Abstract
Characterizing and controlling the out-of-equilibrium state of nanostructured Mott insulators hold great promises for emerging quantum technologies while providing an exciting playground for investigating fundamental physics of strongly-correlated systems. Here, we use two-color near-field ultrafast electron microscopy to photo-induce the insulator-to-metal transition in a single VO2 nanowire and probe the ensuing electronic dynamics with combined nanometer-femtosecond resolution (10â21âmâââs). We take advantage of a femtosecond temporal gating of the electron pulse mediated by an infrared laser pulse, and exploit the sensitivity of inelastic electron-light scattering to changes in the material dielectric function. By spatially mapping the near-field dynamics of an individual nanowire of VO2, we observe that ultrafast photo-doping drives the system into a metallic state on a timescale of ~150âfs without yet perturbing the crystalline lattice. Due to the high versatility and sensitivity of the electron probe, our method would allow capturing the electronic dynamics of a wide range of nanoscale materials with ultimate spatiotemporal resolution.
Similar content being viewed by others
Introduction
The ability to investigate and actively control electronic, optical and structural properties of quantum materials is key to addressing the pressing demands for sustainable energy, high-speed communication/computation, and high-capacity data storage1,2,3. These research aims require the development of quantitative methods and techniques that enable to visualize and control the complex structural, electronic and dielectric evolution of nanomaterials at the proper temporal (femtosecond (fs)) and spatial (nanometer (nm)) scales. This is particularly relevant for the case of strongly correlated materials undergoing electronicâstructural phase transitions, as, for instance, the representative of Mott systems, vanadium dioxide (VO2), which undergoes an insulator-to-metal transition (IMT) slightly above room temperature (~340âK). VO2 has recently attracted a renewed interest due to the promising applications in emerging technologies, such as volatile memories and neuromorphic computation1,4,5. This scenario becomes even more intriguing when the physical dimensions of the Mott systems shrink down to nm length scales. This is, in fact, the typical dimensions of the basic building blocks for most Mottronic devices, where quantum confinement and surface effects may lead to substantial modifications of the structural and electronic dynamics during the Mott transition process. Therefore, it is crucial to provide a deeper understanding of the out-of-equilibrium interplay between electronic and structural degrees of freedom in individual nanoscale Mott systems, which can be achieved only when both spatially and temporally resolved information is simultaneously retrieved.
So far, the underlying mechanism and structural dynamics of the IMT in the VO2 have been intensively studied by ultrafast X-rays diffraction6,7,8 and ultrafast electron diffraction9,10,11, which are indeed able to investigate the materialâs behavior with combined fs/atomic-scale resolution and have been shown to provide crucial insights into the structural mechanisms governing the Mott transitions. However, these approaches are not able to give direct information on the electronic degrees of freedom and are mainly limited to bulk crystals, thin films, or clusters of many nanostructures. On the other hand, time-resolved optical pumpâprobe techniques, such as reflectivity, ellipsometry, and photoemission, can provide access to detailed information on the fs dynamics of the initial electronic processes in the phase transitions by measuring the dielectric response12,13,14. However, such methods are inherently limited to a spatial resolution of micrometer scale, because of the long wavelength of the optical probes. Spatial information at smaller length scales can usually be obtained using conventional electron microscopy techniques15,16 or coherent x-ray imaging methods17,18, which can investigate single nanostructures with high spatial resolution, but without temporal resolution. Recently, a photon gating approach in transmission electron microscopy has been demonstrated for studying the phase transition of VO2 nanostructures19, where the authors have investigated the spatially average IMT dynamics of an ensemble of VO2 nanoparticles. Therefore, hitherto, investigation of the out-of-equilibrium interplay between electronic and structural degrees of freedom in VO2 has been mainly devoted to bulk crystals, thin films or ensemble measurements, whereas it has been challenging on individual nanostructures for which there is a substantial deficiency of relevant experimental data.
Ultrafast electron microscopy (UEM) is the most promising choice to address such challenge due to its unique high spatiotemporal imaging capabilities20,21,22,23,24,25,26,27,28,29,30. The compelling aspect of the UEM technique is the wide range of information provided by the analysis of the transmitted electrons coupled with high temporal resolution not limited by the detector response. It is possible to perform real-space imaging at the nm scale, record diffraction patterns for structural and lattice dynamics investigations, or acquire electron spectra with sub-eV resolution20,21,22,23,24,25,26,27,28,29,30. The latter case is generally referred to as electron energy loss spectroscopy (EELS) and provides a measure of the loss function of electrons scattered from the material (\(\Im \left\{ {1/\varepsilon } \right\}\)). In an ideal case, from the knowledge of the loss function and using KramersâKronig relations, one can retrieve the complex dielectric function of the material under investigation31. As the dielectric function directly correlates with the electronic degrees of freedom in materials, it would be possible to access the electronic dynamics across the IMT in the Mott systems via measuring the dielectric function change. However, such approach works well only when the loss function is known over the whole energy range. In a real situation, such constraint is generally hard to achieve, especially in the low-energy region. Moreover, the typical temporal resolution of UEM experiments is on the order of several hundreds of fs even with a single electron per pulse in the absence of space charge effects23,24,28,29,30. This value is determined by the statistical distribution of the time of arrival of electrons photoemitted from the photocathode with slightly different velocities, and it is generally much larger than the typical timescales of the electronic motion in materials, which tend to be on a few tens of fs or below. Although âphoton gatingâ19,32 and several electron pulse compression schemes, such as microwave compression33 and terahertz compression34, have been proposed to improve the temporal resolution of UEM into the timescale of electronic motion, implementation of pumpâprobe nanoscale imaging of material electronic dynamics only lasting few tens of fs have not been experimentally observed yet.
