ARTICLES PUBLISHED ONLINE: 23 OCTOBER 2011 | DOI: 10.1038/NNANO.2011.180
Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation Mahmood Bagheri, Menno Poot, Mo Li†, Wolfram P. H. Pernice and Hong X. Tang* The ability to control mechanical motion with optical forces has made it possible to cool mechanical resonators to their quantum ground states. The same techniques can also be used to amplify rather than reduce the mechanical motion of such systems. Here, we study nanomechanical resonators that are slightly buckled and therefore have two stable configurations, denoted ‘buckled up’ and ‘buckled down’, when they are at rest. The motion of these resonators can be described by a double-well potential with a large central energy barrier between the two stable configurations. We demonstrate the highamplitude operation of a buckled resonator coupled to an optical cavity by using a highly efficient process to generate enough phonons in the resonator to overcome the energy barrier in the double-well potential. This allows us to observe the first evidence for nanomechanical slow-down and a zero-frequency singularity predicted by theorists. We also demonstrate a non-volatile mechanical memory element in which bits are written and reset by using optomechanical backaction to direct the relaxation of a resonator in the high-amplitude regime to a specific stable configuration.
C
avity optomechanics relies on the use of optical forces to manipulate mechanical resonators1,2. These retarded optical forces have been used to cool mechanical systems3–6, and with the development of nanoscale electromechanical systems (NEMS) and optomechanical systems7 an important milestone was reached recently when a macroscopic resonator was cooled to its quantum ground state8–10. However, rather than quenching the motion of the resonator, it is also possible to transfer energy from the optical field to the resonator and amplify its motion11,12, which has enabled the parametric amplification of small forces13, as well as the study of discrete mechanical states14,15. Although cooling a resonator to its ground state is an advantage for some potential applications of nanoscale mechanical systems, such as quantum information processing with mechanical devices16, the high-amplitude operation of these devices is better suited to room-temperature applications, such as signal processing17 and mass/force sensing18, and could also lead to the development of other new technologies19–23. However, it is difficult to reach the high-amplitude regime in a traditional nanoscale mechanical system because the dynamic range of the system decreases dramatically as the dimensions of the resonator are reduced24. This fall in the dynamic range may be explained by the fact that as the strength of the resonant driving force increases, Duffing nonlinearities shift the resonance frequency away from the drive frequency, so the amplitude of the motion hardly increases. Here, we show that the limitations that restrict the performance of conventional NEMS can be overcome by exploiting cavity optomechanics. In a typical cavity optomechanics experiment (Fig. 1a), an optical cavity is coupled to a mechanical resonator, which allows the electromagnetic energy of the cavity field (that is, photons from a laser) to be converted into mechanical energy (phonons in the resonator), and vice versa. The relevant frequencies are the resonant frequency of the mechanical resonator Vm , the resonant frequency of the optical cavity vc (which is displacement dependent), and the
frequency of the laser vp . The coupling leads to the appearance of sidebands with frequencies of vp+Vm (and also higher-order sidebands at vp+2Vm , vp+3Vm , and so on). Coupling an optical cavity to a mechanical resonator also leads to a variety of effects such as optical bistability25, the optical spring effect26 and motioninduced transparency27–29. Coupled resonator–cavity systems can also display damping and amplification of the thermal motion of the resonator, and it is the latter effect that enables us to operate our devices in the high-amplitude regime. In this regime, the nanomechanical resonator can gain enough energy to overcome the large energy barrier that separates its two stable configurations, which allows us to provide the first evidence for a zero-frequency singularity in a nanomechanical system, as predicted by theorists30. Furthermore, by using real-time optical cooling, we will show that it is possible to controllably quench the oscillator from a high-amplitude state into one of the two energy minima in the double-well potential that describes the out-ofplane motion of the mechanical resonator. This will allow us to demonstrate all-optical operation of a mechanical memory element that stores information in the two mechanically stable states of the resonators31. Because the energy barrier between these two mechanical states is much larger than the thermal energy at room temperature, our mechanical memory is nonvolatile and immune to electromagnetic perturbation, environmental fluctuations and leakage32,33, and could prove to be a useful building block in the effort to develop mechanical computing engines34–37.
