Abstract
Transition metals, with their densely confined and strongly coupled valence electrons, are key constituents of many materials with unconventional properties^{1}, such as hightemperature superconductors, Mott insulators and transition metal dichalcogenides^{2}. Strong interaction offers a fast and efficient lever to manipulate electron properties with light, creating promising potential for nextgeneration electronics^{3,4,5,6}. However, the underlying dynamics is a hardtounderstand, fast and intricate interplay of polarization and screening effects, which are hidden below the femtosecond timescale of electronic thermalization that follows photoexcitation^{7}. Here, we investigate the manybody electron dynamics in transition metals before thermalization sets in. We combine the sensitivity of intrashell transitions to screening effects^{8} with attosecond time resolution to uncover the interplay of photoabsorption and screening. Firstprinciples timedependent calculations allow us to assign our experimental observations to ultrafast electronic localization on d orbitals. The latter modifies the electronic structure as well as the collective dynamic response of the system on a timescale much faster than the lightfield cycle. Our results demonstrate a possibility for steering the electronic properties of solids before electron thermalization. We anticipate that our study may facilitate further investigations of electronic phase transitions, laser–metal interactions and photoabsorption in correlatedelectron systems on their natural timescales.
Main
The characteristic thermalization time of laserexcited hot electrons in solids is in the femtosecond regime and becomes faster with stronger electron interactions^{7}. Attosecond time resolution is thus required to resolve coupled electron dynamics during the laser–matter interaction before electron thermalization has occurred. Attosecond transient absorption spectroscopy has revealed electricfieldguided electron dynamics in simple dielectrics and semiconductors^{9,10,11,12,13,14}. However, transient absorption studies of localized and strongly interacting electrons, such as on the d and f orbitals of transition metals, have been limited to the fewfemtosecond regime^{15}. Transition metal elements are the key constituents of many materials exhibiting remarkable properties, such as Mott insulators, highT_{c} superconductors and transition metal dichalcogenides^{2}. Understanding the coupledelectron dynamics in these systems is central for their applications in optoelectronics, energyefficient electronics, magneticmemory devices, spintronics and new solar cells^{16}. Transition metal elements have been studied with attosecond photoemission spectroscopy^{17,18,19}. However, stateoftheart theoretical treatment^{20} of photoemission from metals on the attosecond timescale neglects any electronic perturbation induced by the optical field beyond the skin effect. This approximation is based on efficient screening of the optical field by surface electrons^{21} and spacecharge limitation of the maximum optical field intensity^{22}. In contrast, femto and picosecond corelevel photoabsorption of metals systematically shows signatures of excitationinduced electronic structure modification at high intensities^{23,24,25,26}.
To bridge this gap in intensities and timescales, we have used attosecond transient absorption spectroscopy to study the collective electron dynamics in the transition metals Ti and Zr. In the following, we discuss the phenomena observed in Ti, while the physically analogous behaviour of Zr is presented in the Supplementary Information. A comprehensive description of our experimental apparatus is provided in refs. ^{12,27}. In the pump–probe experiments (Fig. 1a), fewcycle nearinfrared (NIR) laser pulses excite electrons in a 50nmthick, freestanding Ti film. The induced change in the sample’s transmission around the M_{2,3} absorption edge is probed by single attosecond pulses in the extremeultraviolet range (XUV, ~35 eV, Fig. 1b) with a pulse duration of 260 as. The attosecond pulses are produced via highharmonic generation in Kr. In addition, a Ne gas jet is placed in front of the metal film sample, and photoelectrons from the jet are collected with a timeofflight spectrometer in a streaking experiment, providing precise information on the electric field of the NIR pump pulse.
