The way conduction electrons respond to ultrafast external perturbations in low dimensional materials is at the core of the design of future devices for (opto)electronics, photodetection and spintronics. Highly charged ions provide a tool for probing the electronic response of solids to extremely strong electric fields localized down to nanometre-sized areas. With ion transmission times in the order of femtoseconds, we can directly probe the local electronic dynamics of an ultrathin foil on this timescale. Here we report on the ability of freestanding single layer graphene to provide tens of electrons for charge neutralization of a slow highly charged ion within a few femtoseconds. With values higher than 1012 A cm−2, the resulting local current density in graphene exceeds previously measured breakdown currents by three orders of magnitude. Surprisingly, the passing ion does not tear nanometre-sized holes into the single layer graphene. We use time-dependent density functional theory to gain insight into the multielectron dynamics.
Its exceptionally high carrier mobility1 makes graphene a promising material for future electronic applications. The linear Dirac-like dispersion and the associated constant high carrier velocity promise the realization of ultrafast devices in electronics2, optics3 or even q-bits based on nitrogen vacancies4. The ultra-short timescales involved, <1 ps, provide stringent requirements on material properties. Direct current measurements on supported single layer graphene (SLG) reveal breakdown currents due to Joule heating larger than in copper, with densities of about 108–109 A cm−2 (refs 5, 6, 7, 8). Note that these measurements include substrate and finite size effects, which may increase the breakdown current as compared with pristine freestanding graphene. Indeed, heat dissipation via the substrate seems essential to achieve these numbers9,10. Photoexcitation measurements reveal efficient excited carrier relaxation within a few hundred femtoseconds11,12 yet probe the lattice on the length scale of the optical wavelength. Moreover, large electric fields13,14 and collisions with energetic particles15,16,17,18,19,20,21,22,23,24,25,26,27,28, which allow for tuning the properties of graphene, further modify the response of the material. A reliable tool to locally probe the timescales of the electronic response of pristine graphene to large fields is thus urgently needed.
One way to measure the short-time response of materials is the irradiation with highly charged ions (HCIs), which results in an extremely large, local external field: the Coulomb field of an approaching HCI. A charge state of qin=35 implies a local electric field strength of 1.8 × 1011 V m−1 at 5 Å distance from it. Achieving the same local field strength using laser fields would require power densities above 1017 W cm−2, a field strength where non-destructive measurements become challenging. Previous work on scattering of HCI from solid surfaces or their transmission through freestanding carbon membranes reported unexpectedly large charge capture within 5–30 fs (refs 29, 30, 31, 32, 33, 34).
In this contribution, we take the final step and present the results for the ultimately thin carbon target, a freestanding single layer of graphene. Measurements of the charge state and energy of the transmitted ions and time-dependent density functional theory (TDDFT) calculations show that large number of electrons are extracted from a very small surface area, which implies a high local surface current density. We identify a multielectron process and estimate the relevant timescales for charge transfer along the graphene layer. For example, while passing through SLG, the HCI with initial charge state qin=30 captures ∼25 electrons on a timescale of a few fs. Based on the experimental data, a lower bound for the current densities reached locally within a nm2 area is at least 1012 A cm−2 exceeding the breakdown current densities reported so far5,6,7,8 by three orders of magnitude.
Exit charge state analysis
The amount of charge transferred to the HCI can be estimated by measuring the distribution of exit charge states qout and the energy of highly charged Xe ions after transmission through SLG (for details of sample preparation, see Supplementary Note 1). Initial ion charge states of 10≤qin≤35 and velocities below 0.5 nm fs−1 were used. Ions are transmitted through SLG under normal incidence and analysed with respect to their charge state and kinetic energy by an electrostatic analyser (Fig. 1c). Typical transmission spectra (Fig. 1a) show a distribution of different exit charge states, with a mean value shifted towards smaller exit charge states for slower ions. To extract the abundances and widths of every single peak, the spectra have to be deconvoluted with the analyser function, since the spectra are broadened by the design of the electrostatic analyser (details on the data evaluation can be found in ref. 35). The corrected abundances follow a symmetric Gaussian function with a full width at half maximum of three to five electrons as a result of final de-excitation processes. From these Gaussian fits the mean value is extracted. Even for the smallest velocities (largest interaction times) used in our experiment (vmin=0.13 nm fs−1), remains considerably larger than the equilibrium charge state of a Xe ion in a solid target ()36, indicating incomplete neutralization.