Optomechanics in a racetrack cavity The optical cavity in our experiment is a silicon waveguide in the form of a racetrack, made from commercially available silicon-oninsulator (SOI) wafers, and it is coupled to a nanoscale flexural resonator that is fabricated by etching away the substrate below a short length of the waveguide (Fig. 1a,b). The cavity has a free spectral range of 2 nm and a typical linewidth of 10 GHz. The
Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, USA; † Present address: Department of Electrical and Computer Engineering, University of Minnesota, Minnesota 55455, USA. * e-mail:
[email protected] 726
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Figure 1 | The two states of a coupled mechanical resonator–optical cavity system. a, Generic optomechanical system (top) in which one of the mirrors in an optical cavity illuminated by a pump laser of frequency vp and power Pin is able to oscillate at a resonant frequency Vm. The power circulating inside the cavity, Pcirc , is enhanced by the finesse of the cavity (F ¼ 20). Schematic of the experiment (bottom) showing a nanomechanical resonator embedded in a racetrack-shaped waveguide that serves as the optical cavity (without mirrors). The resonator and waveguide are made of a 110-nm-thick silicon layer. Light is coupled into the bus waveguide via grating couplers (triangles) and then into the cavity. The nanomechanical resonator is made by under-etching a part of the waveguide. The motion of the resonator changes the optical path length (and hence the resonant frequency of the cavity) by changing the effective refractive index of the optical mode. b, Scanning electron micrographs of the nanomechanical resonator in its buckled-up (left) and buckled-down (right) states. c, Optical transmission spectra of the cavity measured at low input power (–5 dBm on coupling bus waveguide) when the resonator is in the up state (blue curve) and the down state (red). The racetrack cavity optical resonances are separated by a free spectral range of 2 nm. d, Optical transmission spectrum of the cavity measured at high input power (green, left axis). When the input power exceeds a certain threshold, the spectrum no longer shows the Lorentzian shape seen at low power; rather, the resonance is dragged from the up state to the down state. Moreover, self-sustained oscillations (red, right axis) are observed when vup , vp , vdown , where vup and vdown are the resonant frequency of the cavity when the resonator is in the up and down states, respectively. e, Thermomechanical noise spectra measured in the up (blue symbols) and down (red) states. Solid black lines are harmonic oscillator responses fitted to the data.
nanomechanical resonator is clamped at both ends and has dimensions of 10 mm × 500 nm × 110 nm, an effective mass of meff ¼ 1.0 pg, a fundamental resonance frequency of Vm/2p ≈ 8 MHz, and a mechanical damping rate of G0/2p ¼ 2.1 kHz. In this coupled system, the out-of-plane motion of the mechanical resonator modulates the path length of the resonant optical field inside the cavity by modifying the effective refractive index of the optical waveguide as it moves towards or away from the substrate. The separation between the resonator and the substrate is 250 nm; this distance is small enough for the optical gradient forces38 between the resonator and the substrate to be quite strong ( g ¼ dvc/dx ¼ 2p × 1 GHz nm21, where g is the optomechanical coupling rate, vc is the resonant frequency of the cavity, and x is position; see Supplementary Information), but it is also large enough to allow large-amplitude oscillations of the resonator. Owing to the residual compressive stress introduced by the SOI wafer bonding process, the resonators are slightly buckled and have two stable configurations at rest39: ‘buckled up’ and ‘buckled down’ (Fig. 1b). This means that the out-of-plane motion of the resonator can be described by a double-well
potential, with the up and down states corresponding to the two minima in the potential. Thermomechanical displacement noise spectra (Fig. 1e) show that the two states have slightly different mechanical resonance frequencies, indicating that the doublewell potential is not completely symmetric. The two mechanical states can be discriminated in optical transmission measurements, since the effective refractive index is larger in the down state because the interaction between the optical field and the substrate is stronger (due to the reduced separation) than in the up state. The resonant frequency of the cavity therefore decreases when the resonator flips from the up state to the down state, as can be seen in low-power optical transmission spectra (Fig. 1c). However, at high optical powers the resonator starts to oscillate when the frequency of the pump laser vp is scanned close to the resonant frequency of the cavity vc. Figure 1d shows the optical transmission spectrum measured when the input optical power is well above threshold (600 mW) for self-sustained oscillations. These oscillations start when the laser becomes blue detuned with respect to the cavity (that is, vp . vc) when the resonator is in the up state, and vc oscillates back and forth with