Figure 1c shows the absorption spectrum of Ti, obtained with attosecond pulse trains covering the photon energy range from 25 to 75 eV (see Methods). We compared this with ab initio calculations based on timedependent density functional theory (TDDFT) in the local density approximation (LDA) for a hexagonal closepacked (hcp) Ti cell (see Methods for details). Note that this theoretical framework has been shown to accurately describe electronic screening effects^{28} as well as attosecond electron dynamics in solids^{10,12,29}. The full calculation (shown in red, Fig. 1c) closely reproduces the experimental spectrum, whereas the independentparticle approximation (Fig. 1c, black), which ignores electron–electron interactions (see Methods for definition), fails to describe it. The underlying manybody process is known as the local field effect^{30}, which is ascribed to the additional potential induced locally by charge displacement. The Ti M_{2,3} absorption edge, located at 32.6 eV (ref. ^{31}), is dominated by the intrashell 3p–3d electronic transition (Fig. 1d), which features a large overlap of initial and finalstate wavefunctions^{8}. The M_{1} absorption edge at 56.1 eV caused by 3s–4p transitions is much less prominent due to the delocalized character of the 4p final states. A strong interaction of electrons participating in the transition and screening processes leads to collective excitation, which manifests as a giant resonance^{32} above the M_{2,3} absorption edge. Our probing mechanism is thus sensitive to the dynamics of screening and collective electron motion^{8,33} via manybody effects. In contrast, a conventional probing mechanism is usually based on the independentparticle picture and only senses the final state occupation. We note that the experimental data in Fig. 1c exhibit no prominent peaks in the region of 32–52 eV, in contrast to the TDDFT calculations (red curve, Fig. 1c). We suggest that this discrepancy originates from the smoothening role of Auger relaxation, which is not included in the calculation.
We recorded the transmitted probe spectra with the pump on and off in a fast sequence (using a mechanical shutter) and calculated the induced optical density (ΔOD, equation (1), Methods). Figure 2a shows the pumpinduced change in absorption as a function of pump–probe delay in a 20 fs window with 250 as delay steps. The pump peak intensity is I_{pump} = 7.5 ± 0.7 × 10^{11} W cm^{−2} and the centre photon energy is 1.55 eV. In the presented data, we have subtracted the delayindependent thermal background (see Methods and Supplementary Information).
The pump–probe spectrogram in Fig. 2a reveals an optical density profile that rapidly increases in amplitude and exhibits several peaks along the energy axis (Fig. 2b). Previous studies of attosecond electron dynamics in semiconductors and dielectrics revealed fielddriven, oscillatory dynamics^{9,10,11,12,13,14}. In contrast, in the metallic system of Ti, we observe a quasiinstantaneous linear response. This behaviour was further confirmed by ab initio calculations of the induced absorption (Supplementary Fig. 8). Whereas intraband motion in bandgap materials induces a periodic modulation of the absorption^{34}, the optical response of Ti is determined by a different mechanism. Figure 2c shows that the optical density transient follows the laser fluence extracted from the streaking experiment (Fig. 2d). By analysing several independent experimental datasets with a linear convolution model, we estimated an upper limit of the microscopic response time to the pump fluence as 1.1 fs with an experimental accuracy of 290 as (see Methods and Supplementary Information). Although the time evolution of the signal is guided by pump absorption, the spectrogram does not display any induced transparency features (Fig. 2a, blue false colour), indicating that the expected statefilling effect is completely cancelled by a manybody phenomenon.
To provide a more detailed understanding of the underlying electronic dynamical rearrangement and its effect on Ti absorption, we simulated the pump–probe experiments with ab initio TDDFT calculations^{12,14,35}. Figure 3a (red line) presents the absorption change in hcp Ti induced by a 10 fs NIR pump pulse with centre photon energy of 1.55 eV and incident intensity of I_{pump} = 1 × 10^{12} W cm^{−2}. Our simulation successfully reproduces the main absorption feature around 32 eV in a highly nonequilibrated state of Ti. We compared these results with the electronthermalized state of Ti and found that a particular excited electron distribution has little influence on the induced spectral feature (Fig. 3a,c). Accordingly, the experiments show that XUV absorption at the end of the pump pulse and 12 fs later differ only slightly, so thermalization has little influence on our observables (Fig. 3b). The independentparticle model (Fig. 3a, black), which ignores electron–electron interactions, merely reflects the electron–hole population (Fig. 3c) and exhibits transparency above the M_{2,3} edge. In contrast, induced transparency is suppressed in the full model, in agreement with the experiment.
