Self-Trapping of Charge Carriers in Semiconducting Carbon Nanotubes: Structural Analysis

Controlling Defect-State Photophysics in Covalently Functionalized Single-Walled Carbon Nanotubes

ConspectusSingle-walled carbon nanotubes (SWCNTs) show promise as light sources for modern fiber optical communications due to their emission wavelengths tunable via chirality and diameter dependency. However, the emission quantum yields are relatively low owing to the existence of low-lying dark electronic states and fast excitonic diffusion leading to carrier quenching at defects. Covalent functionalization of SWCNTs addresses this problem by brightening their infrared emission. Namely, introduction of sp³-hybridized defects makes the lowest energy transitions optically active for some defect geometries and enables further control of their optical properties. Such functionalized SWCNTs are currently the only material exhibiting room-temperature single photon emission at telecom relevant infrared wavelengths. While this fluorescence is strong and has the right wavelength, functionalization introduces a variety of emission peaks resulting in spectrally broad inhomogeneous photoluminescence that prohibits the use of SWCNTs in practical applications. Consequently, there is a strong need to control the emission diversity in order to render these materials useful for applications. Recent experimental and computational work has attributed the emissive diversity to the presence of multiple localized defect geometries each resulting in distinct emission energy. This Account outlines methods by which the morphology of the defect in functionalized SWCNTs can be controlled to reduce emissive diversity and to tune the fluorescence wavelengths. The chirality-dependent trends of emission energies with respect to individual defect morphologies are explored. It is demonstrated that defect geometries originating from functionalization of SWCNT carbon atoms along bonds with strong π-orbital mismatch are favorable. Furthermore, the effect of controlling the defect itself through use of different chemical groups is also discussed. Such tunability is enabled due to the formation of specific defect geometries in close proximity to other existing defects. This takes advantage of the changes in π-orbital mismatch enforced by existing defects and the resulting changes in reactivities toward formation of specific defect morphologies. Furthermore, the trends in emissive energies are highly dependent on the value of mod(n-m,3) for an (n,m) tube chirality. These powerful concepts allow for a targeted formation of defects that emit at desired energies based on SWCNT single chirality enriched samples. Finally, the impact of functionalization with specific types of defects that enforce certain defect geometries due to steric constraints in bond lengths and angles to the SWCNT are discussed. We further relate to a similar effect that is present in systems where high density of surface defects is formed due to high reactant concentration. The outlined strategies suggested by simulations are instrumental in guiding experimental efforts toward the generation of functionalized SWCNTs with tunable emission energies.

Hidden Fine Structure of Quantum Defects Revealed by Single Carbon Nanotube Magneto-Photoluminescence

Organic color-center quantum defects in semiconducting carbon nanotube hosts are rapidly emerging as promising candidates for solid-state quantum information technologies. However, it is unclear whether these defect color-centers could support the spin or pseudospin-dependent excitonic fine structure required for spin manipulation and readout. Here we conducted magneto-photoluminescence spectroscopy on individual organic color-centers and observed the emergence of fine structure states under an 8.5 T magnetic field applied parallel to the nanotube axis. One to five fine structure states emerge depending on the chirality of the nanotube host, nature of chemical functional group, and chemical binding configuration, presenting an exciting opportunity toward developing chemical control of magnetic brightening. We attribute these hidden excitonic fine structure states to field-induced mixing of singlet excitons trapped at sp³ defects and delocalized band-edge triplet excitons. These findings provide opportunities for using organic color-centers for spintronics, spin-based quantum computing, and quantum sensing.

Mod(n-m,3) Dependence of Defect-State Emission Bands in Aryl-Functionalized Carbon Nanotubes

Molecularly functionalized single-walled carbon nanotubes (SWCNTs) are potentially useful for fiber optical applications due to their room temperature single-photon emission capacity at telecommunication wavelengths. Several distinct defect geometries are generated upon covalent functionalization. While it has been shown that the defect geometry controls electron localization around the defect site, thereby changing the electronic structure and generating new optically bright red-shifted emission bands, the reasons for such localization remain unexplained. Our joint experimental and computational studies of functionalized SWCNTs with various chiralities show that the value of mod(n-m,3) in an (n,m) chiral nanotube plays a key role in the relative ordering of defect-dependent emission energies. This dependence is linked to the complex nodal characteristics of electronic wave function extending along specific bonds in the tube, which justifies the defect-geometry dependent exciton localization. This insight helps to uncover the essential structural motifs allowing tuning the redshifts of emission energies in functionalized SWCNTs.

