Unifying the low-temperature photoluminescence spectra of carbon nanotubes: the role of acoustic phonon confinement

Reconciling nonlinear dissipation with the bilinear model of two Brownian particles

The Brownian motion of a single particle is a paradigmatic model of the nonequilibrium dynamics of dissipative systems. In the system-plus-reservoir approach, one can derive the particle's equations of motion from the reversible dynamics of the system coupled to a bath of oscillators representing its thermal environment. However, extending the system-plus-reservoir approach to multiple particles in a collective environment is not straightforward, and conflicting models have been proposed to that end. Here, we set out to reconcile some aspects of the nonlinear and the bilinear models of two Brownian particles. We show how the nonlinear dissipation originally derived from exponential system-reservoir couplings can alternatively be obtained from the bilinear Lagrangian, with a modified spectral function that explicitly depends on the distance between the particles. We discuss applications to the contexts of anomalous diffusion and of hydrodynamic interactions. Our results thus broaden the applicability of the bilinear model.

Electroluminescence from Single-Walled Carbon Nanotubes with Quantum Defects

Individual single-walled carbon nanotubes with covalent sidewall defects have emerged as a class of photon sources whose photoluminescence spectra can be tailored by the carbon nanotube chirality and the attached functional group/molecule. Here we present electroluminescence spectroscopy data from single-tube devices based on (7, 5) carbon nanotubes, functionalized with dichlorobenzene molecules, and wired to graphene electrodes. We observe electrically generated, defect-induced emissions that are controllable by electrostatic gating and strongly red-shifted compared to emissions from pristine nanotubes. The defect-induced emissions are assigned to excitonic and trionic recombination processes by correlating electroluminescence excitation maps with electrical transport and photoluminescence data. At cryogenic conditions, additional gate-dependent emission lines appear, which are assigned to phonon-assisted hot-exciton electroluminescence from quasi-levels. Similar results were obtained with functionalized (6, 5) nanotubes. We also compare functionalized (7, 5) electroluminescence data with photoluminescence of pristine and functionalized (7, 5) nanotubes redox-doped using gold(III) chloride solution. This work shows that electroluminescence excitation is selective toward neutral defect-state configurations with the lowest transition energy, which in combination with gate-control over neutral versus charged defect-state emission leads to high spectral purity.

Recent Advances in Structure Separation of Single-Wall Carbon Nanotubes and Their Application in Optics, Electronics, and Optoelectronics

Structural control of single-wall carbon nanotubes (SWCNTs) with uniform properties is critical not only for their property modulation and functional design but also for applications in electronics, optics, and optoelectronics. To achieve this goal, various separation techniques have been developed in the past 20 years through which separation of high-purity semiconducting/metallic SWCNTs, single-chirality species, and even their enantiomers have been achieved. This progress has promoted the property modulation of SWCNTs and the development of SWCNT-based optoelectronic devices. Here, the recent advances in the structure separation of SWCNTs are reviewed, from metallic/semiconducting SWCNTs, to single-chirality species, and to enantiomers by several typical separation techniques and the application of the corresponding sorted SWCNTs. Based on the separation procedure, efficiency, and scalability, as well as, the separable SWCNT species, purity, and quantity, the advantages and disadvantages of various separation techniques are compared. Combined with the requirements of SWCNT application, the challenges, prospects, and development direction of structure separation are further discussed.

2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges

A grand family of two-dimensional (2D) materials and their heterostructures have been discovered through the extensive experimental and theoretical efforts of chemists, material scientists, physicists, and technologists. These pioneering works contribute to realizing the fundamental platforms to explore and analyze new physical/chemical properties and technological phenomena at the micro-nano-pico scales. Engineering 2D van der Waals (vdW) materials and their heterostructures via chemical and physical methods with a suitable choice of stacking order, thickness, and interlayer interactions enable exotic carrier dynamics, showing potential in high-frequency electronics, broadband optoelectronics, low-power neuromorphic computing, and ubiquitous electronics. This comprehensive review addresses recent advances in terms of representative 2D materials, the general fabrication methods, and characterization techniques and the vital role of the physical parameters affecting the quality of 2D heterostructures. The main emphasis is on 2D heterostructures and 3D-bulk (3D) hybrid systems exhibiting intrinsic quantum mechanical responses in the optical, valley, and topological states. Finally, we discuss the universality of 2D heterostructures with representative applications and trends for future electronics and optoelectronics (FEO) under the challenges and opportunities from physical, nanotechnological, and material synthesis perspectives.

