4288
J. Phys. Chem. B 2000, 104, 4288-4291
Josephson Coupled Quantum Dot Artificial Solids Iris S. Weitz,† Jennifer L. Sample,† Ryan Ries, Eileen M. Spain, and James R. Heath* UCLA Department of Chemistry and Biochemistry, 405 Hilgard AVenue, Los Angeles, California 90095-1569 ReceiVed: January 19, 2000; In Final Form: March 9, 2000
Josephson coupled quantum dot artificial solids were prepared from 20 ( 4 nm diameter organically functionalized Pb particles. Interparticle separation distances were varied from approximately 26 to 11 Å by varying the passivating organic ligand. Isolated particles were too small to exhibit a Meisner effect by themselves, and so it was possible to employ SQUID magnetometry as a zero-background probe for Cooper pair delocalization in these solids. As the interparticle separation distance was decreased, the quantum dot solids progressed from a Mott insulator to a strongly localized superfluid, and finally to a superfluid.
Introduction The electronic properties of a solid are largely determined by the charging energies of the lattice sites, the nature and strength of the interaction between adjacent sites, and the lattice symmetry. In “artificial solids”1 constructed from chemically synthesized quantum dots (QDs), it is, in principle, possible to exert chemical control over each of these parameters and to rationally design quantum phase transitions into such solids.2 In this Letter, we report on the extension of this concept to Josephson exchange coupled artificial solids. Alkanecarboxylate passivated 20 nm diameter Pb QDs were utilized as the “artificial atom” building blocks. The interaction between the QDs was increased stepwise by decreasing the chain length of the surfactants.3 Zero-background measurements of the Josephson coupling were carried out using SQUID magnetometry in the temperature range from 2 to 8 K. For particles separated by 20 Å or more, the QD solid is a Mott insulator.4 For separation distances of ∼15 Å, the QD solid exhibits the characteristic signatures of a highly localized superconductor, with a coherence length of just a few particles. For separation distances of ∼11 Å, the QD solid exhibits superfluid characteristics. Lithographically defined tunnel junctions5,6 and vacuumevaporated metal island thin films7,8 have been prototypical model systems for the investigation of quantum phase transitions in Josephson coupled systems. This letter describes a chemical approach toward investigating similar physics, but with two major differences. First, we control and directly quantify the length scales of both particle size and interparticle separation distance at a resolution beyond that achievable by previously reported techniques. Second, our approach leads to a (threedimensional) macroscopic solid of Josephson junctions, rather than a thin film or a handful of tunnel junctions. Taken together, these advantages allow us to use SQUID magnetometry as a zero-background probe of Josephson coupling, and this, in turn, allows us to carry out the first direct thermodynamic measurements of the various quantum phases in Josephson coupled systems. Experimental Section Solution phase syntheses of many types of metallic nanoparticles and particle colloids are well-known in the literature.9,10 * Corresponding author:
[email protected]. † These authors contributed equally to this work.
Production of lead particles, however, has mainly been limited to evaporated or sputtered Pb island films.11,12 These Pb island films have been utilized in many beautiful and classic experiments aimed at probing superconducting transport mechanisms through the percolation transition. However, to our knowledge, none of the films that have been utilized for those experiments have ever been subjected to any sort of direct structural characterization. Thin Pb films quickly oxidize when exposed to air, and this has made structural characterization very difficult. One chemical synthesis of Pb particles was reported by Fariss13 and co-workers several years ago. The particles produced by that synthesis were not of sufficient quality for allowing any type of quantitative size-dependent measurements of physical properties. To our knowledge, the chemical scheme presented here is the first method that allows for the rational control over particle size, shape, size distribution, and interparticle separation distance. The particles produced for this investigation were spherical and capped with one of several different lengths of carboxylic acid ligand per reaction. The ligands used ranged from sixcarbon chains (∼10 Å ligands) to eighteen-carbon chains (∼28 Å ligands) for control of interparticle spacing. The size of the lead core is 20 ( 4 nm, also controlled by the reaction conditions. Particles of different sizes, size distributions, and shapes have been produced through variations of this synthesis, and those particles and their