Stability and Signatures of Biexcitons in Carbon Nanotubes

Abstract

The linear optical properties of semiconducting carbon nanotubes are dominated by quasi-one-dimensional excitons formed by single electron-hole pairs. Hence, the nonlinear response at high pump levels most likely leads to the formation of exciton complexes involving several electron-hole pairs. Such complexes would therefore play an important role in, e.g., lasing applications. We demonstrate here that the biexciton complex is surprisingly stable for nanotubes in a wide diameter range. Theoretical predictions for the signature of such states in pump-probe spectroscopy are presented.

Theory and application of explicitly correlated Gaussians

“…Results from the ''exact'' diagonalization, DIAG (Hawrylak and Pfannkuche, 1993) and three DMC calculations DMC1 (Bolton, 1996), DMC2 (Pederiva, Umrigar, and Lipparini, 2000), and DMC3 (Harju et al, 1999) are determined by quantum mechanical few-body systems. Carbon nanotubes, for example, offer a novel challenge for few-body approaches where the electrons and holes move on the surface of a cylinder (Pedersen et al, 2005;Kammerlander et al, 2007;Roy and Maksym, 2012). This is a ''fractional dimensional'' few-body system where the 2D problem is embedded into 3D space and one has to use either an appropriate confining potential or an appropriately constrained ECG basis.…”

Exciton dephasing and multiexciton recombinations in a single carbon nanotube

“…2(a), no spectral structures arising from exciton complexes, such as a biexciton, were observed in a lower energy region of the exciton PL line. However, Pedersen et al [31] have discussed the exciton-exciton interaction and the stability of the biexciton in a SWNT based on the effective-mass theory. The biexciton binding energy is estimated at 37 meV in a semiconducting SWNT with a 1.07 nm diameter [corresponding chirality: (11,4)].…”

Multi-excitonic effects on optical spectra of semiconducting carbon nanotubes

“…On the other hand, it slowly increases and saturates as ∆ decreases, and we can extrapolate E XX as 0.031. This value is slightly larger than that obtained by the variational method [4], and about 30 percent smaller than that obtained by DMC method [5]. These results shows that the short-wavelength components are relatively important in the biexciton wavefunction, and give a considerable correction to the value of E XX .…”

“…Because of their one dimensionality, it is found both theoretically [2] and experimentally [3] that the excitons on the semiconducting carbon nanotubes (s-CNTs) have huge binding energies. Further, theoretical studies also predict stable biexcitons with large binding energies [4,5]. However, they have never been observed in the photoluminescence (PL) measurements [6].…”

“…In the present paper, we use the simplified model used in Ref. [4]: we consider the ground subband (n = 0) near the K point, only, and neglect its nonparabolicity, approximating the energy dispersion by ν,n=0 (k) ∼ ± E g /2 +h 2 k 2 /2m with the effective band mass m =h 2 /3γR and the bandgap energy E g = 2γ/3R. The photoexcited electrons and holes interacts via the Coulomb potential ±(2e 2 /πκr)K(−4R 2 /r 2 ), where e is the electron charge, κ is the dielectric constant, K is the elliptic integral, r is the inter-particle separation along the CNT axis, and the sign is positive for the electron-electron (e-e) and holehole (h-h) interactions and negative for the electron-hole (e-h) interaction, respectively.…”