Quantum Light Emission from Coupled Defect States in DNA-Functionalized Carbon Nanotubes

Solid-state single-photon sources are essential building blocks for quantum photonics and quantum information technologies. This study demonstrates promising single-photon emission from quantum defects generated in single-wall carbon nanotubes (SWCNTs) by covalent reaction with guanine nucleotides in their single-stranded DNA coatings. Low-temperature photoluminescence spectroscopy and photon-correlation measurements on individual guanine-functionalized SWCNTs (GF-SWCNTs) indicate that multiple, closely spaced guanine defect sites within a single ssDNA strand collectively form an exciton trapping potential that supports a localized quantum state capable of room-temperature single-photon emission. In addition, exciton traps from adjacent ssDNA strands are weakly coupled to give cross-correlations between their separate photon emissions. Theoretical modeling identifies coupling mechanism as a capture of band-edge excitons. Because the spatial pattern of nanotube functionalization sites can be readily controlled by selecting ssDNA base sequences, GF-SWCNTs should become a versatile family of quantum light emitters with engineered properties.

Low-Temperature Electroluminescence Excitation Mapping of Excitons and Trions in Short-Channel Monochiral Carbon Nanotube Devices

Single-walled carbon nanotubes as emerging quantum-light sources may fill a technological gap in silicon photonics due to their potential use as near-infrared, electrically driven, classical or nonclassical emitters. Unlike in photoluminescence, where nanotubes are excited with light, electrical excitation of single tubes is challenging and heavily influenced by device fabrication, architecture, and biasing conditions. Here we present electroluminescence spectroscopy data of ultra-short-channel devices made from (9,8) carbon nanotubes emitting in the telecom band. Emissions are stable under current biasing, and no enhanced suppression is observed down to 10 nm gap size. Low-temperature electroluminescence spectroscopy data also reported exhibit cold emission and line widths down to 2 meV at 4 K. Electroluminescence excitation maps give evidence that carrier recombination is the mechanism for light generation in short channels. Excitonic and trionic emissions can be switched on and off by gate voltage, and corresponding emission efficiency maps were compiled. Insights are gained into the influence of acoustic phonons on the line width, absence of intensity saturation and exciton-exciton annihilation, environmental effects such as dielectric screening and strain on the emission wavelength, and conditions to suppress hysteresis and establish optimum operation conditions.

Superlocalization of Excitons in Carbon Nanotubes at Cryogenic Temperature

At cryogenic temperature and at the single emitter level, the optical properties of single-wall carbon nanotubes depart drastically from that of a one-dimensional (1D) object. In fact, the (usually unintentional) localization of excitons in local potential wells leads to nearly 0D behaviors such as photon antibunching, spectral diffusion, inhomogeneous broadening, etc. Here, we present a hyperspectral imaging of this spontaneous exciton localization effect at the single nanotube level using a super-resolved optical microscopy approach. We report on the statistical distribution of the trap localization, depth, and width. We use a quasi-resonant photoluminescence excitation approach to probe the confined quantum states. Numerical simulations of the quantum states and exciton diffusion show that the excitonic states are deeply modified by the interface disorder inducing a remarkable discretization of the excitonic absorption spectrum and a quenching of the free 1D exciton absorption.

Intrinsic limits of defect-state photoluminescence dynamics in functionalized carbon nanotubes

Defect states introduced to single wall carbon nanotubes (SWCNTs) by covalent functionalization give rise to novel photophysics and are showing promise as sources of room-temperature quantum emission of interest for quantum information technologies. Evaluation of their ultimate potential for such needs requires a knowledge of intrinsic dynamic and coherence behaviors. Here we probe population relaxation and dephasing time (T1 and T2, respectively) of defect states following deposition of functionalized SWCNTs on polystyrene substrates that are subjected to an isopropanol rinse to remove surfactant. Low-temperature (4 K) photo-luminescence linewidths (∼100 μeV) following surfactant removal are a factor of ten narrower than those for unrinsed SWCNTs. Measured recombination lifetimes, on the order of 1.5 ns, compare well with those estimated from DFT calculations, indicating that the intrinsic radiatively-limited lifetime is approached following this sample treatment. Dephasing times evaluated directly through an interferometric approach compare closely to those established by photoluminescence linewidths. Dephasing times as high as 12 ps are found; a factor of up to 6 times greater than those evaluated for band-edge exciton states. Such enhancement of dephasing and photoluminescence lifetime behavior is a direct consequence of exciton localization at the SWCNT defect sites.

