SUPPLEMENTARY INFORMATION

Transcription

1 doi:1.138/nature9829 Supplementary Information S1: Movie of the photo-induced phase transition: Figures 2b-e show four selected XUV ARPES snapshots illustrating the most pronounced changes in the course of the photo-induced phase transition of 1T-TiSe 2. A complete data set (movie Rohwer et al.mov) is presented here in the form of a time-resolved ARPES movie (excitation fluence: 1.5 mjcm - ²) over a total time span of 1 ps composed of 85 time frames. The XUV delay time with respect to the excitation by the IR pump is indicated at the top (negative delay values: XUV pulse arrives prior to the IR pulse). In contrast to Fig. 2, where high quality data were used (integration time: 15 minutes), the movie was made from analysis-grade data (integration time/frame: 3 minutes). The data shown in the movie were recorded with p- polarized XUV pulses. To some frames lines and text have been added to guide the eye of the viewer. 1

2 Supplementary Information S2: Energy distribution curves at selected momentum values and comparison with synchrotron data: Figure S1a-d show EDCs at selected momentum values taken from the photoemission intensity maps in Fig. 2b-e. Figure S2 shows furthermore a comparison of EDCs (at and ) recorded with high harmonic light (taken from Fig. 2a) and with synchrotron light (taken from Fig. 1f). Figure S1. EDCs of the photoemission transients. Shown are constant momentum cuts for time delays -7 fs, fs, 3 fs and 3 ps at an excitation fluence of 5 mjcm -2. a, point: The 2

3 transient shoulder above E F observed for fs delay and 3 fs delay is attributed to the Ti 3d band backfolded from the point onto the point. b,.15å 1 in direction: The (instantaneous) LAPE signal from the Se 4p band is clearly resolved at an energy E - E F 1 ev (only visible in the EDC at fs delay). The LAPE signal was used to define the time-zero of the measurement and as a measure for the time-resolution of the experiment (see also Fig. 2f). c,.45å 1 in direction: Transient changes are dominated by the population of the Ti 3d band at this momentum value at an energy E - E F.4 ev. The additional signal in the high energy part of the spectrum, E - E F ev, and at fs delay is the LAPE signal from the transient Ti 3d population. e, point: At the applied excitation fluence, the spectral intensity of the folded Se 4p band becomes almost instantaneously reduced with the impact of the IR pulse ( fs delay); the shift in energy ( 15 mev) towards E F reflects the considerable contribution of the transiently populated Ti 3d band to the photoemission signal in this energy regime at fs delay and 3 fs delay. Note that a distinction between Ti 3d band and folded Se 4p band is more obvious by their dispersion properties as evidenced for instance by comparing Fig. 2b and Fig. 2d. Figure S2. Comparison of EDCs recorded with synchrotron light (dark shaded) and with high harmonic light pulses (bright shaded). EDCs are taken from Fig. 1f and Fig. 2a ( and point). The energy resolution of about 4 mev, responsible for the broadening of the high harmonic EDC, is mainly due to the spectral width of the 27 th harmonic and is directly related to the short-pulse (sub-1 fs) time-profile of the high harmonic pulses. 3