To gain further insight, we separated the TDDFT calculation into three physical factors: electronic structure renormalization, statefilling and localscreening modification (see Supplementary Information). Figure 3d shows that the effects of statefilling (blue line) and localscreening modification (black line) dominate the absorbance change. Importantly, the induced transparency above the M_{2,3} edge due to the statefilling effect is primarily cancelled by the localscreening modification. As a result, a single positive peak around the absorption edge is formed, indicating a breakdown of the independentparticle picture by the strong screening of localized d orbitals. The renormalization effect is well approximated by a redshift of the absorption edge (see Supplementary Information). This fact indicates enhancement of the static screening around the Ti atom due to increased electron localization, in agreement with previous calculations of thermoinduced renormalization^{36}. Finally, a modified electron interaction also influences the corehole lifetime, which is determined by superCoster–Kronig Auger decay, involving two interacting 3d electrons. An increase in delectron population thus shortens the semicorehole lifetime. We find that additional empirical broadening of 0.15 eV qualitatively reproduces the second, weaker absorption maximum (35.5 eV, Fig. 3b), although it is slightly shifted to higher energies (Supplementary Fig. 11), thus capturing the essential features of the experimental absorption spectrum.
Based on the agreement between theory and experiments, we proposed that the pump absorption results in an ultrafast modification of screening in the electronic system of Ti. To provide additional support for our hypothesis, we investigated in detail the underlying microscopic dynamics in real time and real space. Figure 4 shows the TDDFT simulation results of a pump field interacting with an hcp Ti cell. The laser electric field is parallel to the c axis of the Ti crystal (Fig. 4a), and we visualize the electronic density transients in the c–a plane.
Figure 4b shows the electron density difference induced by the NIR pump pulse. On top of the fieldinduced polarization dynamics we observe a buildup of charge density, which acquires a distinct dorbital shape by the end of the pulse. Therefore, the pump creates an inflow of electron density towards the Ti atom and localizes it on the d orbitals. To illustrate this, we integrated the localized electron density around a Ti atom and plotted it as a function of time along with the pump fluence (Fig. 4c). As seen from the figure, the electron localization closely follows the laser fluence in time, similar to the peak amplitude of the experimental transient absorption (Fig. 2c). This supports our hypothesis that the transient absorption peak originates from ultrafast electron localization due to the pump pulse. The NIR pump modifies the atomic screening, resulting in the absorption peak structure around the M_{2,3} absorption edge, as discussed.
We note that the observed transient absorption features are robust against variation in experimental parameters such as sample thickness, surface oxidation state and pump photon energy (see Supplementary Information). Additionally, TDDFT calculations show no significant dependence on the crystal structure. We also observe identical induced spectral features at the N_{2,3} absorption edge of zirconium, suggesting a universal character of this phenomenon for transition metals (see Supplementary Information). The possibility of charge localization in the metallic system of Ti is based on the relatively inefficient screening by 4s/4p electrons, because their wavefunctions weakly penetrate the 3d spatial region^{37}. This effect has essentially an atomic origin, suggesting that a photoinduced change in electron localization must also govern the first step of the interaction of light with transition metal compounds. A change in the localization of valence electrons is expected to vary the macroscopic properties of transition metals, such as conductivity, reflectivity, plasmonic behaviour, magnetization and catalytic activity at surfaces. A particularly high electron density in transition metals, associated with the fastest screening rates in the valence band, thus allows us to manipulate these macroscopic properties at unprecedented rates, in agreement with recent studies^{38,39}. Our results unambiguously demonstrate photomanipulation of screening in transition metals via ultrafast electron localization below the electron thermalization timescale.
Methods
Pump–probe setup
The pump–probe experiments were carried out on an attosecond setup as extensively described in refs. ^{12,27}. In this setup, the pump–probe interferometer is actively stabilized by introducing a weak copropagating continuouswave 473 nm laser beam. A fast feedback loop acts on the piezo delay actuator, stabilizing the pump–probe delay to a desired value with 15 as r.m.s. uncertainty. A mechanical shutter in the pump arm of the interferometer is used for data acquisition, with or without the pump, in a fast sequence. We define the pumpinduced optical density as follows:
where \({\it{I}}_{{\it{\mathrm{pr}}}}^{{\it{\mathrm{pump}}}},{\it{I}}_{{\it{\mathrm{pr}}}}^{{\it{\mathrm{no}}}\,{\it{\mathrm{pump}}}}\) are the transmitted probe spectral intensities with and without pump radiation, and τ is the pump–probe delay with positive values for the probe arriving after the pump.
