With the aim to study and understand the optical propertiesof GQD materials, we performed the bottom-up synthesisof different families of nanoparticles exhibiting controlled shapes and edges. Using absorption, steady-state and time-resolved photoluminescence and photoluminescence excitation (PLE) spectroscopy, we try to establish the intrinsic optical propertiesof the GQDs and understand how the structure influences the properties. Here we present the synthesisof a new series of rod-shaped graphene nanoparticles (GNRods); we also present the singlephotonemissionpropertiesof a triangle-shaped GQD (Figure 1). References
Recently, we reported on the synthesisandsinglephotonemissionpropertiesof triangular-shaped GQDs. 5 While, this initial report focused on functionalized nanoparticles, we now turn to non-
functionalized graphenequantumdots that are in terms of structure closer to real graphene. Here, we described the synthesis, the dispersion and optical propertiesof a series of rod-shaped particles and we studied the structure-properties relationship in these graphenequantumdots. To this end, we designed a series of GQDs with a given edge type and by changing only one parameter (one dimension, namely the length or the width – Figure 1), we expect to follow simply the evolution of the optical properties.
CdSe/ZnSe quantumdots (QDs) have attracted much in- terest due to their possible application in optoelectronics. 1 In the 90s, the basic application for CdSe/ZnSe QDs was con- nected to short wave emitters and manufacturing of QDs laser. Recently, CdSe QDs have gained more interest as sources ofsinglephoton operating at room temperature. 2 II–VI self-assembled QDs such as CdSe/ZnSe are promising system for single-photonemission in the blue–green range. 3 The optical propertiesof QDs systems depend on many pa- rameters such as morphology, chemical composition, and chemical environment. 4 In contrast to III-V materials like InAs/GaAs, the formation of CdSe QDs differs significantly from the Stransky-Krastanov growth mode 5 so that inter- diffusion and/or segregation phenomena based on Cd-Zn exchange 6 , 7 may take place in the QD formation mechanism. In order to obtain specific properties, comprehensive nanoscale information about the dotsand their surroundings are required. However, the chemical analysis of embedded QDs is challenging. Transmission electron microscopy (TEM) can give first estimation of the degree of intermixing between CdSe and ZnSe layers. The key strength of TEM is that it can directly visualize the atomic structure of a mate- rial, and a recent approach has aimed at analyzing the CdSe QDs composition using the change in lattice parameters in high resolution TEM (HRTEM) images. 8 , 9 This is an indirect method to derive information about composition. On the other hand, the strength of Atom Probe Tomography (APT) is its ability to give directly information about the 3D com- position of all chemical elements at atomic scale. 10 Thus, APT has been used recently to investigate the composition of III-V QDs, 11 II-VI layers, and II-VI/III-V interface at atomic scale. 12
of its edges, the bottom-up approach is the relevant way to proceed 3 , 4 .
With the aim to study and understand the optical propertiesof GQD materials, we
performed the bottom-up synthesis 5 of different families of nanoparticles exhibiting controlled
shapes and edges. Because of their strong aromatic character graphene nanoparticles tend to aggregate in solution; however, for future application it is of high interest to be able to discriminate the intrinsic absorption andemissionof the GQDs from those of aggregates. For example, we observed that by STM and polarized microscopy the GQDs bearing alkyl chains are forming columnar structures with liquid crystal properties in solvents. Here, we study the optical propertiesofgraphenequantumdots as a function of their individualization. Using absorption, steady-state and time-resolved photoluminescence and photoluminescence excitation (PLE) spectroscopy, we try to establish the intrinsic optical propertiesof the GQDs and understand how the structure influences the properties.
The optical study of large PAHs started with the study of the absorption andemissionof HBC. 187 This compound exhibits a large emission band at 500 nm but its low solubility (especially when the molecule is not functionalized with alkyl chains) makes difficult the identification of the intrinsic emissionpropertiesof HBC versus the emissionpropertiesof aggregates necessarily present in solution. In 2012, J. N. Coleman studied the dispersion of HBC in organic solvents like N-cyclohexylpyrrolidone (CHP) and tetrahydrofurane (THF). 188 They verified the quality of the dispersion by measuring the absorption, the emissionand performing the photoluminescence excitation (PLE) map (Figure 1.29). The map is done by measuring the emission spectra for every excitation. The PL intensity is coded with color from blue to red. For the PL and the PLE, narrow peaks are typical of a good dispersion because aggregation tends to broaden the peaks due to the inter-molecular energy and/or electron transfers. The result in Figure 1.29 on organic solvents clearly shows that CHP is a better solvent for HBC than THF.