Here, we overcame these issues by exploiting a well-established variant of the UEM technique named photon-induced near-field electron microscopy (PINEM). In PINEM, inelastic electronâlight interaction takes place in the presence of nanostructures when the energy-momentum conservation condition is satisfied35. As a result of such interaction, electrons inelastically exchange multiple photon quanta that can be resolved in the electron energy spectrum as a series of discrete peaks, spectrally spaced by multiples of the photon energy (\(n\hbar \omega\)) on both sides of the zero-loss peak (ZLP)35,36,37. The largest electronâlight interaction is achieved when the optical pulse and electron pulse arrive simultaneously at the specimen. As shown in the theory38,39, the fundamental quantity to describe the PINEM process is the scattered field integral β(x, y) defined as:
where Ez is the component of the electric field along z (electrons propagation direction), Ï the frequency of the laser, and ve the speed of electrons. The probability of interaction between the near-field and the electron is determined by:
where Jn is the Bessel function of the first kind of order n, and it represents the probability of exchanging n quanta of light. The PINEM spectrum is then given by the sum over all the contributions:
In the case of weak interaction, one can write that Jn(Ï) â¼ Ïn, and thus the expression for the PINEM spectrum becomes:
For a cylindrical nanowire (NW) and within the weak interaction approximation the field integral \(\beta\) can be approximated at first order as40:
where Ï is the azimuth angle to the polarization direction, \(\chi _c = \frac{{2\varepsilon \left( \omega \right) - 1}}{{\varepsilon \left( \omega \right) + 1}}\) is the cylindrical susceptibility, a is the NW radius, and b is the impact parameter representing the in-plane projected distance between the electron and the NW central axis40,41.
From Eqs. (4) and (5), we note that the dielectric function ε(Ï) at the optical pump frequency Ï is directly encoded in the PINEM signal through the localized near-field generated around the nanostructure. As the lifetime of such near-field is defined by the optical pulse, which is considerably smaller than the electron pulse duration, PINEM is inherently a stationary method. To measure the temporal evolution of the dielectric response and the related electronic dynamics of materials, in addition to the infrared optical pulse (P1) that creates the PINEM, we have introduced an additional visible optical pulse (P2) to excite the sample transiently (Fig. 1a). P1 is synchronous with the electron pulse at the specimen to create PINEM for probe, while P2 is delayed with respect to P1 by a variable delay time for photon pump: a scheme that could be concisely referred to as two-color photon-pump/PINEM-probe experiment19. Such a method takes both advantages of the direct relation between localized near-field intensity and dielectric function, and the strong enhancement of the localized near-field excitation. It can potentially retrieve ε(Ï) with an energy resolution entirely determined by the laser bandwidth (about 20âmeV) rather than the electron bandwidth (about 1âeV) as in the regular EELS case42. Another crucial advantage with respect to regular EELS or PINEM regards the temporal resolution. In our two-color PINEM approach, the probe is no longer the initial, primary photoelectron pulse, whose temporal duration is typically on the order of several hundreds of fs. The probe in this approach is actually given by the inelastically scattered electrons, whose temporal duration is instead determined by the infrared laser pulse (P1) that drives the electronâlight coupling. Thus, the infrared pulse P1 acts as a âtemporal gateâ of the electron pulse19,32. A two-color PINEM experiment, where such gated electrons are measured as a function of the delay time between the two optical pulses (P2 and P1), thus has a temporal resolution only determined by the laser pulse (50âfs in our case), which almost an order of magnitude better than a normal UEM experiment where the gate pulse P1 is absent.
To demonstrate the capabilities of our approach, we have investigated the photoinduced IMT occurring in a single VO2 NW. The two-color PINEM imaging allowed to retrieve the delectric response of the VO2 NW with combined nmâfs resolutions. We reveal that ultrafast photo-doping drives the NW into a metallic state on a timescale of ~150âfs, as a result of a photocarrier-driven change of the interatomic potential, without yet perturbing the crystalline lattice. This is then followed by an ensuing recovery to the electronic equilibrium on a tens of piecosecond (ps) timescale related to the anharmonic excitation of transverse acoustic phonons. Such observations elucidate the crucial role of the electronic dynamics for initiating the IMT in the VO2 NW.
Results and discussion
One-color PINEM of a single VO2 NW
First, we performed a one-color PINEM experiment on a single VO2 NW to characterize the features of its PINEM spectrum at both insulating and metallic phases. The single-crystal VO2 NWs were synthesized by chemical vapor deposition (see âMethodsâ section) and were directly transferred to an amorphous silicon nitride membrane (Si3N4, 20-nm thick) window for measurements. The left panel of Fig. 2a shows a bright-field image of the NW (diameter of ~350ânm). In this experiment, only the first optical pulse P1 (duration of 50âfs, λâ=â800 m, fluence of ~4.1âmJ/cm2) was used to excite the sample with a polarization perpendicular to the NW axis to maximize the near-field excitation. Electron energy spectra were measured as a function of time delay (t1) between the optical pulse P1 and the electron pulse (Fig. 1a). The recorded PINEM spectra are presented in Fig. 1c. Discrete peaks at integer multiples of \(\hbar \omega\) appear on both sides of the ZLP (the latter is shown as a shaded area in Fig. 1b at t1â=â1.0âps and â1.0âps), and exhibit a maximum intensity at t1â=â0âfs (the shaded pink curve). As the P1 optical pulse is much shorter than the electron pulse, the temporal profile of the PINEM intensity shown in Fig. 1d is mainly determined by the electron pulse duration (~650âfs via a Gaussian fitting), which represents the typical temporal resolution of regular UEM experiments. As a result of the âphoton gatingâ in a two-color PINEM experiment, the temporal duration of the inelastically scattered electrons (PINEM electrons) is instead on the order of ~50âfs (given by the gating optical pulse duration19,32), thus improving the temporal resolution of about one order of magnitude.