Samples
The samples consist of passivated 48.6nmthick Ti films (Luxel, https://luxel.com) covered with 4.9 nm of amorphous carbon on both sides (without breaking the vacuum). The films are mounted on copper transmission electron microscopy grids with nine windows. The unsupported window areas are 300 µm in diameter. The pump/probe spot sizes on the sample have dimensions of ~50 µm.
Static absorption
To characterize the absorption of our samples in a broad energy region, we generate attosecond pulse trains in Xe, Kr and Ar. By changing the doublefilament compression parameters we are able to tune the attosecond pulse train spectrum to close the gaps between harmonics. We acquire 10 pairs of signal (sample in) and reference (sample out) spectra in sequence by moving the motorized sample manipulator. Each signal/reference spectrum is an accumulation of ∼10^{4} XUV pulse trains, acquired rapidly in ~10 s. We then calculate the total optical density, 〈α〉, as a weighted average over different probing spectra:
For each shape of the probe i and the corresponding absorption spectrum α_{i} the variance comprises fast and slow fluctuations:
The fast fluctuation term reflects the carrierenvelope phase and laser intensity fluctuation on a timescale of tens of milliseconds:
where j ∈ [1,10] is the index for each signal/reference pair and \(\sigma _j^I\) is the s.d. over 10^{4} laser shots. The slow fluctuation term accounts for drifts between subsequent sample insertions (timescale of tens of seconds) and takes into account the position uncertainty of wrinkled metal foils:
where α_{j,i} is the optical density for each of the 10 signal/reference pairs, taken with the ith probe spectrum. The final uncertainty of the optical density is estimated as
Evaluation of the dynamics
In the course of the pump–probe delay scan the samples are exposed to an average power of ~0.5 mW, resulting in elevated temperature. This effect manifests as a fully reversible, delayindependent background with a lifetime of ~5 ms, which is separated from the transient signal at negative pump–probe delays (see Supplementary Information for more details). By keeping the pump intensity sufficiently low, we have ensured that no permanent sample modification takes place during the experiments. Therefore, in the presented data the background signal has been subtracted.
To characterize the material response time with subcycle resolution, we reconstructed the temporal profile of the pump electric field using a photoelectron streaking experiment^{40,41}. In this investigation, XUVphotoionized electrons are accelerated in the NIR pump field and collected in a timeofflight spectrometer. Their kinetic energy as a function of XUV–NIR delay directly reflects the NIR field vector potential. In contrast to refs. ^{12,14}, we performed the streaking experiment after the transient absorption measurement, with the metallic sample removed so as to avoid the electron background in the timeofflight measurement. The actively stabilized pump–probe delay ensures a timing accuracy between the experiments to a precision of 15 as r.m.s.
We assume that the optical density response is linear and follows the absorbed laser intensity:
with the response function having the form
where t_{jitter} accounts for possible jitter between the streaking and transient absorption data due to acquisition noise, delay drift and spatial separation of the gas and solid targets.
We find the response time by simultaneously fitting seven different pairs of streaking and transient absorption experiments, with parameters a and t_{jitter} being varied, and the response time τ being common for all scans. This approach reflects the fact that τ is a constant of the system being studied, while a and t_{jitter} are attributable to experimental noise contributions. We minimize the sum of χ^{2} of seven scans:
where \(\Delta {\it{\mathrm{OD}}}_{{\it{\mathrm{exp}}}}\) is the experimental pumpinduced optical density change in the energy band from 31.7 to 32.9 eV and \(\sigma _\tau ^2\) is the standard deviation of the optical density. We use the simplexdownhill algorithm to find the minimizing solution, starting with uniformly distributed initial guess parameters to check for local minima effects. To find the uncertainty of the response, a Monte Carlo simulation is used. The experimental uncertainty on the optical density change is calculated as the s.e.m. for 300 pairs of signal (pump on)/reference (pump off) spectra:
where N is the number of signal/reference pairs per delay step. From this distribution, we generate 1,000 transient absorption signals for each attosecond transient absoprtion spectroscopy/streaking pair and run the fitting algorithm. The results of the Monte Carlo simulations give a mean response time of 1.12 fs with a standard deviation of 290 as (see Supplementary Information for more details).
