Blinking statistics in single semiconductor nanocrystal quantum dots

Shimizu, Ken D.; Neuhauser, R. G.; Leatherdale, C. A.; Empedocles, S. A.; Woo, Wing-Keung; Bawendi, Moungi G.

doi:10.1103/physrevb.63.205316

Cited by 571 publications

(871 citation statements)

References 22 publications

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“…At the transition to the nonstationary phase (ν ¼ 2), the stationary result diverges. periods and remain dark during others [63][64][65]. The durations of these on periods and off periods are found to be distributed according to a power law whose exponent is such that the average on and off time is infinite (i.e., of the order of the measurement time), leading to aging in the intensity autocorrelation function [7,66].…”

Section: Blinking Quantum Dots and Lévy Walkmentioning

confidence: 99%

Scaling Green-Kubo Relation and Application to Three Aging Systems

et al. 2014

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The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula that is valid for systems with longrange or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function hvðt þ τÞvðtÞi asymptotically exhibits a certain scaling behavior and the diffusion is anomalous, hx 2 ðtÞi ≃ 2D ν t ν . We show how both the anomalous diffusion coefficient D ν and the exponent ν can be extracted from this scaling form. Our scaling GreenKubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale-invariant dynamics. This includes stationary systems with slowly decaying power-law correlations, as well as aging systems, systems whose properties depend on the age of the system. Even for systems that are stationary in the long-time limit, we find that the long-time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity D ν is not unique, and we determine its values, respectively, for a stationary or nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells, and the Lévy walk with numerous applications, in particular, blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.

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Section: Blinking Quantum Dots and Lévy Walkmentioning

confidence: 99%

Scaling Green-Kubo Relation and Application to Three Aging Systems

et al. 2014

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“…169 It is also possible to observe additional unique behavior such as fluorescence intermittency (i.e., blinking) that cannot be observed for bulk samples. 170 Ensemble studies benefit significantly from the clarification of fundamental photophysical behavior that is exposed on the single particle level, which has catalyzed single molecule studies for many fluorescent systems including dyes, 171-174 polymer chains, 175,176 proteins, [177][178][179] semiconductor quantum dots, 170,180,181 and single-walled carbon nanotubes. 72,77,182 The observation of fluorescence from individual SWNTs was first reported in 2003 and, importantly, confirmed spectral assignments of (n,m) made on the ensemble level.…”

Section: Principles Of Single Molecule Spectroscopymentioning

confidence: 99%

Photophysics of Individual Single-Walled Carbon Nanotubes

2008

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Single-walled carbon nanotubes (SWNTs) are cylindrical graphitic molecules that have remained at the forefront of nanomaterials research since 1991, largely due to their exceptional and unusual mechanical, electrical, and optical properties. The motivation for understanding how nanotubes interact with light (i.e., SWNT photophysics) is both fundamental and applied. Individual nanotubes may someday be used as superior near-infrared fluorophores, biological tags and sensors, and components for ultrahigh-speed optical communications systems. Establishing an understanding of basic nanotube photophysics is intrinsically significant and should enable the rapid development of such innovations. Unlike conventional molecules, carbon nanotubes are synthesized as heterogeneous samples, composed of molecules with different diameters, chiralities, and lengths. Because a nanotube can be either metallic or semiconducting depending on its particular molecular structure, SWNT samples are also mixtures of conductors and semiconductors. Early progress in understanding the optical characteristics of SWNTs was limited because nanotubes aggregate when synthesized, causing a mixing of the energy states of different nanotube structures. Recently, significant improvements in sample preparation have made it possible to isolate individual nanotubes, enabling many advances in characterizing their optical properties. In this Account, single-molecule confocal microscopy and spectroscopy were implemented to study the fluorescence from individual nanotubes. Single-molecule measurements naturally circumvent the difficulties associated with SWNT sample inhomogeneities. Intrinsic SWNT photoluminescence has a simple narrow Lorentzian line shape and a polarization dependence, as expected for a one-dimensional system. Although the local environment heavily influences the optical transition wavelength and intensity, single nanotubes are exceptionally photostable. In fact, they have the unique characteristic that their single molecule fluorescence intensity remains constant over time; SWNTs do not “blink” or photobleach under ambient conditions. In addition, transient absorption spectroscopy was used to examine the relaxation dynamics of photoexcited nanotubes and to elucidate the nature of the SWNT excited state. For metallic SWNTs, very fast initial recovery times (300–500 fs) corresponded to excited-state relaxation. For semiconducting SWNTs, an additional slower decay component was observed (50–100 ps) that corresponded to electron–hole recombination. As the excitation intensity was increased, multiple electron–hole pairs were generated in the SWNT; however, these e−h pairs annihilated each other completely in under 3 ps. Studying the dynamics of this annihilation process revealed the lifetimes for one, two, and three e−h pairs, which further confirmed that the photoexcitation of SWNTs produces not free electrons but rather one-dimensional bound electron–hole pairs (i.e., excitons). In summary, nanotube photophysics is a rapidly developing area o...