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Figure 2 | Resolved and unresolved sideband regimes. a, Schematic plot of the optical transmission spectrum of the cavity as measured by a weak probe laser of frequency v when the resonator is at rest (solid green line). The motion of the resonator modifies the effective path length of the optical cavity (Fig. 1a), so that the position of the peak (that is, the resonant frequency of the cavity) changes when the resonator moves (dashed lines). In the highamplitude regime, the change in the resonance frequency can be larger than the width of the peak. Energy can be exchanged between the laser field and the mechanical motion of the resonator in units of hVm/2p, where h is Planck’s constant and Vm is the resonator frequency, which leads to optical fields (called sidebands) with frequencies of vp+nVm , where vp is the frequency of the pump laser and n is an integer. b, When the width of the cavity spectrum (green line) is smaller than Vm , only one sideband can lie inside the cavity linewidth, and this sideband will be enhanced by the coupling. In this regime, which is called the resolved sideband regime, only one phonon is exchanged between the optical field and the resonator. c, When the width of the cavity spectrum is much larger than Vm , many sidebands can lie inside the cavity linewidth. In this unresolved sideband regime, more than one phonon can be exchanged between the optical field and the resonator. d, Simulations showing the development of self-sustained oscillations over time for a blue-detuned pump laser. The plot at the back shows how the number of photons in the cavity varies with time. The middle plot shows how the resonant wavelength of the cavity varies with time; sometimes it is longer than the wavelength of the pump laser (shown by vertical yellow plane) and sometimes it is shorter. The front plot shows the energy gained (red regions) or lost (blue) by the resonator as a function of time and position.
an amplitude Ap–p g, where Ap–p is the mechanical resonator oscillation amplitude. The self-sustained oscillations in turn modulate the optical transmission at the mechanical oscillation frequency, leading to high-frequency components of the optical transmission (Fig. 1d). The self-sustained oscillations are observed for all laser frequencies between the resonant frequency of the cavity when the resonator is in the up state and the resonant frequency when the resonator is in the down state, which indicates that the energy of the resonator exceeds the energy barrier between the two states. Stable self-sustained oscillators are highly desirable because they can provide low-noise high-frequency signals for potential applications in precision on-chip time-keeping, communications technology and sensing40. Generally, to reduce the effect of noise in such applications, it is essential to increase the oscillation amplitude as much as possible by pumping a large number of phonons into the oscillator. The high-amplitude optomechanical system that we study has very distinctive nonlinear dynamics in both the mechanical and optical domains. In the conventional framework of cavity optomechanics1,2, a blue-detuned pump laser resonantly enhances the sideband at vp2Vm (which is called the Stokes sideband), while the off-resonant sideband at vp þ Vm (the anti-Stokes sideband) is suppressed (Fig. 2a). The imbalance between the Stokes and anti-Stokes photon generation rates results in net phonon emission, thereby amplifying the resonator motion. This dynamical backaction of the cavity on the resonator can be represented by a negative damping rate GBA , which reduces the total mechanical damping rate G ¼ G0 þ GBA. When the pump power is large enough, GBA can become so negative that the total damping rate vanishes, leading to regenerative oscillations sustained by the static pump power. 728
On the other hand, for a red-detuned pump laser (that is, vp , vc), GBA is positive and leads to cooling.
