An atlas of carbon nanotube optical transitions

Abstract

Electron-electron interactions are significantly enhanced in one-dimensional systems, and single-walled carbon nanotubes provide a unique opportunity for studying such interactions and the related many-body effects in one dimension. However, single-walled nanotubes can have a wide range of diameters and hundreds of different structures, each defined by its chiral index (n,m), where n and m are integers that can have values from zero up to 30 or more. Moreover, one-third of these structures are metals and two-thirds are semiconductors, and they display optical resonances at many different frequencies. Systematic studies of many-body effects in nanotubes would therefore benefit from the availability of a technique for identifying the chiral index of a nanotube based on a measurement of its optical resonances, and vice versa. Here, we report the establishment of a structure-property 'atlas' for nanotube optical transitions based on simultaneous electron diffraction measurements of the chiral index and Rayleigh scattering measurements of the optical resonances of 206 different single-walled nanotube structures. The nanotubes, which were suspended across open slit structures on silicon substrates, had diameters in the range 1.3-4.7 nm. We also use this atlas as a starting point for a systematic study of many-body effects in the excited states of single-walled nanotubes. We find that electron-electron interactions shift the optical resonance energies by the same amount for both metallic and semiconducting nanotubes, and that this shift (which corresponds to an effective Fermi velocity renormalization) increases monotonically with nanotube diameter. This behaviour arises from two sources: an intriguing cancellation of long-range electron-electron interaction effects, and the dependence of short-range electron-electron interactions on diameter.

High-throughput optical imaging and spectroscopy of individual carbon nanotubes in devices

“…We compare these transition energies to the atlas of suspended nanotube optical transitions to assign the nanotube chirality 10 . To account for the dielectric screening effect from the substrate, a 40 meV redshift is added to the transition energies from the atlas 32 identify the three nanotubes with chirality of (20,6), (22,16), and (26,22).…”

“…They are semiconducting, metallic and semiconducting nanotubes with diameters of 1.8, 2.6 and 3.3 nm, respectively. Energy (eV) (22,16) Semiconduting: (26,10) …”

“…Currently nanotube research faces two outstanding challenges: (1) achieving chirality-controlled nanotube growth and (2) understanding chirality-dependent nanotube device physics. Addressing these challenges requires, respectively, high-throughput determination of nanotube chirality distribution on growth substrates and in-situ characterization of nanotube electronic structure in operating devices.Direct optical imaging and spectroscopy is well suited for these goals [8][9][10][11][12][13][14] , but its realization for single nanotubes on substrates or in devices has been an outstanding challenge due to small nanotube signal and unavoidable environment background. Here we demonstrate for the first time high-throughput real-time optical imaging and broadband spectroscopy of individual nanotubes in devices using a polarization-based microscopy combined with supercontinuum laser illumination.…”

“…Direct optical imaging and spectroscopy is well suited for these goals [8][9][10][11][12][13][14] , but its realization for single nanotubes on substrates or in devices has been an outstanding challenge due to small nanotube signal and unavoidable environment background. Here we demonstrate for the first time high-throughput real-time optical imaging and broadband spectroscopy of individual nanotubes in devices using a polarization-based microscopy combined with supercontinuum laser illumination.…”

“…Highthroughput and in-situ chirality and electronic structural characterization of individual carbon nanotubes is crucial for addressing these challenges. Optical imaging and spectroscopy has unparalleled throughput and specificity [8][9][10][11][12][13][14] , but its realization for single nanotubes on substrates or in devices has long been an outstanding challenge.…”