Theoretical modelling details
In the framework of the TDDFT, the electron dynamics is described by a singleparticle Schrödingerlike equation—the socalled timedependent Kohn–Sham (TDKS) equation. For laserinduced electron dynamics in solids, the TDKS equation has the following form:
where u_{bk}(r,t) describes electron orbitals with band index b and Bloch wavevector k. The Hamiltonian h_{KS,k}(t) is the socalled Kohn–Sham Hamiltonian, and is given by
where \(\hat v_{\mathrm{ion}}\) is the ionic potential, v_{H}(r,t) is the Hartree potential and v_{xc}(r,t) is the exchangecorrelation potential. Note that the Hartee and exchangecorrelation potentials are functionals of the electron density
where n_{bk} is the occupation factor. In this work, we employ the adiabatic local density approximation (ALDA) for the exchangecorrelation potential^{42}. We describe the laser fields with a spatially uniform vector potential, \({\mathbf{E}}\left( t \right) =  \frac{1}{{{c}}}\frac{{{{{\mathrm{d}}A}}\left( t \right)}}{{{\mathrm{d}}t}}\), assuming that the wavelength of the laser fields is much longer than the spatial scale of electron dynamics (this is nothing but the dipole approximation).
To describe the laserinduced electron dynamics in Ti metal, we employ the hcp structure of Ti. Ti atoms are described with a normconserving pseudopotential method, treating 3s, 3p, 3d and 4s electrons as valence^{43,44}. In the practical calculations, we solve the TDKS equation (6) in real space and real time: the spatial coordinate r is discretized into uniform grid points with spacing h = 0.3 a.u., and the electron orbitals u_{bk}(r,t) are propagated under the influence of the laser fields with a time step Δt = 0.03 a.u. The first Brillouin zone is also discretized into 20^{3} kpoints. All the TDDFT simulations in this work are carried out with the Octopus code^{45}.
One of the most important outputs of the TDDFT calculations is the macroscopic current density, J(t), which is directly related to the optical properties of solids. We compute the current with
where Ω is the volume of the unit cell and J_{PS} is the contribution from the pseudopotential. If the electric current under an impulsive distortion, E(t) = E_{0}δ(t), is computed, the optical conductivity of the system can be evaluated as
where γ is a numerical damping factor. We set this to 0.5 eV ℏ^{−1} in this work. From the optical conductivity, the absorption coefficient can be computed.
The absorption coefficient in Fig. 1c was computed with TDDFT using this scheme. If the time dependence of the Hartree and exchangecorrelation potentials is ignored in the time propagation, this scheme provides the absorption coefficient with the independentparticle approximation in Fig. 1c because the TDKS equation is simply reduced to the Schrödinger equation of an independentparticle system.
Optical response of pumped systems in the nonequilibrium phase
To investigate the modification of the absorbance immediately after the pump laser pulse, we performed a numerical pump–probe simulation based on the TDDFT^{35}. For the pump pulse, we employ the form
in the domain −T_{pump}/2 < t < T_{pump}/2, and zero outside. Here, ω_{pump} is the mean frequency and T_{pump} is the full duration of the pump pulse. We set ω_{pump} to 1.55 eV ℏ^{−1} and T_{pump} to 20 fs. The corresponding fullwidth at halfmaximum of the laser intensity is ~7 fs. We also set the maximum field strength E_{pump} to 9.7 × 10^{8} V m^{−1}, which corresponds to the maximum field strength at the front surface of the sample under an irradiation of 10^{12} W cm^{−}^{2}, taking the surface reflection into account with the stationary solution of the Maxwell equation. For the probe pulse, we employ the impulsive distortion at the end of the pump pulse (t = T_{pump}/2).
To extract the optical property of the pumped system, we performed two TDDFT simulations. One employs both the pump and the probe pulses, while the other employs only the pump pulse. We then define two kinds of electric current. One is computed with the pump–probe calculation and the other with the pumponly calculation. We denote the first the pump–probe current J_{pumpprobe}(t) and the latter the pumponly current J_{pumponly}(t). By subtracting J_{pumponly}(t) from J_{pumpprobe}(t), one may extract the current induced by the probe pulse in the presence of the pump pulse. We shall call it the probe current, J_{probe}(t) = J_{pumpprobe}(t) − J_{pumponly}(t). Applying a Fourier analysis of equation (16) to the probe current, the optical property of the laserexcited system can be computed. As a result of this pump–probe scheme, the absorption coefficient in the nonequilibrium phase is provided.