4 Supplementary Information S3: Data analysis: The photoemission transients of the folded Se 4p signal shown in Fig. 2f were extracted from intensity maps recorded with p-polarized HHG light. Each data point of the traces is a result of a signal integration over an elliptically shaped area at the point in the ARPES maps. The extension of the integration ellipse is shown in supplementary Figs. S3a and S3b. Its area covers the dominant photoemission intensity contribution of the folded Se 4p band as evident from photoemission intensity maps recorded at a temporal delay of -3 fs, that is before the arrival of the IR pump pulse. The ellipse extends over 6 in the angle (momentum) direction and 1 ev in the energy direction. In the transient photoemission maps the Ti 3d band and the folded Se 4p band can be clearly distinguished due to their inverted dispersions (see Fig. 2b in comparison to Fig. 2d). However, in the energy-momentum area of the integration ellipse at positive temporal delays the signal of both bands overlap and a procedure is required to extract the transient signal characteristic for the folded Se 4p band (see also EDCs shown for the point in supplementary Fig. S1). The Ti 3d contribution in the elliptically shaped area was approximated by an extrapolation of the Ti 3d signal from an external energy-momentum area. In detail, the procedure chosen for data evaluation was the following: The total signal of the elliptical area was integrated and subsequently area-normalized. In parallel, an integration and a corresponding normalization of the Ti 3d signal over a parabola-shaped area (excluding the elliptical area, see thin black line in Figs. S3a and S3b) was performed. The area was defined by the obvious extension of the transient population of the Ti 3d band in the photoemission intensity map. Finally, the normalized signal of the parabolic area was subtracted from the normalized signal of the elliptical area. The result was assigned to the folded Se 4p band intensity. This procedure was separately applied for each time delay of the experiment. Area-normalized transients of the Ti 3d signal, the total area-normalized photoemission transient of the elliptically shaped area and the resulting transient of the folded Se 4p are compared in Fig. S4 for the four fluence values shown in Fig. 2f. Relaxation processes of the transient hot carrier population in the Ti 3d band because of intra-band scattering processes can give rise to the accumulation of population at the band bottom located at the point. For this reason our data analysis method may underestimate the contribution of the Ti 3d signal to the total signal in the elliptical area. Consequently, there is the tendency of an underestimation of the maximum breakdown amplitude of the folded Se 4p band in the transients shown in Fig. 2f. To extract the fluence dependent time constant displayed in Fig. 3a the resulting Se 4p transients were fitted with the following function f t convoluted with a Gaussian (FWHM = 32 fs), representing the temporal profile of the infrared pump pulse: 4

5 f t C C A exp ( t t 1 )/ exp[ ( t t )/ 2 t t t t, where 1 corresponds to the signal drop time Se 4p characteristic for the short-time (sub-1 fs) dynamics, and 2 is the characteristic time constant for the (partial) signal recovery on a timescale of several 1 fs. Figure S3. Integration areas for the folded Se 4p and Ti 3d band around the Μ point. Shown are raw data (energy vs. emission angle) recorded at an excitation fluence of 2.5 mjcm -2 with p-polarized HHG light at two different temporal delays (-3ps, Fig S3a and 15 fs, Fig. S3b). The elliptically and the parabola-shaped integration areas used to determine the contributions of Ti 3d and folded Se 4p states in the vicinity of the point are marked. 5

6 Figure S4. Area-normalized photoemission transients of Ti 3d band and folded Se 4p band. Compared are transients of the Ti 3d band (filled dots, parabolic area in Fig. S3 exclusive elliptical-shaped area), transients of the total signal in the elliptical shaped area ( point transient, open squares, contribution from both, Ti 3d band and folded Se 4p band) and the difference of both signals (stars) that we associate with the folded Se 4p band signal for the four fluence values also shown in Fig. 2f (lines are added to guide the eyes). Already the point transients (the normalized raw data) show the fast intensity drop arising from the disappearance of the folded Se 4p band at the point. The general trend of a speed-up of the response with increasing fluence is also visible. The peaking of the signal in the Ti 3d band at short time delays and high fluence values is due to the LAPE signal from the Se 4p branch aligned parallel to the Ti 3d band (see supplementary information S5). This LAPE contribution is also visible in a change of curvature around time zero in the point transients for 2 mjcm -2 and 4 mjcm -2. To proof that the correction of this LAPE contribution is performed in a satisfactory manner, we compare the 4mJcm -2 data with data recorded with s-polarized pump excitation (data shown in bright gray, pump fluence 3.1 mjcm -2, time-zero is chosen to match the p-polarized data). Experiments performed with s-polarized IR excitation do not show any LAPE contribution to the photoemission signal. However, this also inhibits the exact in-situ determination of time-zero and IR-XUV crosscorrelation. 6

7 Supplementary Information S4: Comparison of Ti 3d and folded Se 4p transients: Figure S5 compares transients of the folded Se 4p band and the Ti 3d band in the short term limit for two different excitation fluences (.4 mjcm - ² and 2 mjcm - ²). For low fluences, the response of the measure for the CDW order (the intensity of the folded Se 4p band) is considerably delayed with respect to the initial population of the Ti 3d band. For the high fluence case, the folded Se 4p transient follows the population of the Ti 3d band instantaneously. Figure S5. Comparison of Ti 3d and folded Se 4p transients. Results are shown for two different excitation fluences,.4 mjcm - ² (S5a) and 2 mjcm - ² (S5b). The folded Se 4p signal is shown in red (full circles), the Ti 3d signal is shown in black (open circles, lines are added to 1 guide the eye). Ti 3d transients were taken at k.6 to avoid signal distortions due to Å secondary processes expected in the vicinity of the band minimum. For better comparison, the Ti 3d signal is displayed in an inverted scale (note labelling of the right axis). 7