To quantitatively characterize the localized near-field and the dielectric function of the VO2 NW in insulating and metallic phases, we acquired energy-filtered images while thermally heating the sample across the IMT. A real-space map of the localized near-field is retrieved by selecting only those electrons that have acquired photon energy quanta (see âMethodsâ section). In these measurements, the time delay between the P1 optical pulse and the electron pulse is fixed at t1â=â0âfs to attain the maximum electronâphoton coupling. Typical room temperature bright-field image (left panel) and energy-filtered PINEM image (right panel) are shown in Fig. 2a. The optically induced near-field appears as a bright-contrast region surrounding the VO2 NW. The maximum PINEM coupling at t1â=â0âfs can be also clearly verified by the temporal dependent PINEM images in Movie S1. Figure 2b shows two typical spatial distributions of the PINEM intensity across the NW (obtained by integration along the NW axis in the dashed white box indicated in the right panel of Fig. 2a) at two different set temperatures, Tsetâ= 299âK (blue line) and 353âK (orange line), respectively. Note that the optical pulse P1 also induces an additional temperature jump on the NW (~31âK, see âMethodsâ section), and thus the corresponding effective temperatures are 330âK (below IMT) and 384âK (above IMT), respectively. As shown in Fig. 2b, when thermally heating the nanowire across the IMT temperature (340âK), the PINEM intensity shows a pronounced decrease. This effect is further supported in Fig. 2c, which depicts the temperature dependence of the integrated intensity. An abrupt drop is observed when crossing the transition temperature, where the NW transforms from the monoclinic insulating phase into the rutile metallic phase (see insets in Fig. 2c). Such behavior can be attributed to the sudden decrease of the VO2 dielectric function at the photon energy 1.55 eV43, typical of a first-order transition from the insulating to the metallic phase, which results in a substantially smaller susceptibility. Such weaker dielectric response is thus responsible for a weaker localized near-field, and thus a reduced PINEM coupling.
To further confirm the dielectric origin of the observed behavior, we have performed numerical simulations using a finite element method, where we calculate the scattered field from a single VO2 NW illuminated by an 800-nm optical field (see âMethodsâ section). In the calculations, the incident field is chosen to be linearly polarized along the y-axis (perpendicular to the NW axis) and propagating along z negative direction (Fig. 3a). The transition is modeled as a variation of the dielectric function from εinsâ=â5.68 â i3.59 (ñinsâ=â2.49â+âi0.72) in the insulating phase to εmetâ=â2.38âââi3.26 (ñmetâ=â1.79â+âi0.91) for the metallic phase as derived from ref. 43 for the case of a thin film. In our experiment, we consider that the dielectric function of a thin film might represent a good approximation of the dielectric environment of our VO2 NWs, whose dielectric properties do not significantly differ from those of the bulk or high-quality thin films, especially for optical wavelengths in the visible range as adopted in our experiment44. The dielectric permittivity of the Si3N4 substrate is kept constant45. Also, all plasmonic effects for the investigated VO2 nanowires are intrinsically taken into account within the finite element simulations.
Figure 3b represents the computed spatial distribution of the field integral β projected on the NW plane (xy plane) for the insulating and metallic cases, together with their difference map. In Fig. 3c, we plot instead the absolute value of β for the two phases integrated along the x-direction and shown as a function of the spatial y-coordinate across the NW. The simulations clearly confirm that the reduced permittivity in the metallic phase is responsible for a weaker scattered field at the NW/vacuum interface, which results in the lower intensity of the PINEM signal as observed in our one-color experiment (Fig. 2b, c).
Such pronounced contrast in the PINEM signal and the qualitative agreement between experiments and simulations attest to the sensitivity of our approach to probe modifications of the dielectric function crossing the IMT and thus the ability to monitor its ultrafast dynamics with a two-color PINEM approach. Such high sensitivity of the technique is obviously not limited to the 800-nm light used here, but it extends to a wide range of light wavelengths.
Two-color PINEM of a single VO2 NW
We present here the two-color PINEM experiment performed on a single VO2 NW. As we will describe below, such a method allowed us to monitor the transient change of the dielectric function of the NW accessing the IMT dynamics with combined fs and nm resolutions. For a conceptually clean experiment (Fig. 1a), two essential requirements need to be fulfilled: (i) the pump optical pulse P2 driving the Mott transition must photo-excite the VO2 NW into the metallic phase without producing any appreciable near-field (i.e., PINEM signal), and (ii) the optical gating pulse P1 must have sufficient fluence to produce PINEM with an intense near-field signal but be below the threshold to trigger the Mott transition. In our case, an optical pulse (P2) with a central wavelength of 400ânm (duration of 50âfs) drives the transition, at which VO2 exhibits a significant optical absorption. This P2 optical pulse was set at a fluence of ~15.3âmJ/cm2 and was characterized by a polarization parallel to the NW axis, which minimizes the near-field excitation as the near-field only occurs at the end of the NW in such configuration (see the right panel of Fig. 2a). For the PINEM probe, the electron pulse was spatiotemporally coincident with a low fluence (~4.1âmJ/cm2) gating optical pulse (P1) with a central wavelength of 800ânm (duration of 50âfs). This P1 optical pulse was polarized along the direction perpendicular to the NW axis to maximize the optically induced near-field, and its time delay relative to the electron pulse was fixed at t1â=â0âfs to maximize the PINEM coupling (see Movie S1).