With the aim to study and understand the optical propertiesof GQD materials, we performed the bottom-up synthesis e
of different families of nanoparticles exhibiting controlled shapes and edges. Because of their strong aromatic character graphene nanoparticles tend to aggregate in solution; however, for future application it is of high interest to be able to discriminate the intrinsic absorption andemissionof the GQDs from those of aggregates. For example, we observed that by STM and polarized microscopy the GQDs bearing alkyl chains are forming columnar structures with liquid crystal properties in solvents. Here, we study the optical propertiesofgraphenequantumdots as a function of their individualization. Using absorption, steady-state and time-resolved photoluminescence and photoluminescence excitation (PLE) spectroscopy, we try to establish the intrinsic optical propertiesof the GQDs and understand how the structure influences the properties.
Measurement of biexciton emission in C168 is extremely challenging on account of the low photoluminescence quantum yield of C168 single excitons (∼0.002) and rapid rate (3 ps −1 ) of biexciton Auger recombination. 31 Moreover, rapid carrier cooling allows for measurement of photoluminescence only from the lowest-energy single- and biexciton states. Therefore, we study biexcitons by transient absorption (TA) measure- ments in which the single-to-biexciton transition does not require a long-lived biexciton for its observation and in which one can access higher-energy biexcitons. TA measurements on C168 were performed as described previously. 31 C168 was prepared following the synthesisof Yan and Li. 11 Prior characterization has established the high structural and size uniformity of the synthetic product. 11 C168 was dissolved in anhydrous toluene, and loaded in a nitrogen atmosphere in a 1 mm path length fused-silica cuvette sealed with Teﬂon valves. GQD solutions were prepared to optical densities of ∼0.2 at 3.1 eV. C168 in toluene was excited at 3.1 eV and probed with ∼130 fs temporal resolution using a broadband continuum (for Figure 1. Extrapolated singlet exciton (X) and biexciton (XX) states,
states . Therefore, the two PLE bands at 580 nm and 630 nm can tentatively be attributed to the intrinsic α and p bands while the main one at 475 nm would be assi- gned to the β band. However, both PLE and PL spectra are more complex than this first description. Especially, the PL spectrum ofsingle GQDs is composed of seve- ral lines. The almost 170 meV energy splitting between each PL line suggests potential vibronic effects. It can be seen here that further studies, including calculations, are necessary for a full understanding of the electronic struc- ture. An interesting point will be for instance to search for signatures of the band diagram ofgraphene, such as valley structure. Finally, the polarization response of a single GQD is shown on the inset of Fig. 1c. Here, the emission polarization profile is recorded on the line 1 at ∼650 nm. It is linearly polarized at a fixed direction certainly related to the geometry of the GQD. Likewise the excitation diagram is also linearly polarized in the same direction than the emission one. Therefore, it can be concluded that absorption and main emission dipoles are parallel. Further investigations, including theoretical modeling, are also needed to explain this experimental observation.
phonon emission line of the α band followed up with vibronic replicas, with a quantumof vibration ħΩ ∼ 170 meV. We also performed photoluminescence excitation (PLE) experiments in solution (See Supplementary Fig. 4). The PLE curves detected on the two highest energy PL lines of GQD superimpose well with the absorption spectrum of the solution. Besides, the PLE highlights the existence of two lines at 580 and 630 nm. The energy splitting between those states is also ∼170 meV revealing the Franck–Condon series of vibronic lines. The intense absorption line at high energy could be tentitatively attributed to the β band in the Clar’s notation 12 , 13 . Finally, the polarization response of a single GQD is shown in the inset of Fig. 1 d. Here, the emission polarization proﬁle is recorded on the line 1 at ∼650 nm. It is linearly polarized at a ﬁxed direction certainly related to the geometry of the GQD. Likewise the excitation diagram is also linearly polarized in the same direction than the emission one. Therefore, it can be concluded that absorption and main emission
This has opened the door to great achievements in many scien- tific disciplines, as exemplified by the use of these materials as bio-labels, lasers, light-emitting diodes (LEDs), and solar cells. 1-5 However, most such advancements have been achieved for toxic Cd- and Pb-based systems, while others, such as III-V semicon- ductors (in particular InP), 6-7 have not been as thoroughly studied. Indeed, the more covalent nature of the In-P solid and its high sensitivity toward oxidation account for the complexity of con- trolling both the InP surface chemistry and, in the case of core/shell systems, the shelling interface. 8-9 We and others have demonstrated the sensitivity of these materials to the water present in solution either as a reactant impurity or as a by-product gener- ated under the high-temperature conditions of currently reported syntheses. 8-12 This results in the formation of oxide and hydroxide species, which dramatically and irreversibly alter the surface. It is important to note that the presence of water in the InP synthesis medium is not an exception but rather the general case. Most procedures are predicated on the use of indium carboxylate pre- cursors and/or other oxygen-containing ligands at high tempera-