Optical response of pumped systems in the electronthermalized phase
To theoretically investigate the effect of electron thermalization, we computed the optical properties of hcp Ti with a finite electron temperature^{46}. In this process, we first compute the ground state, assuming the Fermi–Dirac distribution for the electron occupation n_{bk} for the density in equation (14). As a result, the initial electron orbitals u_{bk}(r,t = 0) and the occupation n_{bk} with finite electron temperature can be prepared consistently. Applying the impulsive distortion and computing the electron dynamics based on the above scheme, we then compute the optical properties of hcp Ti with the finite electron temperature. Here, we set the electron temperature T_{e} to 0.315 eV so that the excess energy of the finite electrontemperature system becomes identical to that of the system pumped by the laser used in the above analysis.
To clarify the microscopic mechanism of the absorption change induced by the pump pulse, we performed a theoretical decomposition of the computed transient absorption coefficient. Given that the thermal and nonequilibrium electronic distributions provide qualitatively equivalent results, we focused on the thermal distribution for simplicity.
To construct the theoretical decomposition, we first revisit the linear response in the TDDFT with a weak electric field. In the weak perturbation limit, the Kohn–Sham Hamiltonian (equation (13)) under the ALDA can be rewritten as
where \(v_{H_{{\mathrm{xc}}}}\)[ρ(r,t = 0)] is the sum of the Hartree and the exchangecorrelation potentials evaluated with the initial electron density ρ(r,t = 0). The dynamical part of the Kohn–Sham potential can be evaluated with the Hartree–exchangecorrelation kernel \(f_{H_{{\mathrm{xc}}}}\)(r,r′) and the induced density δρ(r,t) = ρ(r,t) − ρ(r,t = 0). An essential difference between the optical response in the electronthermalized phase and in the ground state is the choice of the occupation factor n_{bk}. In the present work, we use the Fermi–Dirac distribution with finite temperature T_{e} = 0.315 eV for the electronthermalized phase and almost zero temperature T_{e} = 0.01 eV for the ground state. Therefore, the change in the absorption due to the electron temperature can be analysed based on the occupation factor contribution. In the linear response TDDFT calculation, the occupation factor affects the following three features: (1) electronic structure renormalization via the initial Hartree–exchangecorrelation potential \(v_{H_{{\mathrm{xc}}}}\)[ρ(r,t = 0)] and the initial density ρ(r,t = 0); (2) modification of the localscreening effect via modification of the induced potential and the induced density δρ(r,t); (3) the statefilling effect via the current evaluation with equation (15).
Quantifying the electron localization
To quantify the localization dynamics under a pump pulse, we compute the local induced density as
where ρ(r,t) is the electron density under the pump pulse and R_{Ti} is the position of a Ti atom. The width of the Gaussian window σ was set to 1 a.u.
Data availability
The data that support the findings of this study are available via https://doi.org/10.3929/ethzb000345468 or from the corresponding author upon reasonable request.
Code availability
The Octopus code for TDDFT is available at https://octopuscode.org.
References
 1.
Kotliar, G. & Vollhardt, D. Strongly correlated materials: insights from dynamical meanfield theory. Phys. Today 57, 53–59 (2004).
 2.
Manzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A. 2D transition metal dichalcogenides. Nat. Rev. Mater. 2, 17033 (2017).
 3.
Nasu, K. Photoinduced Phase Transitions (World Scientific, 2004).
 4.
Wegkamp, D. et al. Instantaneous band gap collapse in photoexcited monoclinic VO_{2} due to photocarrier doping. Phys. Rev. Lett. 113, 216401 (2014).
 5.
Fausti, D. et al. Lightinduced superconductivity in a stripeordered cuprate. Science 331, 189–191 (2011).
 6.
Zhou, Y. & Ramanathan, S. Correlated electron materials and field effect transistors for logic: a review. Crit. Rev. Solid State Mater. Sci. 38, 286–317 (2013).
 7.
Bauer, M., Marienfeld, A. & Aeschlimann, M. Hot electron lifetimes in metals probed by timeresolved twophoton photoemission. Prog. Surf. Sci. 90, 319–376 (2015).