High-amplitude motion in the unresolved sideband regime In cavity optomechanics, the resolved sideband regime (Fig. 2b) is regarded as the most efficient way to cool the mechanical resonator. However, it is only possible for each pump photon to generate a single phonon in this regime41, and the unresolved sideband regime (Fig. 2c) is preferable for amplifying the motion of the resonator to reach the high-amplitude regime because each photon can generate many phonons42,43 (Fig. 2c). (A more detailed analysis of the phonon generation process in the unresolved sideband regime can be found in the Supplementary Information.) In a system operated in the unresolved sideband regime, the oscillations can actually shift the cavity resonance significantly beyond the cavity linewidth (that is, Ap–pg ≫ g; Fig. 2d). As the oscillations move the cavity out of resonance with the pump laser, the cavity is empty most of the time and the resonator undergoes damped harmonic motion. However, when the resonator motion brings the cavity into resonance with the pump laser, the cavity fills quickly with photons that generate (or absorb) large numbers of phonons in an avalanche process, exciting self-sustained oscillations to large amplitudes. In this work, we were able to experimentally excite the nanomechanical resonator to high amplitudes by using a deeply unsolved sideband cavity system (g/2p ¼ 10 GHz versus Vm/2p ≈ 8 MHz) in combination with a large cavity dynamic range44 (g/g ¼ 10 nm), so that very large oscillation amplitudes (.300 nm, equivalent to more than 1012 phonons) were obtained. Figure 3a–c illustrates the high-amplitude optomechanical amplification processes in the time domain (see Supplementary
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Information for experimental details). When the nanomechanical resonator resides in the down state, a blue-detuned pump laser initiates the optomechanical amplification (phonon generation) process and starts coherent oscillations of the mechanical resonator. When the kinetic energy of the mechanical resonator becomes larger than the double-well potential barrier, the resonator can relax into either the down state (Fig. 3b) or up state (Fig. 3c) after the pump laser has been turned off45. Figure 3d shows the time evolution of the nanomechanical resonator response when the resonator is initially in its down state. When the blue-detuned pump laser is switched on at zero time, the resonator starts to oscillate coherently. The amplitude grows in time until it saturates after 250 ms. The resonator then oscillates in a high phonon number state above the double-well potential barrier. Note, that for Ap2p . g/g the cavity is no longer a linear transducer and the output signal has a distorted waveform (Supplementary Figs S6 and S7b), which makes direct determination of the amplitude difficult. Here, instead, we monitor the resonant frequency of the mechanical resonator Vm to map out the vibration amplitude; in a double-well potential as the oscillation amplitude goes up and down, Vm varies over a large range, a feature that is not available in a harmonic resonator. Figure 3g shows the digital Fourier transform spectra of the nanomechanical response for different times as the coherent oscillations build up. Initially, the resonator
is in the down state and oscillates with its intrinsic resonance frequency (Vm ¼ 7.4 MHz). However, when it is excited to high amplitudes and its energy exceeds the potential barrier, the resonance frequency drops to 3.1 MHz. Such a large change in the resonance frequency is characteristic of a mechanical resonator with a double-well potential, and is different from those induced by the optical spring; that is, the effect where the photon pressure is displacement-dependent, as reported in other optomechanical systems26. This resonant behaviour is further confirmed by switching off the pump laser and subsequently using a weak probe laser to monitor the nanomechanical motion as its energy is dissipated at a rate G0 while the resonator relaxes towards one of its two stable states (Fig. 3e,f ). The probe beam is too weak to change the frequency of the resonator by means of back-action (Fig. 3h,i), which confirms the mechanical origin of the observed frequency shift. Without active control, the resonator can relax into either the down or up states, as shown in the middle and right panels of Fig. 3, respectively. Later, we show that by manipulating the optomechanical damping GBA (that is, by actively cooling) we can reproducibly control into which well the resonator relaxes.
Zero-frequency singularity and slow down effect Figure 4a shows the continuous evolution of the oscillation frequency as it relaxes from the high-energy state towards the two
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Figure 4 | Ring-down and zero-frequency singularity. a,b, Oscillation frequency (a) and amplitude (b) versus time during free decay into the up (blue curve) and down (red) states. The two curves in a represent the instantaneous frequency of the resonator obtained from the time traces; the open symbols show the frequency determined from the digital Fourier transform spectra at different times (Fig. 3). The zero-frequency singularity appears as a pronounced dip in the oscillation frequency at 0.02 ms, which coincides with a large change in the oscillation amplitude. c, Simulated phase portrait of a resonator relaxing from a high-amplitude state into the up state. The symbols indicate the values at a fixed interval. The parameters used for simulation are extracted from the experiment; however, for clarity, a smaller mechanical quality factor (Qm ¼ 50) was used.