Carbon nanotubes as emerging quantum-light sources

Progress in quantum computing and quantum cryptography requires efficient, electrically triggered, single-photon sources at room temperature in the telecom wavelengths. It has been long known that semiconducting single-wall carbon nanotubes (SWCNTs) display strong excitonic binding and emit light over a broad range of wavelengths, but their use has been hampered by a low quantum yield and a high sensitivity to spectral diffusion and blinking. In this Perspective, we discuss recent advances in the mastering of SWCNT optical properties by chemistry, electrical contacting and resonator coupling towards advancing their use as quantum light sources. We describe the latest results in terms of single-photon purity, generation efficiency and indistinguishability. Finally, we consider the main fundamental challenges stemming from the unique properties of SWCNTs and the most promising roads for SWCNT-based chip integrated quantum photonic sources.

Suppression of exciton dephasing in sidewall-functionalized carbon nanotubes embedded into metallo-dielectric antennas

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) is a promising route to enhance the quantum yield of exciton emission and can lead to single-photon emission at room temperature. However, the spectral linewidth of the defect-related E11* emission remains rather broad. Here, we systematically investigate the low-temperature exciton emission of individual SWCNTs that have been dispersed with sodium-deoxycholate (DOC) and polyfluorene (PFO-BPy), are grown by laser vaporization (LV) or by CoMoCat techniques and are functionalized with oxygen as well as 3,5-dichlorobenzene groups. The E11 excitons in oxygen-functionalized SWCNTs remain rather broad with up to 10 meV linewidth while exciton emission from 3,5-dichlorobenzene functionalized SWCNTs is found to be about one order of magnitude narrower. In all cases, wrapping with PFO-BPy provides significantly better protection against pump induced dephasing compared to DOC. To further study the influence of exciton localization on pump-induced dephasing, we have embedded the functionalized SWCNTs into metallo-dielectric antenna cavities to maximize light collection. We show that 0D excitons attributed to the E11* emission of 3,5-dichlorobenzene quantum defects of LV-grown SWCNTs can display near resolution-limited linewidths down to 35 μeV. Interestingly, these 0D excitons give rise to a 3-fold suppressed pump-induced exciton dephasing compared to the E11 excitons in the same SWCNT. These findings provide a foundation to build a unified description of the emergence of novel optical behavior from the interplay of covalently introduced defects, dispersants, and exciton confinement in SWCNTs and might further lead to the realization of indistinguishable photons from carbon nanotubes.

Interplay of spectral diffusion and phonon-broadening in individual photo-emitters: the case of carbon nanotubes

At cryogenic temperatures, the photoluminescence (PL) spectrum of nano-emitters may still be significantly broadened due to interactions with the environment. The interplay of spectral diffusion (SD) and phonon broadening in this context is still a debated issue. Singlewall carbon nanotubes (SWNTs) are a particularly relevant system to address this topic as they show intense spectral diffusion and undergo a high exciton-phonon coupling due to their one-dimensional geometry. Here, we investigate the correlations between the spectral diffusion of the main line and that of the wings in SWNTs quantitatively and demonstrate that the photoluminescence spectrum undergoes spectral jumps as a whole, without distortions. This behavior suggests that the spectral shape of SWNT PL is defined by exciton-phonon interactions and that spectral diffusion results in an additional flat broadening. The methodology developed here can be used to investigate a broad range of non-Lorentzian emitters undergoing spectral diffusion.

