Elucidation of the Electronic Structure of Semiconducting Single-Walled Carbon Nanotubes by Electroabsorption Spectroscopy

We report benchmark calculations of electroabsorption in semiconducting single-walled carbon nanotubes that provide motivation to perform electroabsorption measurement on these systems. We show that electroabsorption can detect the continuum bands in different energy manifolds. Direct determination of the binding energies of excitons in higher manifolds thereby becomes possible. We also find that electroabsorption can provide evidence for Fano-type coupling between the second exciton and the lowest continuum band states.

Figure 1

(a) Linear absorption (dashed line), and EA spectrum of (10,0) NT in the $n=1$ energy region for $F=10\mathrm{kV}/\mathrm{cm}$. (b)–(d) EA spectra for $F=50$, 100, and $200\mathrm{kV}/\mathrm{cm}$, respectively.

Figure 2

(a) Field dependence of $\Delta E_{Ex1}$ (open circles), the EA amplitude of $Ex1$ (solid squares), and $n{B}_u$ (solid triangles) for the (6,5), (7,6), and (10,0) $S$-SWCNTs. (b) and (c) Field dependence of EA signals for the (6,5) $S$-SWCNT due to the $Ex1$ and the $n{B}_u$, respectively.

Figure 3

Linear absorption (a) and EA spectrum (b) in the energy region covering both $n=1$ and 2 energy manifolds for the (6,5) $S$-SWCNT for $F=50\mathrm{kV}/\mathrm{cm}$. The arrow indicates $Ex2$. (c) Superposition of the EAs for the $n=1$ and 2 manifolds, calculated independently of one another.