In VO2, a density-driven photoinduced IMT has been proven to occur with a critical energy dose ÎHC of 2âeV/nm3,46. For the case of a NW, the optical energy densities injected by the P1 and P2 pulses can be evaluated by resorting to scattering theory. In such framework, we determined the absorption cross section, Cabs, for the case of an infinite cylinder (see âMethodsâ section). The evaluated cross section is 2.63âÃâ10â7 m in the case of 400ânm (P2), while at 800ânm (P1) Cabs is 3.06âÃâ10â7âm. We then computed the absorbed optical energy density (energy per unit volume) injected within the NW as:
where Ïinc is the incident fluence and a is the cylinder radius. By considering the experimentally adopted parameters and geometrical configurations, we found that ÏE,ph is about 1âeV/nm3 at 800ânm, while increases to 3.5âeV/nm3 at 400ânm. The fact that ÏE,ph for 800ânm excitation is well below the critical energy dose ÎHC, whereas ÏE,ph for 400ânm is well above, is a strong confirmation that P2 is able to trigger the ultrafast IMT while P1 acts only as PINEM probe. Note that, electron beam may also induce effects on the IMT in VO2, such as lowering the IMT temperature by creating oxygen vacancies47. However, the dose of the electron pulse in our experiment is several orders of magnitude smaller than the conventional thermal electron beam and its effect is negligible.
As mentioned above, the amplitude of the localized near-field created around the NW by the P1 optical pulse (800ânm) strongly depends on the susceptibility and thus on ε(Ï). Besides the amplitude, also the decay length of such near-field can be directly connected to the material permittivity. In fact, according to Mie scattering theory for an infinite long cylinder the complex refractive index exhibits a direct spatial dependence48. This means that a change in the dielectric response induced by the P2 optical pulse (400ânm) can lead both to a modification of the PINEM intensity and, at the same time, to a different decay length of the PINEM signal at the NW/vacuum interface. To combine spatial and spectroscopic information, we acquired energy-filtered PINEM images at different delay times of t2 (see âMethodsâ section). Figure 4a shows the bright-field image of the investigated VO2 NW sitting on the Si3N4 membrane (left panel), and one of its corresponding energy-filtered PINEM image (t1â=â0âps, t2â=â0âps) (right panel), in which the transient near-field appears as a bright-contrast region surrounding it. To quantify the dielectric response to the IMT, we integrated the PINEM signal along the NW axis (within the area indicated by the blue box in the middle panel of Fig. 4a) and plotted it as a function of the position across the NW. Typical plots of such spatial distribution are shown in Fig. 4b for two different delay times, t2â=ââ0.4âps and t2â=â0.8âps (t1â=â0âps). For a more clear comparison of their lateral decay length, we also plot them in Fig. 4c with each curve normalized to its own maximum. The PINEM intensity shows a substantial decrease at 0.8âps, while the lateral decay length shows a simultaneous increase. The variation of the integrated PINEM intensity as a function of the delay time t2 is plotted in Fig. 4d. Upon the 400ânm pump, the PINEM intensity shows an initial ultrafast decrease of ~30% with a time constant of ~155âfs, followed by a slower recovery on tens of ps timescale. Such behavior is consistent with a transformation to a metallic phase with a smaller permittivity, which results in a weaker PINEM coupling (consistently with the observations of one-color PINEM at high temperatures). Figure 4e shows the temporal evolution of the lateral width (measured as the full width at half maximum, FWHM) of the integrated PINEM signal surrounding the NW. We observed an ultrafast lateral increase of the localized near-field profile of about 40â60ânm with a time constant of ~240âfs, followed by a slower recovery on a ~10âps timescale, whose dynamics is consistent with the intensity variation. Therefore, using our approach, it is also possible to follow the transition by looking at the change of the nanoscale spatial decay of the localized near-field. In both Fig. 4d, e, the red curves represent the best fit of the experimental data with a biexponential model where the temporal duration of the gated PINEM electrons and pump optical pulse P2 is explicitly taken into account. Importantly, it is also worth noting that the observed experimental behavior is well confirmed by the numerical simulations obtained for the two phases (see Fig. 2b), which show a lower interaction strength and a longer spatial decay in the metallic case with respect to the initial insulating state (see Fig. 3c).
Microscopic mechanism for the IMT dynamics
At a microscopic level, the Mott transition of bulk VO2 from the monoclinic insulating phase to the rutile metallic phase proceeds through a series of transient steps characterized by a well-defined character and time constants49. The photoexcitation of the insulating phase corresponds to a photo-doping of the conduction band with excited electrons50,51, and thus induces a redistribution of the electronic population within the 3d-symmetry bands. Such electronic rearrangement is thus responsible for a bandgap renormalization, which leads to an instantaneous collapse of the insulating bandgap (0.7âeV), rendering VO2 metallic50. At the same time, the depopulation of bonding V-V orbitals is responsible for a strong modification of the double-well interatomic potential of the monoclinic lattice, which becomes highly anharmonic and flat. Ultrafast optical probes, which are particularly sensitive to the dielectric environment, have shown that such lattice potential change, which is related to a modified screening of the Coulomb interaction, occurs with a sub-100 fs time constant in bulk VO2. At this point, the presence of a flat, anharmonic single-well potential triggers the atomic motions and leads to a removal of the long-range Peierls V-V dimerization. This has been observed with ultrafast structural probes to evolve on a 300â500âfs timescale6,7,10. Recently, large-amplitude uncorrelated atomic motions have also been noted to play a role in the V-V bond dilation on a timescale of about 150âfs7. Finally, the thermalization of the electronic population mediated by the excitation of transverse acoustic phonons over several ps temporal range can drive the lattice toward the final rutile metallic phase9,10,49,51.