 8.
Amusia, M. Y. & Connerade, J.P. The theory of collective motion probed by light. Rep. Prog. Phys. 63, 41–70 (2000).
 9.
Schultze, M. et al. Controlling dielectrics with the electric field of light. Nature 493, 75–78 (2013).
 10.
Schultze, M. et al. Attosecond bandgap dynamics in silicon. Science 346, 1348–1352 (2014).
 11.
Mashiko, H., Oguri, K., Yamaguchi, T., Suda, A. & Gotoh, H. Petahertz optical drive with widebandgap semiconductor. Nat. Phys. 12, 741–745 (2016).
 12.
Lucchini, M. et al. Attosecond dynamical Franz–Keldysh effect in polycrystalline diamond. Science 353, 916–919 (2016).
 13.
Moulet, A. et al. Soft Xray excitonics. Science 357, 1134–1138 (2017).
 14.
Schlaepfer, F. et al. Attosecond opticalfieldenhanced carrier injection into the GaAs conduction band. Nat. Phys. 14, 560–564 (2018).
 15.
Jager, M. F. et al. Tracking the insulatortometal phase transition in VO_{2} with fewfemtosecond extreme UV transient absorption spectroscopy. Proc. Natl Acad. Sci. USA 114, 9558–9563 (2017).
 16.
Akama, T. et al. Schottky solar cell using fewlayered transition metal dichalcogenides toward largescale fabrication of semitransparent and flexible power generator. Sci. Rep. 7, 11967 (2017).
 17.
Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007).
 18.
Tao, Z. et al. Direct timedomain observation of attosecond finalstate lifetimes in photoemission from solids. Science 353, 62–67 (2016).
 19.
Kasmi, L. et al. Effective mass effect in attosecond electron transport. Optica 4, 1492 (2017).
 20.
Ambrosio, M. J. & Thumm, U. Electronic structure effects in spatiotemporally resolved photoemission interferograms of copper surfaces. Phys. Rev. A 96, 051403 (2017).
 21.
Lucchini, M. et al. Light–matter interaction at surfaces in the spatiotemporal limit of macroscopic models. Phys. Rev. Lett. 115, 137401 (2015).
 22.
Swoboda, M. et al. Intensity dependence of laserassisted attosecond photoionization spectra. Laser Phys. 19, 1591–1599 (2009).
 23.
Cho, B. I. et al. Electronic structure of warm dense copper studied by ultrafast Xray absorption spectroscopy. Phys. Rev. Lett. 106, 167601 (2011).
 24.
Dorchies, F. et al. Time evolution of electron structure in femtosecond heated warm dense molybdenum. Phys. Rev. B 92, 144201 (2015).
 25.
Principi, E. et al. Free electron laserdriven ultrafast rearrangement of the electronic structure in Ti. Struct. Dyn. 3, 023604 (2016).
 26.
Williams, G. O. et al. Tracking the ultrafast XUV optical properties of Xray freeelectronlaser heated matter with highorder harmonics. Phys. Rev. A 97, 023414 (2018).
 27.
Locher, R. et al. Versatile attosecond beamline in a twofoci configuration for simultaneous timeresolved measurements. Rev. Sci. Instrum. 85, 013113 (2014).
 28.
Marques, M. A. L., Maitra, N. T., Nogueira, F. M. S., Gross, E. K. U. & Rubio, A. Fundamentals of TimeDependent Density Functional Theory 837 (Springer, 2012).
 29.
Sommer, A. et al. Attosecond nonlinear polarization and light–matter energy transfer in solids. Nature 534, 86–90 (2016).
 30.
Krasovskii, E. & Schattke, W. Local field effects in optical excitations of semicore electrons. Phys. Rev. B 60, 16251–16254 (1999).
 31.
Fuggle, J. C. & Mårtensson, N. Corelevel binding energies in metals. J. Electron Spectros. Relat. Phenom. 21, 275–281 (1980).
 32.
Connerade, J. P. in Giant Resonances in Atoms, Molecules, and Solids Vol. 151 (eds Connerade, J. P., Esteva, J. M. & Karnatak, R. C.) 3–23 (Springer, 1987).
 33.