syntheses will be reported elsewhere. Materials. The following chemicals were used as obtained from Aldrich: trioctylphosphine (90% tech), 1-octadecanol (99%), cis-5-dodecenoic acid (99%), elaidic acid (98%), 2-octenoic acid (predominantly trans, 97%), trans-3-hexenoic acid (97%), and tetraethyllead (99.99%). The solvent, octyl ether (99%), was obtained from Aldrich and vacuum distilled over sodium metal before use. Synthesis. A typical reaction scheme producing 20 nm octenoic acid capped particles follows. Thirty milliliters of dry dioctyl ether was added with stirring to 0.487 g (1.2 equiv) of 1-octadecanol under argon at room temperature. After purging the solution repeatedly with argon and then vacuum, 0.66 mL of trioctylphosphine (1.0 equiv) and 0.23 mL (1.0 equiv) of 2-octenoic acid were added. The solution was then heated to 80 °C under vacuum, allowed to stand for 5 min maintaining that temperature, then heated to 278 °C under argon. At 278
10.1021/jp000238+ CCC: $19.00 © 2000 American Chemical Society Published on Web 04/14/2000
Letters °C, 0.3 mL (l.0 equiv) of tetraethyllead was injected into the mixture. The resulting exothermic reaction first turned yellow and then began to turn gray. This second color change in the reaction is the “nucleation” of particles. The reaction gradually grew darker until it became black, 10-14 min past nucleation. The reaction was quenched by removing the heating mantle at this point. The solution was cooled to room temperature and centrifuged at 3500 rpm to separate the particles from the reaction mixture. After decanting the supernatant, the particles were rinsed with 2-propanol and dried in a vacuum desiccator. The resulting (slightly greasy) powder was then dissolved in anhydrous chloroform, passed successively through 0.45 and 0.2 µm PTFE membrane filters, and evaporated into a small quartz tube that served as the sample holder for SQUID magnetometry measurements. Although this solvent evaporation procedure does produce small three-dimensional Pb QD superlattices, these solids are probably best described as amorphous materials rather than a polycrystalline superlattice. In general, the Pb nanoparticles are soluble in chloroform and hexane. They decompose or oxidize readily if stored in air at room temperature and are therefore kept under vacuum or argon in a freezer. The particles are exposed to air during the centrifugation or filtration steps, and such brief exposure does not cause noticeable oxidation, as probed by TEM. When the particles are exposed to air for time periods of 1 h or more, they begin to develop an oxide shell that is discernible by TEM. After several hours of exposure, the particles will be completely oxidized. Even with proper storing, the particles should be used within a week to obtain reliable results, and all data reported here were obtained within a day or two of particle preparation. All of the particles utilized for the SQUID measurements were also interrogated using TEM for both particle size and interparticle separation distance. Several representative batches of particles were also subjected to elemental analysis. Magnetometry measurements were carried out on a Quantum Design model MPMS-XL SQUID magnetometer operating in the reciprocating sample mode with a sensitivity of a few parts in 108 of the magnetic susceptibility of a sample, measured in emu. All results reported here were background-subtracted zerofield cooled experiments. Field-cooled measurements yielded identical results. Results and Discussion Small metal particles are characterized by a size-dependent capacitance C(r) ) 4πor and a charging energy EC ) e2/2C(r).14 Here, is the dielectric constant of the organic medium surrounding the particles, o is the vacuum permittivity constant, and r is the particle radius. For a 20 nm diameter particle covered with organic surface groups, EC ≈ 45 meV. This means that a solid of weakly interacting Pb particles is a Mott insulator, because it has an energy band gap defined by EC. This holds, even below the temperature of the superconducting transition for Pb (Tc), in which case the individual Pb particles may be superconducting.15 An insulator to superconductor (S/I) transition for the superlattice can be driven by quantum fluctuations when the Josephson coupling energy EJ becomes comparable to EC.16 At some small value of interparticle separation distance, such a transition is expected. Below Tc, a type I superconductor (such as Pb) becomes a perfect diamagnet. Valence electrons near the Fermi energy condense to form Cooper pairs, which are a type of boson. When a magnetic field is applied to the sample, a “supercurrent” of the Cooper pairs is generated, resulting in an opposing magnetic
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4289
Figure 1. Transmission electron micrograph of oleic acid (C17H33CO2H) passivated 20 nm diameter Pb quantum dots.