As shown in Fig. 4b, d, the localized PINEM signal from the VO2 NW observed in our experiments exhibits an initial ultrafast dynamical process with a time constant of ~150âfs followed by a slower recovery process, which indicates the transition from the insulating to metallic phase without evidence of passing through any intermediate states. Furthermore, this value is nearly twice shorter than the ~300âfs of the coherent V-V displacement motions observed from previous structural probes9,10, while it is consistent with the timescale for photo-doping-induced lattice potential change, which could abruptly unlock the V dimers and yield large-amplitude uncorrelated motions, as also observed from the ultrafast optical studies on the bulk crystals7. Thus, with our approach, we could capture the transient state in which the NW has become metallic as induced by the photocarrier-induced change of the interatomic potential, but before the crystalline lattice perturbations occur and so the structure remains in the monoclinic phase, namely, the transient quasi-rutile metallic phase7. Since both the PINEM intensity and its spatial distribution can be directly related to the dielectric function, our method is inherently sensitive to the electronic dynamics of the VO2 NW. The advantage of our approach is the ability to retrieve such electronic dynamic information on a single nanostructure with combined nmâfs spatiotemporal resolution, which is particularly relevant, especially when nanoscale inhomogeneity plays a decisive role in the transition process18. Following the fs dynamics, we also observe a slower recovery toward the electronic equilibrium through the electronâlattice coupling on a timescale of tens of ps, which can be readily associated with anharmonic excitations of acoustic phonons. Thus, a themodynamically stable metallic rutile phase is not fully reached and then the system relaxes back to the insulating monoclinic phase.
It is worth noting that, because the photon-pump/PINEM-probe experiment was carried out in an ultrafast electron microscope, it would be possible to interrogate similar nanostructured materials under the same experimental conditions by ultrafast dark-field imaging or ultrafast diffraction using the temporally gated PINEM electrons. The latter would provide structural information with similar enhanced temporal and spatial resolutions and enable the possibility to simultaneously explore both the electronic (dielectric) and structural dynamics of the investigated individual nanostructures on a few tens of fs timescale.
In this work, we have implemented a two-color near-field UEM method and demonstrated its ability to access the initial ultrafast electronic process in the optically induced IMT in an individual VO2 NW. We observed the temporal evolution of its dielectric response with PINEM imaging on nm and fs scales, achieving a combined spatiotemporal resolution several orders of magnitude larger than the conventional optical probes and static imaging. The high sensitivity of PINEM to the ultrafast dielectric response driven by laser photoexcitation attests to the high versatility of our approach for spatially resolved investigation of electronic dynamics and phase transitions that last a few tens of fs. Furthermore, incorporating with the advanced attosecond optical pulse generation techniques32,52, it is feasible to achieve sub-fs and even attosecond temporal resolution in UEM via our approach. Therefore, this demonstration would be an important step towards the ultimate establishment of sub-fs/as resolution in electron microscopy for capturing electron motion in nanomaterials in real space and time.
Methods
Synthesis of VO2 NWs
The single-crystal VO2 NWs were synthesized in a low-pressure horizontal quartz tube furnace by a chemical vapor transport deposition (CVD) method. In brief, V2O5 powder was placed in a quartz boat at the center of a horizontal quartz tube furnace, and a ~1.5âcm downstream unpolished quartz (~1âcmâÃâ0.6âcm) was used as product collecting substrate. The furnace was heated to 950â°C to evaporate the V2O5 powder. Then the evaporated V-related species were transported by Ar carrier gas (6.8 sccm, 4âTorr) to the quartz substrate, and free-standing VO2 NWs grew on the substrate surface. After 15âmin, the CVD system naturally cooled down to room temperature.
One- and two-color PINEM experiments
A sketch of our one- and two-color PINEM experiments is depicted in Fig. 1a. The UEM used in this work, which is detailed in ref. 21, is a modified JEOL 2100 TEM integrated with an ultrafast amplified laser system delivering 50-fs pulses at 50âkHz repetition rate. The UV pulse (266ânm) impinges on the cathode photo-emitting electron pulses, while the 400ânm (P2) and 800ânm (P1) optical pulses (duration of 50âfs) are directly focused on the sample. The TEM is equipped with a Gatan imaging filter spectrometer, which allows us to acquire an energy-filtered image with a tuneable energy window. For the images presented in this work, we used a 15âeV wide energy window centered in the gain part of the spectrum with exposure time for the CCD sensor of about 60â90âs. For the one-color PINEM experiment, only use the 800ânm (P1) optical pulses to excite the specimen, with the optical polarization perpendicular to the NW axis to maximize the localized near-field excitation and PINEM coupling. For the two-color PINEM experiment, both 400ânm (P2) and 800ânm (P1) optical pulses were used to illuminate the specimen: the 800ânm (P1) optical pulse is linearly polarized perpendicular to the NW axis and fixed at the zero-time delay (t1â=â0âfs) relative to the electron pulse to maximize the localized near-field excitation and PINEM coupling, whereas the 400ânm (P2) optical pulse for pump is linearly polarized parallel to the NW axis to minimize the localized near-field excitation and PINEM coupling.
