coulomb potential in the presence of cylindrical dielectric medium, and a method of calculation of exciton states.…”

Effects of environmental and exciton screening in single-walled carbon nanotubes

“…Due to the parity of the interaction potential the exciton states should split into the odd and even series. In [12] we show that for the bare e-h interaction potentials V (z) = −e 2 /|z| and (1.3), and for the e-h interaction potentials screened by the nanotube bound electrons or by free charges, which may appear in a SWCNT at rather high temperature, the binding energy of even excitons for SWCNTs in vacuum in the ground state well exceeds the energy gap. This may lead to instability of the single-electron states at least in the vicinity of the energy gap with respect to formation of excitons.…”

“…where I i and K i are the modified Bessel functions of the order i of the first and second kind, respectively. For a nanotube in medium internal screening is mainly induced by the nanotube π-electrons and in this case we take ε int (k) obtained in [12] in section 3.…”

“…This may lead to instability of the single-electron states at least in the vicinity of the energy gap with respect to formation of excitons. In [12] we also briefly discussed the factors, which could prevent the collapse of single-electron states in isolated semiconducting SWCNTs. Here we present more detailed analysis of those factors (with the corresponding calculations), namely we consider: the environmental screening of e-h interaction for nanotubes in a medium (section 2) and the screening by excitons, which appear in a nanotube in vacuum due to the mentioned instability of single-electron states (section 3).…”

Impurity enhanced coherent polarization of excitons in single‐walled zigzag nanotubes

“…Many optical properties of carbon nanotubes can be understood in terms of excitons 1–17. In the design of opto‐electronic devices based on the exciton effects, how to control the excitonic excitation becomes the crux of the matter.…”