IV. PARAMETER FITTING
The fitting of the band structures from the M point to Ŵ to the A point is performed using a conjugate gradient method with stochastic basin hopping to avoid trapping in shallow local minima. For each material, there are 33 tight- binding parameters for structures in absence of strain and 37 additional strain correction parameters. Due to this large parameter space, many different parametrizations can yield similarly good fits. Also, the target function to be optimized is not unambiguous. For example, the overall widths of the lowest conduction and the highest valence bands span several eV. However, it is highly desirable to model the region around the direct gap close to the Ŵ point, which determines the low-energy physics as well as the optical properties, with a much better accuracy of a few meV. In order to achieve a good compromise, we first perform an unweighted least-squares fit for the lowest conduction bands and the highest valence bands for 20 evenly spaced points along the M-Ŵ path and for 10 points along the Ŵ-A path through the Brillouin zone for a good qualitative overall description of the relevant bands. Then, we successively add increasing weights to achieve a bet- ter description at Ŵ, M, and A as well as at a few discretization points close to Ŵ in order to reproduce the effective mass. With careful adjustment of the weights the optimization procedure eventually localizes in one minimum, in which we then fine tune the parameters, e.g., by increasing the weights around the Ŵ point to about 10 000 compared to intermediate points in the Brillouin zone. This makes it possible to gradually bend the bands towards the final result, where we aim at a good compromise between the overall band structure and a resolution at the Ŵ point with an error of ∼5 meV by shifting regions with larger error to intermediate k vectors.
multiexcitons, does not go to zero at low powers. For NCs under weak continuous excitation, instead of pulsed excitation, an analogous argument to the above (detailed in the Supplementary) gives g (2) (τ= 0)/g (2) (τ → ∞) = η bx /η x .
Figure 2 shows data from an experiment on a single CdSe/CdZnS NC under pulsed weak excitation. We ensured that our data is representative of the 〈N〉 → 0 limit by operating far below signal saturation, in a regime where the measured was insensitive to ±50% changes in the excitation power. In all of the NCs that we studied, the center peak clearly rises above the noise levels. More importantly, the sizes of the center peak in our g (2) are well above those attributable to extraneous sources such as stray light or neighboring NCs (see Methods). Therefore we assign the 0-time coincidence feature to cascaded BX,X emission. The data shown in Figure 2 implies a BX to X quantum yield ratio of
Nanomanipulator. This tool is capable of positioning and aligning nano-sized objects with < 250 nm position resolution and <1° rotation resolution. It consists of a tungsten tip mounted on a xyz high-precision differential stage, all integrated in a high-resolution imaging system. Relying on van der Waals forces between the nanowires and the tungsten tip, nanowires can be selectively transferred from the growth chip to another substrate for further processing. More details about the nanowire transfer process and the nanomanipulator can be found in ref. 7 . Photonic circuit fabrication: encapsulation device. Starting with a bare silicon wafer, 2.4 µm of thermal oxide is formed to serve as the bottom cladding of the waveguide. Using e-beam lithography, metal evaporation, and lift-off process, metallic structures, including marker ﬁelds and heaters (resistance 2.8 kΩ) were created on the oxide layer. Next, nanowire QDs were transferred with the nanomanipulation tool to the substrate, followed by a deposition of 200 nm of SiN using plasma-enhanced chemical vapour deposition (PECVD) process at 300 °C 28 . Waveguides and ring resonators were patterned using 100 keV e-beam lithography on a 950 K PMMA resist. After developing the resist, features were transferred to the SiN by complete etching of the SiN layer using CHF3/Ar-based reactive ion etching. This was followed by a short O2 plasma-cleaning step. Next, the devices were covered with ~ 1 μm-thick PMMA to provide symmetric mode conﬁnement 1.0
Quantum key distribution (QKD) has been an active research area ofquantum in- formation science, since Bennett and Brassard  proposed their QKD protocol in 1984 (BB84), whose security is protected by the no-cloning theorem . Due to its relatively simple configuration, BB84 has been implemented by many groups in free- space [47, 48, 49, 50] as well as in fiber [51, 52, 53]. Security of BB84 also has been the subject of many analyses [98, 99, 47, 100], particularly for configurations that involve non-ideal operating conditions [101, 102, 103], such as the use of weak laser pulses in lieu ofsingle photons. However, a more fundamental question is how much informa- tion the eavesdropper (Eve) can gain under ideal BB84 operating conditions. A series of work by Fuchs and Peres , Slutsky et al. , and Brandt  show that the most powerful individual-photon attack can be accomplished with a controlled-not (cnot) gate. In this scheme, Eve supplies the probe qubit to the cnot gate, which entangles this probe qubit with the BB84 qubit that Alice is sending to Bob. Eve then makes her measurement of the probe qubit to obtain information on the shared key bit at the expense of imposing detectable errors between Alice and Bob.