Optical properties of semiconducting zigzag carbon nanotubes with and without defects

The excited states of a series of semiconducting zigzag (n, 0) tubes are studied using the GW method and the Bethe-Salpeter equation within the ab initio many-body perturbation theory. The optical variation rule of the excitation energy with the tube diameter exhibits a family pattern, which arises from the electronic structure of the pristine tube and depends on the value of n mod 3. The introduction of single vacancy and Stone-Wales defects with different orientations affords an effective route for modulating the band structures and optical spectra, resulting in the variation of the selection rules of the excitons and turning dipole-forbidden excitons into dipole-allowed ones. The new localized impurity states in defected tubes will provide additional optically allowed transitions and give rise to pronounced satellite red-shifted peaks. These findings provide inspiration for the tune of optical properties of carbon nanotubes in the future for applications in optoelectronics.

Exciton Self-Trapping in sp2 Carbon Nanostructures Induced by Edge Ether Groups

Recent experiments have suggested that exciton self-trapping plays an important role in governing the optical properties of graphene quantum dots (GQDs) and carbon dots (CDs), while the molecular structures related to this phenomenon remain unclear. This theoretical study reports exciton self-trapping induced by edge-bonded ether (C-O-C) groups in graphene nanosheets. Density functional theory (DFT) and time-dependent DFT calculations show that the initially delocalized electron and hole are trapped in the vicinity of the edge ether groups on graphene nanosheets upon excited-state (S1) relaxation, accompanied by structural planarization of the seven-membered cyclic ether rings in the same region. The resulted significant structural deformation leads to large Stokes shift energies, which are comparable to the magnitudes of the notably large emission shift observed in experiments. This study provides a feasible explanation of the origin of exciton self-trapping and offers guidance for experiments to investigate and engineer exciton self-trapping in relevant materials.

Solvent- and Wavelength-Dependent Photoluminescence Relaxation Dynamics of Carbon Nanotube sp3 Defect States

Photoluminescent sp³ defect states introduced to single wall carbon nanotubes (SWCNTs) through low-level covalent functionalization create new photophysical behaviors and functionality as a result of defect sites acting as exciton traps. Evaluation of relaxation dynamics in varying dielectric environments can aid in advancing a more complete description of defect-state relaxation pathways and electronic structure. Here, we exploit helical wrapping polymers as a route to suspending (6,5) SWCNTs covalently functionalized with 4-methoxybenzene in solvent systems including H₂O, D₂O, methanol, dimethylformamide, tetrahydrofuran, and toluene, spanning a range of dielectric constants from 80 to 3. Defect-state photoluminescence decays were measured as a function of emission wavelength and solvent environment. Emission decays are biexponential, with short lifetime components on the order of 65 ps and long components ranging from around 100 to 350 ps. Both short and long decay components increase as emission wavelength increases, while only the long lifetime component shows a solvent dependence. We demonstrate that the wavelength dependence is a consequence of thermal detrapping of defect-state excitons to produce mobile E₁₁ excitons, providing an important mechanism for loss of defect-state population. Deeper trap states (i.e., those emitting at longer wavelengths) result in a decreased rate for thermal loss. The solvent-independent behavior of the short lifetime component is consistent with its assignment as the characteristic time for redistribution of exciton population between bright and dark defect states. The solvent dependence of the long lifetime component is shown to be consistent with relaxation via an electronic to vibrational energy transfer mechanism, in which energy is resonantly lost to solvent vibrations in a complementary mechanism to multiphonon decay processes.

Correction Scheme for Comparison of Computed and Experimental Optical Transition Energies in Functionalized Single-Walled Carbon Nanotubes

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) introduces red-shifted emission features in the near-infrared spectral range due to exciton localization around the defect site. Such chemical modifications increase their potential use as near-infrared emitters and single-photon sources in telecommunications applications. Density functional theory (DFT) studies using finite-length tube models have been used to calculate their optical transition energies. Predicted energies are typically blue-shifted compared to experiment due to methodology errors including imprecise self-interaction corrections in the density functional and finite-size basis sets. Furthermore, artificial quantum confinement in finite models cannot be corrected by a constant-energy shift since they depend on the degree of exciton localization. Herein, we present a method that corrects the emission energies predicted by time-dependent DFT. Confinement and methodology errors are separately estimated using experimental data for unmodified tubes. Corrected emission energies are in remarkable agreement with experiment, suggesting the value of this straightforward method toward predicting and interpreting the optical features of functionalized SWCNTs.