minima of the potential. The low-energy frequencies closely match the resonance frequencies obtained from the displacement noise spectra (Fig. 1e). The asymmetry in the potential implies a bifurcation once the resonator gets trapped in either of the two wells during the relaxation from a high-amplitude state. Figure 4a shows that the bifurcation point coincides with a divergence in the oscillation period. This is the first demonstration of the zerofrequency singularity in nanomechanical devices, which can be explained as follows: when the resonator energy approaches the top of the potential barrier, the kinetic energy of the resonator vanishes, so the resonator slows down. The resonator thus dwells for a long time near this potential extremum, before speeding up again after getting trapped in either of the two potential wells46 (Fig. 4c). In the actual measurement, the lowest frequency achieved depends statistically on the point of the phase trajectory at which the pump laser is turned off and the force noise experienced by the resonator during its ring-down (see Supplementary Information). This operation regime of NEMS provides a new mechanism to tune the resonance frequency of the resonator over a large range. This wide tunability of resonant frequency has important consequences for building tunable NEMS oscillators and for synchronization of large NEMS oscillator arrays47. The dependence of the mechanical resonance frequency on the energy of the resonator portrays the trajectory of the resonator and the slowed resonator effect when it is traversing the doublewell potential. This dependence is used to gauge the high-amplitude motion when the resonator is oscillating between the up and down states. (This would otherwise not be possible due to the limited sensing range of the optical cavity, as explained earlier.) The instantaneous frequency (that is, the inverse of the duration of each period) is extracted from the measured time traces. Then, using the relation between the motion amplitude and the oscillation period, the amplitude is determined. Figure 4b shows the extracted peak-to-peak oscillation amplitude Ap–p as the mechanical resonator relaxes towards its resting points. The novel operation of the optomechanical system thus yields amplitudes as high as Ap–p ¼ 350 nm. Comparing this amplitude with the threshold of Duffing bistability in the resonator, which is an intrinsic length scale of the mechanical resonator and varies from device to device, our work is the first to exceed this limit by almost two orders of magnitude (see Supplementary Information for details on the measurement of Duffing limits). As shown in Fig. 4c, an amplitude of 350 nm corresponds to a resonator energy of 9 fJ or, equivalently, to 4 × 1012 phonons in the resonator. 730
Demonstration of non-volatile mechanical memory operation Once the optomechanical interactions have raised the resonator above the potential well barrier and the pump laser has been turned off, the resonator stochastically relaxes into either the up or down state. However, controlling the final state is essential for many applications. We show that a deterministic selection of the final state is possible by using a second cooling laser to damp the oscillations of the resonator towards either the up or down state. The final state is selected by tuning the cooling laser to the red side of the optical resonances of the selected state (Fig. 1c); when the frequency of the cooling laser is between the two optical resonances (that is, to the red side of the up state), it damps the motion in the up potential well but amplifies the motion in the down potential well, so there is a higher probability of the resonator relaxing to the up state. On the other hand, when the cooling laser is tuned to the red side of the down state, the cooling power into the down state is much larger than into the up state, which is many linewidths away, so the down state is selected as the final state. By repeatedly exciting the resonator to large oscillations and subsequently cooling its motion, the asymmetry in the final state probability can be mapped out. Figure 5a shows the probability of relaxing into the up and down states as a function of the wavelength of the cooling laser: at wavelengths around l1 ¼ 1,560.75 nm the resonator always relaxes into the up state, whereas around l0 ¼ 1,561.00 nm it always relaxes into the down state. This enables the operation of our optomechanical system as a non-volatile memory element, where the up and down states of the resonator correspond to the ‘1’s and ‘0’s. The barrier between the states is large compared to the thermal energy (5 fJ corresponds to 350,000,000 K), so after the data are stored, the memory state is maintained without requiring optical power to retain it. This is in contrast to bit storage in the phase of an excited mechanical resonator34,35,48, which loses stored information when the input power is disconnected. Figure 5b shows a schematic representation of the sequence that we used to write, read and erase information. First a reset pulse of blue-detuned light was used to excite the resonator over the energy barrier via oscillations. A write pulse at the appropriate wavelength (either l1 or l0) was then used to direct the resonator in the up or down state as required. Finally, a weak probe pulse tuned to one of the optical resonances associated with the up or down states was used to read the state of the memory. Figure 5c shows a series of consecutive ‘1’s and ‘0’s written into the memory element. Sequences of 010101 and 001001 were
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Figure 5 | All-optical, non-volatile nanomechanical memory. a, Probability of the resonator relaxing to the up state (blue) or down state (red) versus wavelength of the cooling laser (Pin ¼ 7.5 dBm). For certain ranges of wavelengths there is a 100% probability of the resonator relaxing to a given state, so lasers with these wavelengths are used to write data to the nanomechanical memory. An optomechanical instability around 1,560.6 nm is highlighted. b, Writing a ‘1’ (left) and a ‘0’ (right) to a nanomechanical memory. First, a reset pulse (blue) excites the resonator to a high-amplitude state. A write pulse of wavelength l1 (pink, left) or l0 (red, right) then cools the motion of the resonator into the up state (which represents ‘1’, left) or the down state (‘0’, right). A weak probe laser (dark blue) then reads the state of the resonator. c, Non-volatile memory operation of the resonator. The upper panel shows a series of 10101. . . written onto the state of the resonator, while in the lower panel a series of 01001. . . bits are stored in the memory element. The blue time traces show the series of pulses that reset the memory by exciting large-amplitude oscillations in the resonator. The red (pink) pulses then cool the resonator from the high-amplitude regime into the selected down (up) state; the green time sequence shows the weak probe signal that traces the state of the mechanical resonator. The dark blue shows the state of the memory element.