8 Supplementary Information S5: Carrier excitation density and plasma oscillation period: In the following we give a quantitative estimate of the plasma response time of the electron system after photoexcitation at = 79 nm (h = 1.57 ev). We consider the case of an absorbed fluence of 1 mjcm - ² = absorbed photons/cm². The absorbed fluence values given in the manuscript have been calculated from the measured incidence fluence under consideration of experimental data for the real and imaginary part of the dielectric function at = 79 nm ( 1 -.1, 2 2) as given in supplementary reference [1]. For p-polarized light at an incidence angle of 45 with respect to the TiSe 2 (1) surface these values yield an absorption of approximately 6% of the incident light. In this calculation the anisotropy of the dielectric function because of the layered structure of the crystal was not taken into account. The penetration depth of the 79 nm light was determined to be 21 nm using the experimental value for the absorption index (79 nm) 3.25 given in supplementary reference [1]. For an absorbed fluence of 1 mjcm - ² this value yields an excitation density of electron-hole pairs/cm³ or excited carriers/cm³, under the assumption of a cross section = 1, equivalent to.129 absorbed photons/ti atom taking into account the volume of the unit cell of 1T-TiSe 2 of 65.2 Å 3. 2 In supplementary reference [3] the unscreened plasma frequency pl /2 = 81 THz observed at T = 1 K in an infrared study of TiSe 2 could be associated with a free carrier density of /cm³ under the assumption of an effective mass of the free carrier equal to the free electron mass m e. In a first approximation these thermal equilibrium values can be scaled ( pl n ) to estimate the corresponding plasma frequency for the photo-excitation density observed in our experiment. For an absorbed fluence of 1 mj/cm² we find a screened plasma frequency of pl /2 = 63 THz, corresponding to a plasma oscillation period of 16 fs. Although somewhat smaller then the measured drop time of the backfolded Se 4p band at this fluence value ( Se 4p = 45 fs), this value is within the right order of magnitude. Indeed, thermal equilibrium conditions are not necessarily appropriate to quantify the effect of a photoinduced carrier density induced by the absorption of 79 nm light pulses onto the plasma response of the system. The location of the photo-induced carriers in momentum space must also be considered to be able to correctly account for their effective mass. In the present case the main contribution to the absorption arises from an interband excitation between the Se 4p band and the Ti 3d band in an extended momentum area along the direction of the first Brillouin zone, near the point, where a branch of the Se 4p band is aligned almost parallel to the Ti 3d band at an energy distance of about 1.5 ev. 4 This resonance condition gives rise to a distinct maximum in the absorption spectrum of TiSe 2 at 8 nm and is responsible for the efficient population of the Ti 3d band observed in our photoemission data. 8

9 The (unscreened) plasma frequency associated with a free carrier density is given by: 2 2 pl e n h n, (1) e 2 * * 2π (2π) mh me where e is the elementary charge, is the permittivity of free space, n h and n e the hole and electron density, and m h * and m e * are the effective masses of holes and electrons. For the (parabolic) Ti 3d band at T = 141 K an effective mass in the direction and in the vicinity of the point of m e * = 6.4 m e has been reported (reference [19] of main text). With this value for electrons and holes, equation (1) yields an unscreened plasma frequency pl /2 = 231 THz. Screening of the plasma response by the dielectric background of TiSe 2 reduces the plasma frequency by a factor of ~9 (Ref. [3]) so that for an absorbed fluence of 1 mjcm - ² we calculate a screened plasma frequency pl /2 = 25 THz and a plasma oscillation period of 4 fs in reasonable quantitative agreement with the experimental value of Se 4p = 45 fs. 1. Buslaps, T. Johnson, R.L. Jungk, G. Spectroscopic ellipsometry on 1T-TiSe 2. Thin Solid Films 234, (1993). 2. Riekel, C. Structure Refinement of TiSe 2 by Neutron Diffaction. J. Sol. State Chem. 17, (1976). 3. Li, G. et al. Semimetal-to-Semimetal Charge Density Wave Transition in 1T-TiSe 2. Phys. Rev. Lett. 99, 2744 (27). 4. Reshak, A.H. Auluck, S. Electronic and optical properties of the 1T phases of TiS 2, TiSe 2, and TiTe 2. Phys. Rev. B 68, (23). 9