Depending on the initial charge state the HCI captures and stabilizes between 20 and 30 electrons during its transmission through graphene (Fig. 1e). The experimentally observed average electron capture is extracted from the mean exit charge state of each transmission spectrum. The transmission time through graphene can be defined by τ=deff/v, where v is the ion velocity. The effective interaction length deff corresponds to the projectile-surface distance where the electron transfer processes between the HCI and graphene take place. The values of deff can be obtained from the TDDFT calculations which yield for qin=20 a value of Å. This is in good agreement with predictions of the classical over the barrier model37.
The number of captured and stabilized electrons (they are not reemitted due to autoionization processes) as function of interaction time is shown in Fig. 1e. The data can be well fitted by the simple expression
with an effective neutralization time constant . Using deff=9 Å we obtain =2.1 fs for qin=35, and =1.4fs for qin=20, respectively. The performed TDDFT study (for details, see Supplementary Note 2 and Supplementary Fig. 4) shows a multielectron character of the charge transfer that can explain the experimentally observed strong reduction of the charge state of the HCI. We calculate that HCIs with initial charge states qin=10, 20 and 40 capture ∼9, ∼17 and ∼34 electrons during the passage through the graphene layer, respectively.
Since at least qin− electrons are transferred from the graphene sheet to the HCI during the interaction, the lower bound for the electron transfer rate is given by (qin−)/τ, which corresponds to 1016 electrons per second as can be estimated from the experimental data. This corresponds to a local current of I≳1.5 mA. The TDDFT study shows on the one hand that the charge is extracted from the graphene area with lateral radius R=5 Å around the impact point that we can define as an interaction region (Figs 1b and 2), and on the other hand that the electron flow along the graphene layer compensates the electron extraction by the HCI on the timescale of the collision (fs), otherwise the neutralization of the projectile would be stopped by the local charging of the target. The latter is in accord with experimental data that shows the absence of the post-collisional defects that would result from Coulomb explosion (see the section Transmission electron microscopy results). The electrons moving along graphene enter the interaction region crossing the surface S=2πRh (h=3.4 Å is the width of the graphene layer that we estimate from the interlayer spacing of graphite38). Thus, a time averaged electron current density J=I/S in the graphene plane exceeding ∼6 × 1011 A cm−2 is reached. This value, however, is just a lower limit because it only accounts for the electrons captured by the projectile. Indeed, because of the interaction with HCI Nvac electrons will also be emitted into vacuum. We calculate that for each captured electron approximately one additional electron is emitted. Nvac can be even larger if one accounts for Auger processes involving tightly bound electronic shells of the projectile. Estimations as high as Nvac≈3 × qin (ref. 39) have been reported.
Transmission electron microscopy results
Failure to sufficiently resupply the lost charge and to dissipate the absorbed energy on a timescale small compared with lattice vibrations would result in Coulomb explosion tearing large holes (of the order of 10 nm) into the SLG, as we have observed for carbon nanomembranes35,40. Despite the possible self-healing of localized defects in graphene41, such extended structural modifications should be detectable using transmission electron microscopy (TEM) or scanning transmission electron microscopy (STEM), yet careful investigation of the irradiated SLG does not reveal any nanometre-sized defect structures. Note that for freestanding SLG used in our study, in contrast to supported graphene layers, the defect formation because of a collision cascade in the substrate42 is not operative. In our case, elastic collisions (nuclear stopping) may cause direct knockout of carbon atoms, but less than one carbon atom is sputtered on average by a 10–100 keV Xe ions according to Lehtinen et al.43. Even if point defects are produced, they will likely disappear due to dissociation of ubiquitous hydrocarbon molecules41. In Fig. 1d, a typical TEM image of a freestanding monolayer of graphene after irradiation with Xe40+ ions with a kinetic energy of 180 keV is shown. The applied fluence of 1012 ions per cm2 corresponds to approximately six ion impacts within this 25 nm × 25 nm frame. No rupture could be detected. This is in strong contrast to ultrathin polymeric carbon nanomembranes, where, because of low electron mobility, creation of pores with diameters of up to a few nanometre was observed after exposure to HCIs35,40. The absence of any traces of large-scale lattice deformations thus confirms the intrinsic ability of suspended SLG to locally sustain exceptionally high current densities, even though it cannot efficiently diffuse heat to a substrate9,10.