field. The result is that the applied magnetic field only penetrates the solid to a characteristic depth (γ) of a few tens of nanometers. This is the Meisner effect, and its measurement via SQUID magnetometry is a standard technique for detecting the superconducting transition. The applied field increases the kinetic energy of the superconducting phase, eventually quenching superconductivity at high enough field, and so magnetometry provides a direct measurement of the thermodynamic differences between the normal and superconducting state. SQUID magnetometry requires a macroscopic amount of sample and so has not been previously used as a probe of Josephson exchange coupling. To use the Meisner effect as a zero-background probe of Cooper pair delocalization, the size of our particles needed to be much less than γ, since such small particles will not exhibit a Meisner effect by themselves. In addition, we wanted particles that were sufficiently large (>10 nm diameter) that superconductivity within the individual quantum dots would be firmly established.15 Thus, we carried out a series of SQUID magnetometry measurements on solids of well-separated Pb particles (particles capped with 18-carbon atom chains) with diameters ranging from 15 to 70 nm. Particles smaller than about 45 nm exhibited no Meisner effect when cooled below Tc. Larger particles, however, exhibited a Meisner effect that was similar to the bulk. This size is consistent with theoretical expectations17 but, to our knowledge, has not been previously reported. All experiments aimed at investigating Cooper pair delocalization in QD solids utilized particles of diameter 20 ( 4 nm (Figure 1). In this way, the only signal observed was due to the response of Cooper pairs that were delocalized over at least several particles. Approximately 20 separate batches of Pb QD solids were prepared and analyzed. No diamagnetic response was observed for any C18- or C12-capped particles, regardless of applied field or temperature. For all batches of C8- or C6-capped particles, a diamagnetic response below the Tc for bulk Pb was observed, and the C6-capped particles consistently exhibited the strongest response (Figure 2). The diamagnetic response is a direct signature of Josephson coupling, and so it will increase exponentially with respect to decreasing interparticle separation distance. Therefore, small fluctuations in the various particle preparations led to large amplitude changes (factors of 2-3) in diamagnetic response.
4290 J. Phys. Chem. B, Vol. 104, No. 18, 2000
Letters
Figure 2. Magnetic susceptibility of various Pb QD solids at 400 G plotted versus temperature. The plots are mass-normalized to 1 mg of sample. Only the C8- and C6-capped particles exhibited a diamagnetic response. The onset of the response was 7.2 K, which is the 0-field superconductor transition temperature for bulk Pb.
Contour plots of the magnetic susceptibility versus applied field and temperature for four representative particle batches are presented in Figure 3. The plots are ordered in terms of decreasing magnitude of the mass normalized diamagnetic response (measured at 2 K and 400 G). Data from the bulk are included at the top. This series of plots rather strikingly exhibits the transition from a delocalized superfluid phase characteristic of a bulk superconductor to a localized superfluid phase. The plot of the bulk response is obviously representative of the superfluid phase, and it provides a useful comparison for the QD solids data. For the bulk, the region to the high field of the contour lines is the quenched superconductor. The steep contour gradient at the interface between the superfluid and the quenched phase represents a plot of the critical field versus temperature and is a measurement of the free energy difference between the superconducting and normal state. Figure 3B is the contour plot of the QD solid of the C6-capped particles that exhibited the strongest diamagnetic response. This plot exhibits many of the superfluid characteristics of the bulk, including a field dependence that, while weaker than the bulk, is still indicative of superfluid behavior. All of our C6-capped particles exhibited such a field-dependent component, and that fielddependent component was always quenched at around 2000 G at 2 K. This may reflect the characteristic superfluid length scale in these QD solids. These same QD solids also were characterized by a minority component of the diamagnetic response that exhibited only a weak field dependence, so there is not a clear field-dependent quenching of all the superconducting character. In Figure 3C, the field-independent component has grown relative to the superfluid, and by Figure 3D (C8-capped particles), it is the only component observed. Barber and Dynes correlated coherence length scales with magnetoresistance measurements in granular Pb films.18 They used the relationship lφ ) (Φo/Hx)1/2, where lφ is the supercurrent phase coherence length, Φo is the superconducting flux quantum, and Hx is that field where a flux quantum is enclosed by an area roughly the
Figure 3. Countour plots of the mass-normalized diamagnetic response of (A) bulk Pb, (B) a QD solid of C6-capped particles with a susceptibility of -4.8 × 10-6 emu/mg at 2 K, (C) a QD solid of C6capped particles with a susceptibility of -2.2 × 10-6 emu/mg at 2 K, and (D) a QD solid of C8-capped particles with a susceptibility of -1.5 × 10-6 emu/mg at 2 K. The trend, from top to bottom, is from solids that exhibit a strong field and temperature-dependent tuning of the susceptibility, to solids that exhibit a very weak field and temperaturedependent tuning. This trend represents the onset of localization of the superfluid state.
size of the phase coherence. This represents the maximum area over which screening supercurrents can be sustained. The point here is that smaller coherence length scales require higher fields to quench superconductivity. We investigated samples similar to the QD solid represented in Figure 3D up to fields of 1.3 T (13 000 G) and observed Tc to decrease by about 1 K. The clear implication is that those QD solids are characterized by very localized regions of supercurrent phase coherencesprobably just a few particles in size. This localized superconductor is reminiscient of the so-called Bose glass.19 However, transport measurements are necessary to make any definite assignments of this localized phase. We have demonstrated that it is possible to prepare Josephson coupled artificial solids from organically functionalized Pb quantum dots and that SQUID magnetometry may be utilized as a zero-background probe of Cooper pair delocalization in these solids. Three types of behaviorsthe Mott Insulator, the localized superfluid, and the superfluidswere synthetically designed into the solids. We have reported on well-ordered monolayers of chemically similar particles,20 and shown that such monolayers can be probed using transport measurements.21,22 Transport measurements on Pb QD monolayers should enable us to investigate issues related to quantum criticality and dissipation driven phase transitions, for example, in effectively infinite arrays of well-characterized Josephson coupled tunnel junctions.