In our experiments, we have recorded four scans in imaging mode and two scans in spectroscopy mode. They are all showing very similar results and therefore in the manuscript, we plot a representative dataset, which has been obtained by properly averaging the near-field around the NW.
Scattering theory for an infinite cylinder
To determine the absorption cross section for an infinite cylinder, we have resorted to scattering theory. In particular, we have used the derivation provided by Bohren & Huffman48, where the scattering and extinction efficiencies in case of parallel (I) polarization (used for P2) are given by:
whereas in the case of normal (II) polarization (used for P1) we have:
Thus, the absorption efficiencies can be evaluated as:
where a is the NW radius, L its length, an and bn are coefficients that depend on the Hankel and Bessel functions, as reported in Bohren & Huffman53. The absorption cross section per unit length Cabs is related to the corresponding efficiency via the geometrical factor 2a as Cabsâ=â2a Qabs. The evaluated cross section Cabs is 2.63âÃâ10â7 m in the case of 400ânm, while at 800ânm Cabs is 3.06âÃâ10â7âm. We then computed the absorbed optical energy density (energy per unit volume) injected within the nanowire as:
where Ïinc is the incident laser fluence. The numerical evaluation has been implemented using two different codes: MatScat54,55 and ICOTOOL56, which provided identical results. Here, we have considered ñinsâ=â2.49â+âi0.72 at 800ânm and ñinsâ=â2.09â+âi1.31 at 400ânm. By considering the experimentally adopted parameters and geometrical configuration, we found that the energy density injected at 800ânm is about 1âeV/nm3, while at 400ânm we have about 3.5âeV/nm3. The fact that ÏE,ph for 800ânm excitation is well below the critical energy dose ÎHC for a photoinduced IMT phase transition of 2âeV/nm3, whereas ÏE,ph for 400ânm is well above, is a strong confirmation that only the blue light pulse will be able to drive the transition.
Equilibrium heating model
For the static heating experiment, it is important to estimate the contribution to the nanowire equilibrium temperature from the 800-nm light pulse. In first approximation, such temperature change can be obtained following a phononic heat capacity approach57. In this model, the absorbed flux, fabs, is given by:
where Cph is the phononic heat capacity. The expression for the absorbed flux depends on the geometry of the structure. For the planar Si3N4 membrane, we can consider:
where α is the absorption coefficient, hv the photon energy, Eg the energy gap, R the reflectivity, and Ïinc the laser fluence. For the case of a nanowire modeled by an infinite cylinder, the absorbed flux is instead given by:
where Cabs is the absorption cross section and a is the cylinder radius.
The heat capacity can be written as:
where na is the atomic density, and θD is the Debye temperature. When solving the integral equation Eq. (10) for the VO2 NW using Eq. (12) for fabs and with the parameters specified in Table 143,44,45,58, we find that the temperature jump associated with the 800-nm infrared pulse is 31âK, thus below the critical transition temperature change (~60âK) and consistent with the observation of the thermally induced IMT. For the planar Si3N4 substrate, following the same approach although using Eq. (11) for fabs, the temperature variation induced by the laser is smaller than 1âK and thus negligible.
Numerical simulations
The experimental geometry has been replicated to perform a finite element method simulation using COMSOL multiphysics. The 3D model is composed of the VO2 NW and a thin Si3N4 substrate. In the outer part, a perfect matching layer (PML) was added to confine the solution. The Si3N4 substrate passes through the PML and can be considered infinite. The incident light wave is chosen to be linearly polarized along the y-axis (perpendicular to the NW axis) and propagating along z negative direction. A parametric sweep of the real and imaginary part of the VO2 complex refractive index ñ, using the values reported in ref. 43, replicates the insulator-to-metal transition. The dielectric permittivity of the Si3N4 layer remains constant since it exhibits a negligible variation over a temperature range of several hundreds of °C45. Moreover, the temperature change induced by the pump optical pulse on the Si3N4 membrane is much smaller than 1âK. The study is solved at a frequency of νâ=â374âTHz (1.55âeV, 800ânm), considering a NW with dimensions 3âμm as length and 300ânm as diameter, placed on a 20ânm thick Si3N4 substrate. By taking advantage of the symmetry of both geometry and field source, the simulation volume has been reduced to one quarter, placing PMC and PEC surfaces in the yz and xz planes, respectively. The PINEM field β and its spatial integral has been performed over a 3-μm region along z and of 4âμm along x, i.e., a smaller region compared to the actual size of the simulation domain in order to minimize possible residual reflections from the boundary conditions.
Supplementary Movie S1: Temporal evolution of one-color PINEM images of a single VO2 NW with P1 optical pulse (duration of 50âfs, λâ=â800âm, fluence of ~4.1âmJ/cm2) polarized perpendicularly to the NW axis.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Change history
01 April 2021
A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-22477-6
References
Del Valle, J. et al. Subthreshold firing in Mott nanodevices. Nature 569, 388â392 (2019).
Wang, S. et al. Vanadium dioxide for energy conservation and energy storage applications: synthesis and performance improvement. Appl. Energy 211, 200â217 (2018).
Yang, J. J., Strukov, D. B. & Stewart, D. R. Memristive devices for computing. Nat. Nanotechnol. 8, 13 (2013).