Local current density
To illustrate the way the electronic processes take place, in Fig. 2, we show snapshots of the current density for a qin=20 projectile incident at graphene with velocity v=0.87 nm fs−1. Results of the TDDFT calculations are presented for four different HCI–graphene distances zion along the ingoing trajectory path. We use cylindrical (ρ, z) coordinates, with the z axis set along the projectile trajectory assuming normal incidence geometry. Note that because of the cylindrical symmetry in our calculations (see Supplementary Note 2 for details), there is no azimuthal angular dependence. Already at Å charge transfer from graphene to the HCI is sizable. For Å, the Jz component of the current density along the direction of motion is further increased and a significant transverse current density along the graphene layer (located at z=0) can be observed.
The current density along the direction of motion Jz determines the charge exchange and energy loss of the HCI (see the section Energy loss), while the current density along the transverse direction Jρ shows the fast local response of graphene to the strong HCI perturbation. In fact, our calculations reproduce our experimental estimate since the transverse current densities in the proximity of the graphene layer reaches values as high as 1012 A cm−2. This means that, transiently and locally, in the femtosecond and nanometre scale, graphene is able to sustain extremely high current densities. The positive charges created by electron capture and electron emission are spread over the entire layer44.
As neutralization is incomplete in our measurements charge state effects on the energy loss become experimentally accessible. As observed earlier with thicker foils31,34,45, the energy loss of a HCI passing through thin sheets strongly depends on the number of electrons transferred to the ion. The energy loss as experimentally deduced from the positions of the peaks for exit charge states qout=2 and qout=4 increases quadratically with the incident charge state (Fig. 3a). We observe keV energy losses, which are more than an order of magnitude larger than the result from a TRIM simulation (nuclear and electronic stopping) for neutral Xe transmitted through a layer with areal density of 3.82 × 1015 at cm−2 representing the target46 (dashed line in Fig. 3a). This simulation predicts an energy loss of 228 eV taking into account our detector acceptance angle. The TRIM value is close to the energy loss expected from an extrapolation of our fit functions through our experimental data at qin=0 representing equilibrium stopping.
According to our TDDFT calculations, the non-adiabaticity of the charge-exchange and ionization processes introduced by the ion motion translates into an electronic energy loss of similar magnitude and charge state dependence as that observed in the measurements, although somewhat underestimated. The lower values in the theory as compared with the experiment are due to the fact that the used pseudo-potential description of the HCI does not include the full Coulomb singularity at distances r smaller than a cutoff radius R. As discussed in the Supplementary Note 2 and shown in Supplementary Fig. 5, a simple change in the cutoff radius from R=0.53 Å to R=0.26 Å increases the value of the energy loss by a factor of two. Since the actual HCI would correspond to the value R=0 and our aim is not to reproduce the data but to explain them, we consider our results rather satisfactory. In addition, the overestimation of the minimum excitation energy of graphene valence electrons in the jellium model is another reason for the underestimation of the energy loss, as it has been explicitly checked for helium ions (Supplementary Note 2; Supplementary Figs 2 and 3). Reproducing the dependence and the order of magnitude of measured energy losses by our TDDFT calculations shows again that electronic response of the simulated system is well described.
The fact that the measured projectile energy loss can be assigned to the electronic excitations agrees with results obtained in ab initio studies for low projectile charges38. It provides a consistent link between charge transfer and energy loss processes and allows to explain the absence of the induced damage despite the large energy deposition. Indeed, owing to the high electron mobility of graphene the positive charges created in the local surface area by electron capture and electron emission into vacuum are promptly screened thus reducing the local electronic temperature.
A detailed view on the neutralization dynamics is given in Fig. 3b, where we show a two-dimensional plot of the induced density along the direction of the ion motion at different ion positions from a simulation done for qin=20 using our TDDFT description. The horizontal axis represents the distance to the graphene layer located at z=0 and the vertical axis corresponds to the timescale. The HCI starts capturing electrons from graphene already at 9 Å. The strong attractive potential accelerates electrons towards the HCI and, approximately, half of them end up captured by it along the incoming path before penetration into the graphene sheet. The induced electronic charge density as the HCI approaches the graphene layer has two components (Fig. 3c–f): one is formed by the convoy electrons around the HCI position, forming an asymmetric wake potential that slows down the ion, and the other one is located at the graphene layer due to the target polarization. Both components merge as the HCI gets closer to the target (Fig. 3e) and forward electron emission starts. Finally, after crossing the layer (Fig. 3f) the projectile is nearly neutralized and the corresponding induced electronic charge is centred around the HCI along its outgoing path. The actual HCI is probably not fully relaxed at the instant of crossing the graphene layer and, therefore, it still suffers a number of autoionization processes (not described in TDDFT) and subsequent de-excitation without a significant energy loss.