Ankudinov, A. L., Nesvizhskii, A. I. & Rehr, J. J. Dynamic screening effects in Xray absorption spectra. Phys. Rev. B 67, 115120 (2003).
 34.
Sato, S. A. et al. Role of intraband transitions in photocarrier generation. Phys. Rev. B 98, 035202 (2018).
 35.
Sato, S. A., Yabana, K., Shinohara, Y., Otobe, T. & Bertsch, G. F. Numerical pump–probe experiments of laserexcited silicon in nonequilibrium phase. Phys. Rev. B 89, 064304 (2014).
 36.
Bévillon, E., Colombier, J. P., Recoules, V. & Stoian, R. Freeelectron properties of metals under ultrafast laserinduced electron–phonon nonequilibrium: a firstprinciples study. Phys. Rev. B 89, 115117 (2014).
 37.
Anisimov, V. I. & Gunnarsson, O. Densityfunctional calculation of effective Coulomb interactions in metals. Phys. Rev. B 43, 7570–7574 (1991).
 38.
Bévillon, E. et al. Ultrafast switching of surface plasmonic conditions in nonplasmonic metals. Phys. Rev. B 93, 165416 (2016).
 39.
Winter, J., Rapp, S., Schmidt, M. & Huber, H. P. Ultrafast laser processing of copper: a comparative study of experimental and simulated transient optical properties. Appl. Surf. Sci. 417, 2–15 (2017).
 40.
Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).
 41.
Itatani, J. et al. Attosecond streak camera. Phys. Rev. Lett. 88, 173903 (2002).
 42.
Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electrongas correlation energy. Phys. Rev. B 45, 13244–13249 (1992).
 43.
Troullier, N. & Martins, J. L. Efficient pseudopotentials for planewave calculations. Phys. Rev. B 43, 1991–1997 (1991).
 44.
Reis, C., Pacheco, M. & Martins, J. Firstprinciples normconserving pseudopotential with explicit incorporation of semicore states. Phys. Rev. B 68, 155111 (2003).
 45.
Andrade, X. et al. Realspace grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. Phys. Chem. Chem. Phys. 17, 31371–31396 (2015).
 46.
Sato, S. A., Shinohara, Y., Otobe, T. & Yabana, K. Dielectric response of laserexcited silicon at finite electron temperature. Phys. Rev. B 90, 174303 (2014).
Acknowledgements
The authors acknowledge discussions with E. Krasovskii. S.A.S. and A.R. thank M. J. T. Oliveira for helping with the generation of a transferable pseudopotential for Ti, dealing with semicore electrons. This work was supported by the National Center of Competence in Research – Molecular Ultrafast Science and Technology (NCCR MUST) funded by the Swiss National Science Foundation. The authors acknowledge financial support from the European Research Council (ERC2015AdG694097) and the European Union’s Horizon 2020 Research and Innovation programme under grant agreement no. 676580 (NOMAD). S.A.S. acknowledges support from the Alexander von Humboldt Foundation.
Author information
Affiliations
Contributions
M.V., S.A.S., L.G., A.R. and U.K. supervised the study. M.V., F.S., N.H., L.K. and M.L. conducted the experiments. M.V. and F.S. analysed the experimental data. S.A.S. and A.R. developed the theoretical modelling. All authors were involved in the interpretation of data and contributed to the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information: Nature Physics thanks Pablo Maldonado and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Information
Rights and permissions
About this article
Cite this article
Volkov, M., Sato, S.A., Schlaepfer, F. et al. Attosecond screening dynamics mediated by electron localization in transition metals. Nat. Phys. 15, 1145–1149 (2019). https://doi.org/10.1038/s4156701906029
Received:
Accepted:
Published:
Issue Date:
Further reading

Source noise suppression in attosecond transient absorption spectroscopy by edgepixel referencing
Optics Express (2021)

Role of electron scattering on the highorder harmonic generation from solids
Physical Review Research (2020)

XUV Induced Bleaching of a Tin Oxo Cage Photoresist Studied by High Harmonic Absorption Spectroscopy
Journal of Photopolymer Science and Technology (2020)

Attosecond timing of the dynamical Franz–Keldysh effect
Journal of Physics: Photonics (2020)

Femtosecond soft Xray absorption spectroscopy of warm dense matter at the PALXFEL
Journal of Synchrotron Radiation (2020)