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“…The development of techniques in probing single molecules has provided a tool to study its intrinsic properties and its interaction with the surroundings. One of the unusual phenomena observed in nanoparticles is fluorescence intermittency of quantum dots and the power-law statistics for the duration time for the ''on'' an ''off'' events [1][2][3][4][5][6][7][8][9][10]. Supplementing previous theoretical studies [6,7,[11][12][13][14][15][16], a mechanism is provided in this Letter to elucidate these phenomena.…”

mentioning

confidence: 91%

Diffusion-Controlled Electron Transfer Processes and Power-Law Statistics of Fluorescence Intermittency of Nanoparticles

2005

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A mechanism involving diffusion-controlled electron transfer processes in Debye and non-Debye dielectric media is proposed to elucidate the power-law distribution for the lifetime of a blinking quantum dot. This model leads to two complementary regimes of power law with a sum of the exponents equal to 2, and to a specific value for the exponent in terms of a distribution of the diffusion correlation times. It also links the exponential bending tail with energetic and kinetic parameters. DOI: 10.1103/PhysRevLett.95.107401 PACS numbers: 78.67.Bf, 73.21.La, 73.63.Kv, 78.67.Hc Recent advances in nanoscience and nanotechnology and their potential applications have generated wide interest. The development of techniques in probing single molecules has provided a tool to study its intrinsic properties and its interaction with the surroundings. One of the unusual phenomena observed in nanoparticles is fluorescence intermittency of quantum dots and the power-law statistics for the duration time for the ''on'' an ''off'' events [1][2][3][4][5][6][7][8][9][10]. Supplementing previous theoretical studies [6,7,[11][12][13][14][15][16]], a mechanism is provided in this Letter to elucidate these phenomena. This model involves diffusioncontrolled charge transfer processes in energy or configuration space [17,18]. For fast diffusion, the model yields the well-known simple exponential decay. However, in the regime of slow diffusion, the model leads naturally to a power-law behavior. To be more general, we consider anomalous diffusion in a non-Debye dielectric medium with a distribution of diffusion correlation times. There exists in the literature two approaches, partial ordering prescription (POP) with a time-dependent but nonretarded diffusion coefficient, and chronological ordering prescription (COP) with convolution of a time-retarded diffusion kernel [19]. POP is more commonly used in treating electron transfer reactions [20], These diffusion-controlled reaction models provide physical insight into the specific value of the exponent, a reason for the bending tail at longer times, and the connection of the bending factor to the activation energy of the electron transfer rate constant.In this work, one models stochastic processes in the energy or configuration space that represent the fluctuating interactions of a probe (a single molecule or a quantum dot) with its surrounding heat bath (supporting substrate or anchored organic molecules). We consider a POP type 1D non-Markovian equation, with a population sink at the potential energy crossing (Q Q c ) between U 1 Q for the ''light'' state j1i and U 2 Q for the ''dark'' state j2i. One hasOne can obtain the Green function for sink-free diffusion in a harmonic potential q 2 =2 as [20]where the diffusion constant D k t is related to the dielectric response function s and the dielectric permittivity " s by [20]For a Debye medium CD . At times t much longer than the diffusion correlation time, however, 2 t becomes a constant as the system approaches thermal equilibrium. The asym...

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Blinking statistics in single semiconductor nanocrystal quantum dots

Cited by 571 publications

References 22 publications

Scaling Green-Kubo Relation and Application to Three Aging Systems

Scaling Green-Kubo Relation and Application to Three Aging Systems

Photophysics of Individual Single-Walled Carbon Nanotubes

Diffusion-Controlled Electron Transfer Processes and Power-Law Statistics of Fluorescence Intermittency of Nanoparticles

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