Low-Temperature Single Carbon Nanotube Spectroscopy of sp3 Quantum Defects

Aiming to unravel the relationship between chemical configuration and electronic structure of sp³ defects of aryl-functionalized (6,5) single-walled carbon nanotubes (SWCNTs), we perform low-temperature single nanotube photoluminescence (PL) spectroscopy studies and correlate our observations with quantum chemistry simulations. We observe sharp emission peaks from individual defect sites that are spread over an extremely broad, 1000-1350 nm, spectral range. Our simulations allow us to attribute this spectral diversity to the occurrence of six chemically and energetically distinct defect states resulting from topological variation in the chemical binding configuration of the monovalent aryl groups. Both PL emission efficiency and spectral line width of the defect states are strongly influenced by the local dielectric environment. Wrapping the SWCNT with a polyfluorene polymer provides the best isolation from the environment and yields the brightest emission with near-resolution limited spectral line width of 270 μeV, as well as spectrally resolved emission wings associated with localized acoustic phonons. Pump-dependent studies further revealed that the defect states are capable of emitting single, sharp, isolated PL peaks over 3 orders of magnitude increase in pump power, a key characteristic of two-level systems and an important prerequisite for single-photon emission with high purity. These findings point to the tremendous potential of sp³ defects in development of room temperature quantum light sources capable of operating at telecommunication wavelengths as the emission of the defect states can readily be extended to this range via use of larger diameter SWCNTs.

Solitary Oxygen Dopant Emission from Carbon Nanotubes Modified by Dielectric Metasurfaces

All-dielectric metasurfaces made from arrays of high index nanoresonators supporting strong magnetic dipole modes have emerged as a low-loss alternative to plasmonic metasurfaces. Here we use oxygen-doped single-walled carbon nanotubes (SWCNTs) as quantum emitters and couple them to silicon metasurfaces to study effects of the magnetic dipole modes of the constituent nanoresonators on the photoluminescence (PL) of individual SWCNTs. We find that when in resonance, the magnetic mode of the silicon nanoresonators can lead to a moderate average PL enhancement of 0.8-4.0 of the SWCNTs, accompanied by an average increase in the radiative decay rate by a factor of 1.5-3.0. More interestingly, single dopant polarization experiments show an anomalous photoluminescence polarization rotation by coupling individual SWCNTs to silicon nanoresonators. Numerical simulations indicate that this is caused by modification of near-field polarization distribution at certain areas in the proximity of the silicon nanoresonators at the excitation wavelength, thus presenting an approach to control emission polarization. These findings indicate silicon nanoresonators as potential building blocks of quantum photonic circuits capable of manipulating PL intensity and polarization of single photon sources.

Quantum dot-like excitonic behavior in individual single walled-carbon nanotubes

Semiconducting single-walled carbon nanotubes are one-dimensional materials with great prospects for applications such as optoelectronic and quantum information devices. Yet, their optical performance is hindered by low fluorescent yield. Highly mobile excitons interacting with quenching sites are attributed to be one of the main non-radiative decay mechanisms that shortens the exciton lifetime. In this paper we report on time-integrated photoluminescence measurements on individual polymer wrapped semiconducting carbon nanotubes. An ultra narrow linewidth we observed demonstrates intrinsic exciton dynamics. Furthermore, we identify a state filling effect in individual carbon nanotubes at cryogenic temperatures as previously observed in quantum dots. We propose that each of the CNTs is segmented into a chain of zero-dimensional states confined by a varying local potential along the CNT, determined by local environmental factors such as the amount of polymer wrapping. Spectral diffusion is also observed, which is consistent with the tunneling of excitons between these confined states.

Widely Tunable Single-Photon Source from a Carbon Nanotube in the Purcell Regime

The narrow emission of a single carbon nanotube at low temperature is coupled to the optical mode of a fiber microcavity using the built-in spatial and spectral matching brought by this flexible geometry. A thorough cw and time-resolved investigation of the very same emitter both in free space and in cavity shows an efficient funneling of the emission into the cavity mode together with a strong emission enhancement corresponding to a Purcell factor of up to 5. At the same time, the emitted photons retain a strong sub-Poissonian statistics. By exploiting the cavity feeding effect on the phonon wings, we locked the emission of the nanotube at the cavity resonance frequency, which allowed us to tune the frequency over a 4 THz band while keeping an almost perfect antibunching. By choosing the nanotube diameter appropriately, this study paves the way to the development of carbon-based tunable single-photon sources in the telecom bands.

Ubiquity of Exciton Localization in Cryogenic Carbon Nanotubes

We present photoluminescence studies of individual semiconducting single-wall carbon nanotubes at room and cryogenic temperatures. From the analysis of spatial and spectral features of nanotube photoluminescence, we identify characteristic signatures of unintentional exciton localization. Moreover, we quantify the energy scale of exciton localization potentials as ranging from a few to a few tens of millielectronvolts and stemming from both environmental disorder and shallow covalent side-wall defects. Our results establish disorder-induced crossover from the diffusive to the localized regime of nanotube excitons at cryogenic temperatures as a ubiquitous phenomenon in micelle-encapsulated and as-grown carbon nanotubes.

