Band-edge exciton states in a single-walled carbon nanotube revealed by magneto-optical spectroscopy in ultrahigh magnetic fields

Abstract

We report high field magneto-optical study on the first and second sub-band transitions of singlechirality single-walled carbon nanotubes. The ordering and relative energy splitting between bright and dark excitonic states were found to be inversed between the first and second subbands. We verified that the zero-momentum dark singlet exciton lies below the bright exciton for the first subband transitions, while for the second sub-band transitions, it was found to have higher energy than the bright excitonic state. Effect of this peculiar excitonic structure was found to manifest itself in distinctive Aharonov-Bohm splitting in ultra-high magnetic fields up to 190 T.

Magnetoexcitons and Faraday rotation in single-walled carbon nanotubes and graphene nanoribbons

“…Comparing our results to the experimental results in Refs. [20][21][22][23][24][25][26], we see a larger value of bd and a smaller field-dependent increase in the splitting. As mentioned, this is due to the smaller diameter of the CNTs under consideration in this paper.…”

“…Additionally, an accurate understanding of the dynamics of magnetoexcitons reveals details of the role played by magnetic fields in optoelectronic devices [15,16]. The electronic and optical properties of CNTs in the presence of a static magnetic field were considered theoretically in a series of papers by Ando [17][18][19], and the results were later verified experimentally [20][21][22][23][24][25][26]. However, the off-diagonal elements of the conductivity tensor were not evaluated in these papers.…”

Relative Ordering between Bright and Dark Excitons in Single-walled Carbon Nanotubes

“…4(a–b). For E 11 transition, fitting using the above formulae gives Δ bd ≈ 9.1 meV and μ ≈ 0.55 meV/T for the (6,4) SWNTs and Δ bd ≈ 8.5 meV, μ ≈ 0.57 meV/T for the (6,5) SWNTs21. For E 22 transition, the fitting parameters are: Δ bd ≈ 10.9 meV and μ ≈ 0.54 meV/T for (6,4) and Δ bd ≈ −9.0 meV and μ ≈ 0.65 meV/T for (6,5) SWNTs.…”

“…Our high-field magneto-absorption measurements up to 190 T, as analyzed in detail in Ref. 21, reveal that the relative ordering between bright and dark excitons is inverse for the 1 st and 2 nd sub-band transitions for the (6,5) SWNTs: while the dark exciton lies ~8.5 meV below the bright exciton in the 1 st sub-band transition, the dark exciton in the 2 nd sub-band transition was found to be ~9.0 meV higher in energy than the bright excitonic state21. Compared with the results of the (6,4) SWNTs, one could find that the dark exciton can be either higher or lower than the bright one in the E 22 transitions.…”

“…A schematic diagram for these two cases, similar to that in Ref. 21, was shown in Fig. 3(c) and (d), for the readers' convenience.…”