Letters Acknowledgment. We would like to acknowledge Prof. S. Kivelson for helpful discussions, and we would like to acknowledge Dr. Chris Murray for early advice on Pb nanocrystal synthesis routes. This work was funded by the National Science Foundation. References and Notes (1) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Science 1995, 270, 1335. (2) Collier, C. P.; Henrichs, S.; Shiang, J. J.; Saykally, R. J.; Heath, J. R. Science 1997, 277, 1978. (3) Interparticle separation distances were measured using transmission electron microscopy (TEM) of monolayer films of Pb particles supported on an amorphous carbon-coated substrate. The (111) lattice spacing of the FCC lattice of Pb was imaged at high resolution and used as a distance metric. The measured distances, as a function of ligand carbon-chain length, were C18 (26 Å), C12 (22 Å), C8 (15 Å), and C6 (11 Å). Statistical uncertainties in these numbers are high (σ ) (5 Å or more). This is due not only to size and packing fluctuations but also to the fact that the measurement was of the 2D projection of a film that undoubtedly exhibited fluctuations in 3D. However, both the trend and the absolute numbers are reasonably consistent with previous measurements on highly ordered monolayers of organically passivated silver, gold, and cobalt quantum dots. (4) Here we refer to the distance between the surfaces of the metal cores of adjacent nanoparticles. (5) Geerligs, L. J.; Peters, M.; de Groot, L. E. M.; Verbruggen, A.; Mooij, J. E. Phys. ReV. Lett. 1989, 63, 326. (6) Rimberg, A. J.; Ho, T. R.; Kurdak, C.; Clarke, J.; Campman, K. L.; Gossard, A. C. Phys. ReV. Lett. 1997, 78, 2632. (7) Jaeger, H. M.; Haviland, D. B.; Orr, B. G.; Goldman, A. M. Phys. ReV. B 1989, 40, 182.
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4291 (8) Barber, R. P., Jr.; Merchant, L. M.; La Porta, A.; Dynes, R. C. Phys. ReV. B 1994, 49, 3409. (9) Henglein, A. Top. Curr. Chem. 1988, 143, 113. (10) Schmid, G. Chem. ReV. 1992, 92, 1709. (11) Neugebauer, C. A.; Webb, M. B. J. Appl. Phys. 1961, 33, 74. (12) Morozov, Y. G.; Petinov, V. I. Solid State Commun. 1981, 40, 991. (13) Fariss, T. L.; Nixon, W. E.; Bucelot, T. J.; Deaver Jr. B. S.; Mitchell, J. R. J. Appl. Phys. 1982, 53, 6316. (14) Lambe, J.; Jaklevic, R. C. Phys. ReV. Lett. 1969, 22, 1371. (15) In sufficiently small particles the electronic density of states is sparse, and there may be insufficient electron density near the Fermi level for Cooper pair formation below the superconducting transition temperature. Such size-dependent effects are expected near about 5 nm diameter particles. In a 20 nm diameter Pb particle, no such effects are expected, and superconductivity should be well-established in the particle below the transition temperature. See: Anderson, P. W. J. Phys. Chem. Solids 1959, 11, 28. Ralph, D. C.; Black, C. T.; Tinkham, M. Phys. ReV. Lett. 1997, 78, 4087. (16) Wagenblast, K.-H.; Otterlo, A. V.; Schon, G.; Zimanyi, G. T. Phys. ReV. Lett. 1997, 79, 2730. (17) Buckel, W. SuperconductiVity: Fundamentals and Applications; VCH Publishers: New York, 1991. (18) Barber, R. P., Jr.; Dynes, R. C. Phys. ReV. B 1993, 48, 10618. (19) Fisher, M. P. X.; Weichman, P. B.; Grinstein, G.; Fisher, D. S. Phys. ReV. B 1989, 40, 546. (20) Heath, J. R.; Knobler, C. M.; Leff, D. V. J. Phys. Chem. B 1997, 101, 198. (21) Kim, S.-H.; Medeiros-Ribeiro, G.; Ohlberg, D. A. A.; Williams, R. S.; Heath, J. R. J. Phys. Chem. B 1999, 103, 10341. (22) Kim, S.-H.; Markovich, G.; Rezvani, S.; Choi, S. H.; Wang, K. L.; Heath, J. R. Appl. Phys. Lett.. 1999, 74, 317.