Quantum emission from hexagonal boron nitride monolayers

Artificial atomic systems in solids are widely considered the leading physical system for a variety of quantum technologies, including quantum communications, computing and metrology. To date, however, room-temperature quantum emitters have only been observed in wide-bandgap semiconductors such as diamond and silicon carbide, nanocrystal quantum dots, and most recently in carbon nanotubes. Single-photon emission from two-dimensional materials has been reported, but only at cryogenic temperatures. Here, we demonstrate room-temperature, polarized and ultrabright single-photon emission from a colour centre in two-dimensional hexagonal boron nitride. Density functional theory calculations indicate that vacancy-related defects are a probable source of the emission. Our results demonstrate the unprecedented potential of van der Waals crystals for large-scale nanophotonics and quantum information processing.

Strong Acoustic Phonon Localization in Copolymer-Wrapped Carbon Nanotubes

Understanding and controlling exciton-phonon interactions in carbon nanotubes has important implications for producing efficient nanophotonic devices. Here we show that laser vaporization-grown carbon nanotubes display ultranarrow luminescence line widths (120 μeV) and well-resolved acoustic phonon sidebands at low temperatures when dispersed with a polyfluorene copolymer. Remarkably, we do not observe a correlation of the zero-phonon line width with (13)C atomic concentration, as would be expected for pure dephasing of excitons with acoustic phonons. We demonstrate that the ultranarrow and phonon sideband-resolved emission spectra can be fully described by a model assuming extrinsic acoustic phonon localization at the nanoscale, which holds down to 6-fold narrower spectral line width compared to previous work. Interestingly, both exciton and acoustic phonon wave functions are strongly spatially localized within 5 nm, possibly mediated by the copolymer backbone, opening future opportunities to engineer dephasing and optical bandwidth for applications in quantum photonics and cavity optomechanics.

Influence of exciton dimensionality on spectral diffusion of single-walled carbon nanotubes

We study temporal evolution of photoluminescence (PL) spectra from individual single-walled carbon nanotubes (SWCNTs) at cryogenic and room temperatures. Sublinear and superlinear correlations between fluctuating PL spectral positions and line widths are observed at cryogenic and room temperatures, respectively. We develop a simple model to explain these two different spectral diffusion behaviors in the framework of quantum-confined Stark effect (QCSE) caused by surface charges trapped in the vicinity of SWCNTs. We show that the wave function properties of excitons, namely, localization at cryogenic temperature and delocalization at room temperature, play a critical role in defining sub- and superlinear correlations. Room temperature PL spectral positions and line widths of SWCNTs coupled to gold dimer nanoantennas on the other hand exhibit sublinear correlations, indicating that excitonic emission mainly originates from nanometer range regions and excitons appear to be localized. Our numerical simulations show that such apparent localization of excitons results from plasmonic confinement of excitation and an enhancement of decay rates in the gap of the dimer nanoantennas.

Electronic structure and chemical nature of oxygen dopant states in carbon nanotubes

We performed low temperature photoluminescence (PL) studies on individual oxygen-doped single-walled carbon nanotubes (SWCNTs) and correlated our observations to electronic structure simulations. Our experiment reveals multiple sharp asymmetric emission peaks at energies 50-300 meV red-shifted from that of the E11 bright exciton peak. Our simulation suggests an association of these peaks with deep trap states tied to different specific chemical adducts. In addition, oxygen doping is also observed to split the E11 exciton into two or more states with an energy splitting <40 meV. We attribute these states to dark states that are brightened through defect-induced symmetry breaking. While the wave functions of these brightened states are delocalized, those of the deep-trap states are strongly localized and pinned to the dopants. These findings are consistent with our experimental observation of asymmetric broadening of the deep trap emission peaks, which can result from interaction between pinned excitons and one-dimensional phonons. Exciton pinning also increases the sensitivity of the deep traps to the local dielectric environment, leading to a large inhomogeneous broadening. Observations of multiple spectral features on single nanotubes indicate the possibility of different chemical adducts coexisting on a given nanotube.