We have studied the electronic response of SLG to a large external field of an approaching HCI. We find an ultrafast neutralization within a few femtoseconds timescale leading to the capture and stabilization of almost (90%) all the missing electrons in the projectile. Our experiments and TDDFT calculations, both suggest local current densities in the graphene plane exceeding 1012 A cm−2, at least three orders of magnitude higher than previously established local breakdown currents, however, on a timescale of a few femtoseconds only. The exceptional electronic properties of graphene allow for a resupply of charge and distribution of the impact energy promptly enough to prevent Coulomb explosion in the electron-depleted region. In addition, the surprisingly large energy loss of the ion of a few keV, which is strongly connected with the charge-exchange process and depends on the incident and exit charge state, could be successfully explained. Our study revealed how graphene responds to extremely high fields and our results underline the exceptional properties of graphene for ultrafast electronic applications at high current densities.
The measurements are performed at the Ion Beam Center of the Helmholtz-Zentrum Dresden-Rossendorf. Highly charged Xe ions are produced in a room temperature electron beam ion trap, charge state separated by an analysing magnet and then guided by several electrostatic lenses into the target chamber. Due to an electrostatic deceleration system, the kinetic energy of the extracted Xe ions can be varied between 0.1 and 4.4q keV corresponding to velocities between 0.13 and 0.5 nm fs−1. The pressure in the experimental chamber is kept below 5 × 10−9 mbar during measurements to prevent charge-exchange processes of the ions before interaction with the target.
The freestanding SLG sheets, which span over a regular array of holes in a TEM grid, are produced at the University Duisburg-Essen and transferred without the use of polymer coating (see Supplementary Note 1 and Supplementary Fig. 1 for details on the sample preparation and characterization). Before performing the transmission measurements, the graphene sheets are inspected by STEM to check the sample coverage and the grade of residual contamination. Contamination of the surface by water was either not present or does not affect the charge-exchange processes as the results of the experiments did not change when heating the samples up to 200 °C in ultra-high vacuum before and during the measurements. A heatable target holder and an electrostatic analyser are mounted in the target chamber (Fig. 1c). The electrostatic analyser is equipped with two channeltrons to analyse the charge state and energy of the transmitted ions and to count neutralized particles in forward direction. The analyser has an acceptance angle of 1.6°, the energy resolution was determined to be ΔE/E≈1.5 × 10−3. The analyser’s maximum operation voltage of 5,000 V limits the range of measurable charge states for projectiles with larger kinetic energies.
Our TDDFT simulations are done following the time evolution of the Kohn–Sham orbitals (see Supplementary Note 2 for details) of the system defined by the constant velocity approach of a model pseudo-potential HCI (cutoff radius R=0.26 Å, Coulomb tail Q/r) and a planar jellium disk with the correct work function value (4.6 eV)13,47 representing the graphene layer. A non-uniform real space grid in cylindrical coordinates is used to treat properly the Coulomb singularity close to r=R. Finite size effects have been checked using jellium disks of different sizes containing 500, 1,004 and 2,000 electrons (Supplementary Figs 6 and 7). The Gunnarson and Lundqvist approximation48 for the exchange correlation Kernel was used.
The data that support the findings of this study are available from the corresponding author upon request.
How to cite this article: Gruber, E. et al. Ultrafast electronic response of graphene to a strong and localised electric field. Nat. Commun. 7, 13948 doi: 10.1038/ncomms13948 (2016).
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We acknowledge funding by Austrian Science Fund (FWF): project number: I1114-N20 and the German DFG (project number:WI 4691/1-1). We also acknowledge partial financial support from Gobierno Vasco project number IT-756-13 and MINECO project number FIS2013-48286-C2-1-P. We further acknowledge funding and fruitful discussions within the SPP 1495 ‘Graphene’ and the collaborative research centre SFB 1242 ‘Non-equilibrium dynamics in condensed matter in the time domain’ funded by the DFG. B.C.B. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 656214-2DInterFOX. We are grateful for discussions with C. Lemell, J. Burgdörfer, P. Tiwald and I. Floss. We thank M. Heidelmann from the Interdisciplinary Center for Analytics on the Nanoscale (ICAN, core facility funded by the German Research Foundation, DFG) for support with the TEM Measurements.
The video illustrates the induced charge density for an incoming ion with qin=20 at v=0.87 nm fs-1. The polarization of the surface of graphene due to the approaching HCI, the charge transfer from graphene to the projectile and the excitation of the graphene layer while and after the crossing of the ion are clearly visible.
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