The procedure of isolating single electron or hole should occur regardless of the size of the system since the top layer has always one less zero-energy state than the bottom one. In order to investigate the size dependence, in Fig. 4(a) we show the energy difference between the ferromagnetic and antiferromagnetic (FM-AFM) states calculated in the mean-field Hubbard approximation as a function of applied voltage for several sizes up to 1507 atoms. We note that, due to the unusually high degeneracy of the states, self-consistent iterations occasionally get trapped in local energy minima. We have thus repeated the calculations several times using different initial conditions and/or convergence schemes to assure that the correct ground state was reached. As expected, at V = 0, the FM-AFM gap increases with the size of the system N . In fact, the FM-AFM gap energy per N side ,
approximation, the two |J z =±2i states are dark and the
two |J z =±1i states are bright and coupled to orthogonal
circularly polarized light states. The short-range part of the electron-hole exchange interaction lifts their de- generacy and the dark states lie a few hundreds of µeV below the degenerate bright states . However, different microscopic effects such as the anisotropy of the QD con- finement potential but also the atomistic symmetry of the crystal  modify this simple picture and break the QD rotational invariance. The fine structure of the exciton ground state is determined by the subtle interplay be- tween the spin-orbit and exchange interactions as a func- tion of the crystal atomistic symmetry and QD shape, as discussed in detail in Ref. . The most important result is that the new bright states |Xi and |Y i are no longer degenerate and correspond to two linearly polar- ized transitions which are aligned along two orthogonal principal axes of the QD. Furthermore, the symmetry reduction gives rise, through a heavy-light hole mixing  or through a deformation of the wave-function enve-
Optical Characterization. In order to monitor the nucleation and growth of the nanocrystals, small aliquots (∼0.01 mL) of the reaction mixture were taken quickly at diﬀerent growth periods/temperature; each aliquot was then dispersed in toluene with a concentration of 10 μL/1.0 mL. Optical absorption spectra were collected with a PerkinElmer Lambda 45 ultraviolet−visible (UV−vis) spectrometer using a 1 nm data collection interval. Photoluminescent (PL) emission experiments were performed on a Fluoromax-3 spectrometer (Jobin Yvon Horiba, Instruments SA), with a 150 W Xe lamp as the excitation source, an excitation wavelength of 350 nm, an increment of data collection of 1 nm, and the slits for excitation andemissionof 3 or 2 nm. For the emission peak, baseline-subtracted and Gaussian-ﬁtted integration was performed with built-in DataMax software, to yield the peak position, full width at half-maximum (fwhm), and peak area for the calculation ofquantum yield (QY). Relative PL QY was determined by comparing the integrated emissionof a given QD sample in dilute toluene dispersion (∼0.1 absorbance at the excitation wavelength of 430 nm) with that of coumarin 334 in ethanol (lit. QY ∼ 0.69, 46 see Figure S1B ). Corrections were made for the refractive indices of the diﬀerence solvents.
Ω a direct analogue of the lower bound
as in the Faber-Krahn inequality (1.1) holds.
One should also mention numerous results in the differential geometry litera- ture, where lower and upper bounds have been found for Dirac operators on two- dimensional manifolds without boundary (see for instance  and [1, 7]). In , manifolds with boundaries are investigated and note that the mentioned CHI (chi- ral) boundary conditions correspond to our infinite mass boundary conditions. For two-dimensional manifolds, the author of  provides a lower bound on the first eigenvalue which is actually (1.3). We remark that upon passing to the more gen- eral setting of manifolds the equality in (1.3) is attained on hemispheres.