Prezioso, M. et al. Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature 521, 61â64 (2015).
Sun, W. et al. Understanding memristive switching via in situ characterization and device modeling. Nat. Commun. 10, 1â13 (2019).
Cavalleri, A. et al. Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition. Phys. Rev. Lett. 87, 237401 (2001).
Wall, S. et al. Ultrafast disordering of vanadium dimers in photoexcited VO2. Science 362, 572â576 (2018).
Cavalleri, A. et al. Ultra-Broadband Femtosecond Measurements of the Photo-Induced Phase Transition in VO2: From the Mid-IR to the Hard X-rays. J. Phys. Soc. Jpn. 75, 011004 (2006).
Baum, P., Yang, D.-S. & Zewail, A. H. 4D visualization of transitional structures in phase transformations by electron diffraction. Science 318, 788â792 (2007).
Morrison, V. R. et al. A photoinduced metal-like phase of monoclinic VO2 revealed by ultrafast electron diffraction. Science 346, 445â448 (2014).
Yang, D.-S., Baum, P. & Zewail, A. H. Ultrafast electron crystallography of the cooperative reaction path in vanadium dioxide. Struct. Dyn. 3, 034304 (2016).
Giannetti, C. et al. Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach. Adv. Phys. 65, 58â238 (2016).
Rini, M. et al. Photoinduced phase transition in VO2 nanocrystals: ultrafast control of surface-plasmon resonance. Opt. Lett. 30, 558â560 (2005).
Madan, I. et al. Real-time measurement of the emergence of superconducting order in a high-temperature superconductor. Phys. Rev. B 93, 224520 (2016).
He, X. et al. In situ atom scale visualization of domain wall dynamics in VO2 insulator-metal phase transition. Sci. Rep. 4, 6544 (2014).
Hu, B. et al. Externalâstrain induced insulating phase transition in VO2 nanobeam and its application as flexible strain sensor. Adv. Mater. 22, 5134â5139 (2010).
Kübler, C. et al. Coherent structural dynamics and electronic correlations during an ultrafast insulator-to-metal phase transition in VO2. Phys. Rev. Lett. 99, 116401 (2007).
Vidas, L. et al. Imaging nanometer phase coexistence at defects during the insulatorâmetal phase transformation in VO2 thin films by resonant soft X-ray holography. Nano Lett. 18, 3449â3453 (2018).
Hassan, M. T., Liu, H., Baskin, J. S. & Zewail, A. H. Photon gating in four-dimensional ultrafast electron microscopy. Proc. Natl Acad. Sci. USA 112, 12944â12949 (2015).
Zewail, A. H. Four-dimensional electron microscopy. Science 328, 187â193 (2010).
Piazza, L. et al. Design and implementation of a fs-resolved transmission electron microscope based on thermionic gun technology. Chem. Phys. 423, 79â84 (2013).
Fu, X., Chen, B., Tang, J., Hassan, M. T. & Zewail, A. H. Imaging rotational dynamics of nanoparticles in liquid by 4D electron microscopy. Science 355, 494â498 (2017).
Yurtsever, A., van der Veen, R. M. & Zewail, A. H. Subparticle ultrafast spectrum imaging in 4D electron microscopy. Science 335, 59â64 (2012).
Barwick, B., Park, H. S., Kwon, O.-H., Baskin, J. S. & Zewail, A. H. 4D imaging of transient structures and morphologies in ultrafast electron microscopy. Science 322, 1227â1231 (2008).
Lorenz, U. J. & Zewail, A. H. Observing liquid flow in nanotubes by 4D electron microscopy. Science 344, 1496â1500 (2014).
Fu, X., Chen, B., Tang, J. & Zewail, A. H. Photoinduced nanobubble-driven superfast diffusion of nanoparticles imaged by 4D electron microscopy. Sci. Adv. 3, e1701160 (2017).
Chen, B. et al. Dynamics and control of gold-encapped gallium arsenide nanowires imaged by 4D electron microscopy. Proc. Natl Acad. Sci. USA 114, 12876â12881 (2017).
Vanacore, G., Fitzpatrick, A. & Zewail, A. Four-dimensional electron microscopy: Ultrafast imaging, diffraction and spectroscopy in materials science and biology. Nano Today 11, 228â249 (2016).
Feist, A. et al. Ultrafast transmission electron microscopy using a laser-driven field emitter: femtosecond resolution with a high coherence electron beam. Ultramicroscopy 176, 63â73 (2017).
Houdellier, F., Caruso, G. M., Weber, S., Kociak, M. & Arbouet, A. Development of a high brightness ultrafast transmission electron microscope based on a laser-driven cold field emission source. Ultramicroscopy 186, 128â138 (2018).
Stöger-Pollach, M., Laister, A. & Schattschneider, P. Treating retardation effects in valence EELS spectra for KramersâKronig analysis. Ultramicroscopy 108, 439â444 (2008).
Hassan, M. T., Baskin, J., Liao, B. & Zewail, A. High-temporal-resolution electron microscopy for imaging ultrafast electron dynamics. Nat. Photonics 11, 425 (2017).
Gliserin, A., Walbran, M., Krausz, F. & Baum, P. Sub-phonon-period compression of electron pulses for atomic diffraction. Nat. Commun. 6, 1â8 (2015).
Ryabov, A. & Baum, P. Electron microscopy of electromagnetic waveforms. Science 353, 374â377 (2016).
Barwick, B., Flannigan, D. J. & Zewail, A. H. Photon-induced near-field electron microscopy. Nature 462, 902â906 (2009).