repeated thousands of times with no error detected in the readout signal. The device shows no signs of wear or fatigue after more than one billion operations. The energy cost of the data operations can be estimated by adding the energies of the reset and write laser pulses. The current value of 10 mJ could be reduced by using optical cavities with higher quality factors (Qopt ¼ 20,000 for current devices) and by engineering the elastic energy profile of nanomechanical resonators.
and to demonstrate a non-volatile optical memory element. Moreover, these experiments have been performed on a scalable silicon platform, which should make it possible to exploit on-chip optical cooling and amplification in practical device applications such as optically multiplexed memory storage, addressable mechanical switch arrays, tunable optical filters and reconfigurable optical networks.
Methods
Conclusions By leveraging cavity optomechanical backaction in the unresolved sideband regime, we have been able to operate nanomechanical resonators at much higher amplitudes than previously achieved. We have also used the dynamic control made possible by optical backaction to observe the zero-frequency singularity, to actively manipulate the mechanical states of a resonator, to modify the damping dynamics in real time through external optical signals,
Device fabrication. The devices were fabricated from SOI wafers with a 110-nmthick silicon layer and a 3-mm-thick layer of buried oxide. Nanophotonic circuits were patterned by electron-beam lithography (Vistec Ebpg 5000þ), and a plasma dry etch using inductively coupled Cl2 gas chemistry. A wet etch release window was patterned using direct write photolithography, followed by a buffered oxide etch. Finally, the resonators were dried in a critical point dryer. Nanomechanical resonators with lengths of 10, 12.5, 15, 17.5 and 20 mm were fabricated. All device lengths demonstrated two stable states at rest. The measurements presented here were measured on a 10 mm resonator.
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Measurement. The measurements were performed in a vacuum chamber with a base pressure of 100 mtorr. Light was coupled in and out of the waveguide using an array of cleaved single-mode polarization-maintaining fibres aligned to the input/output grating couplers (Fig. 2a). The typical coupling efficiency was 30% per grating coupler. Three tunable diode lasers (two Santec TSL-210 and one HP 8648F) were used to amplify the motion of the resonator and subsequently quench the motion into the target state (see Supplementary Information for more details).
Received 29 July 2011; accepted 21 September 2011; published online 23 October 2011
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Acknowledgements The authors thank M. Rooks (Yale Institute for Nanoscience and Quantum Engineering) for help with electron-beam lithography, and M. Power for help with device fabrication. The authors also acknowledge funding support from the DARPA/MTO ORCHID programme through a grant from the Air Force Office of Scientific Research (AFOSR). H.X.T. acknowledges support from a Packard Fellowship in Science and Engineering and a career award from the National Science Foundation. M.P. acknowledges a Rubicon fellowship from the Netherlands Organization for Scientific Research (NWO)/Marie Curie Cofund Action.
Author contributions M.B. performed the device fabrication and carried out measurements and data analysis under the supervision of H.X.T. M.B. and M.P. contributed to numerical analysis of the coupled optomechanical system. M.B., M.P., M.L., W.P.H.P. and H.X.T. discussed the results and all authors contributed to the writing of the manuscript.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://www.nature.com/reprints. Correspondence and requests for materials should be addressed to H.X.T.
NATURE NANOTECHNOLOGY | VOL 6 | NOVEMBER 2011 | www.nature.com/naturenanotechnology
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