Feist, A. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200â203 (2015).
Piazza, L. et al. Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field. Nat. Commun. 6, 1â7 (2015).
Park, S. T. & Zewail, A. H. Photon-induced near-field electron microscopy: mathematical formulation of the relation between the experimental observables and the optically driven charge density of nanoparticles. Phys. Rev. A 89, 013851 (2014).
GarcÃa de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Multiphoton absorption and emission by interaction of swift electrons with evanescent light fields. Nano Lett. 10, 1859â1863 (2010).
Park, S. T., Lin, M. & Zewail, A. H. Photon-induced near-field electron microscopy (PINEM): theoretical and experimental. N. J. Phys. 12, 123028 (2010).
Park, S. T., Yurtsever, A., Baskin, J. S. & Zewail, A. H. Graphene-layered steps and their fields visualized by 4D electron microscopy. Proc. Natl Acad. Sci. USA 110, 9277â9282 (2013).
Pomarico, E. et al. meV resolution in laser-assisted energy-filtered transmission electron microscopy. ACS Photonics 5, 759â764 (2017).
Wan, C. et al. On the optical properties of thinâfilm vanadium dioxide from the visible to the far infrared. Ann. Phys. 531, 1900188 (2019).
Fu, D. et al. Comprehensive study of the metal-insulator transition in pulsed laser deposited epitaxial VO2 thin films. J. Appl. Phys. 113, 043707 (2013).
Lukianova, O. & Sirota, V. Dielectric properties of silicon nitride ceramics produced by free sintering. Ceram. Int. 43, 8284â8288 (2017).
Tao, Z. et al. The nature of photoinduced phase transition and metastable states in vanadium dioxide. Sci. Rep. 6, 1â10 (2016).
Zhang, Z. et al. Nanoscale engineering in VO2 nanowires via direct electron writing process. Nano Lett. 17, 851â855 (2017).
Bohren, C. F. & Huffman, D. R. Absorption and scattering of light by small particles. (John Wiley & Sons, 2008).
Wegkamp, D. & Stähler, J. Ultrafast dynamics during the photoinduced phase transition in VO2. Prog. Surf. Sci. 90, 464â502 (2015).
Wegkamp, D. et al. Instantaneous band gap collapse in photoexcited monoclinic VO2 due to photocarrier doping. Phys. Rev. Lett. 113, 216401 (2014).
Cavalleri, A. et al. Band-selective measurements of electron dynamics in VO2 using femtosecond near-edge X-ray absorption. Phys. Rev. Lett. 95, 067405 (2005).
Hassan, M. T. Attomicroscopy: from femtosecond to attosecond electron microscopy. J. Phys. B Mol. Opt. Phys. 51, 032005 (2018).
Bohren, C. & Huffman, D. A. Potpourri of Particles. Absorption and scattering of light by small particles. 181â183 (John Wiley & Sons, Hoboken, NJ, USA, 1983).
Schäfer, J.-P. Implementierung und Anwendung analytischer und numerischer Verfahren zur Lösung der Maxwellgleichungen für die Untersuchung der Lichtausbreitung in biologischem Gewebe, Verlag nicht ermittelbar, (2011).
Schäfer, J., Lee, S.-C. & Kienle, A. Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence. J. Quant. Spectrosc. Ra. 113, 2113â2123 (2012).
Wriedt, T. & Hellmers, J. New scattering information portal for the light-scattering community. J. Quant. Spectrosc. Ra. 109, 1536â1542 (2008).
Lee, S. et al. Anomalously low electronic thermal conductivity in metallic vanadium dioxide. Science 355, 371â374 (2017).
Chandrashekhar, G., Barros, H. & Honig, J. Heat capacity of VO2 single crystals. Mater. Res. Bull. 8, 369â374 (1973).
Acknowledgements
This work was supported by the Materials Science and Engineering Divisions, Office of Basic Energy Sciences of the U.S. Department of Energy under contract no. DESC0012704, and the National Nature Science Foundation of China (NSFC) at grant no. 11974191. The LUMES laboratory acknowledges support from the NCCR MUST and ERC Consolidator Grant ISCQuM. G.M.V. is partially supported by the EPFL-Fellows-MSCA international fellowship (grant agreement no. 665667). F.B. was supported by the Swiss National Science Foundation (Project no. 200020-179157). The materials synthesis was supported by U.S. NSF grant no. DMR-1608899.
Author information
Authors and Affiliations
Contributions
X.F. and Y.Z. conceived the research project. X.F., F.B., S.G., I.M., G.B. and G.M.V. did the experimental measurements and data analysis. L.J. and J.W. synthesized the sample. X.F., F.B., S.G., I.M., and G.M.V. wrote the manuscript with input from Y.Z., F.C., J.W., and T.L.G.. S.G. developed the model and performed the numerical simulations. All the authors contributed to the discussion and the revision of the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information Nature Communications thanks Mohammed Hassan, Anatoli Ischenko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Publisherâs note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the articleâs Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the articleâs Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Fu, X., Barantani, F., Gargiulo, S. et al. Nanoscale-femtosecond dielectric response of Mott insulators captured by two-color near-field ultrafast electron microscopy. Nat Commun 11, 5770 (2020). https://doi.org/10.1038/s41467-020-19636-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-020-19636-6
This article is cited by
-
Time-resolved transmission electron microscopy for nanoscale chemical dynamics
Nature Reviews Chemistry (2023)
-
Spatio-temporal shaping of a free-electron wave function via coherent lightâelectron interaction
La Rivista del Nuovo Cimento (2020)