Plasmon scattering probing of electronic states in diamond at extreme conditions

Transcription

1 OPEN ACCESS Plasmon sattering probing of eletroni states in diamond at extreme onditions S. H. Glenzer, 1 L. B. Flether, 1 H. J. Lee, 1 M. J. MaDonald, 2, 3 U. Zastrau, 4 M. Gauthier, 1 D. O. Gerike, 5 J. Vorberger, 6 E. Granados, 1 J. B. Hastings, 1 and E. J. Gamboa 1 1 SLAC National Aelerator Laboratory, 2575 Sand Hill Road, MS 72, Menlo Park, CA 94025, USA 2 SLAC National Aelerator Laboratory, 2575 Sand Hill Road, MS 72, Menlo Park, CA USA 3 University of Mihigan, 2455 Hayward St, Ann Arbor, MI USA 4 High-Energy Density Siene Group, European XFEL, Albert-Einstein-Ring 19, Hamburg, Germany 5 Centre for Fusion, Spae and Astrophysis, Department of Physis, University of Warwik, Coventry CV4 7AL, United Kingdom 6 Institute of Radiation Physis, Helmholtz Zentrum Dresden-Rossendorf e.v., Dresden, Germany (Dated: July 8, 2016) We measured the olletive plasmon sattering spetrum from diamond at pressures approahing 370 GPa. Samples are dynamially ompressed employing ounter-propagating laser beams where the ompression states are determined by Bragg sattering. X-ray energy loss spetrosopy with 8 kev photons from the Lina Coherently Light Soure (LCLS) is then applied to probe the eletroni state. The x-rays exite a olletive interband transition, leading to a lear plasmon signal whose dispersion mathes density funtional theory. The data reveal a pressure-dependent Penn gap and demonstrate a non-onduting warm dense matter state for onditions of planetary interiors. SLAC-PUB The extraordinary mehanial and optial properties of arbon are the basis of numerous tehnial appliations [1] and make diamond anvil ells the premier devie to explore the high-pressure properties of materials [2, 3]. In ontrast, the behavior of arbon at the high pressure and moderate temperatures typially ourring in planetary interiors [4, 5] is poorly understood. Here, predition for the boundaries between the different high-pressure phases, their mirosopi struture, and the ondutivity at high pressure arry large unertainties. As there is growing evidene of the abundane of arbon in the interiors of several planets, these information are urgently needed for modelling planetary strutures, their evolutions and the generation of the external magneti fields. Moreover, the behavior of arbon under large pressures is also one of the major inputs for desribing inertial onfinement fusion experiments [6, 7], where an ablator made of high-density arbon rather than plasti has been shown to redue the entropy in implosions [8]. One of the most important problems at high pressures is the losure of the band gap and the reation of a highly onduting, metalli phase (Mott transition). Although this is a general behavior, the transition point and the path towards this phase transition pose severe hallenges for theoretial preditions [9]. Unlike for most semiondutors, both the diret and indiret band gaps of diamond have been predited to first inrease with ompression [10, 11] before dereasing and eventually ollapsing at extremely high pressures. Ab initio simulations have predited a stable insulating phase under purely hydrostati pressures of over 1 TPa [12, 13] and a band gap ollapse at a ombination of high uniaxial stresses >400 GPa and hydrostati pressures of >100 GPa [14]. Indiations for the unusual opening of the band gap only exists at very low pressures; measurements have been performed for pressures smaller than 10 GPa by stati ompression experiments [15, 16]. Conversely, a red shift of the absorption edge was observed at uniaxial pressures of over 300 GPa [17, 18]. However, until now it remains unknown whether this behavior is a onsequene of the intrinsi losure of the diamond band gap, is related to the impurities in natural diamond, or omes from deformation of the highly strained anvils leaving onsiderable unertainties about the pathway towards the Mott transition in arbon. The transition to a onduting fluid has been inferred for onditions under dynami shok-ompression, whih is onneted to a onsiderable temperature rise at several hundred GPa [19]. In this Letter, we present the first dynami highpressure experiments at LCLS that ramp-ompress solid samples to pressure of 370 GPa. These onditions provide temperatures below 3000 K, lose to the Neptune adiabat, and allow aess of ultra bright x-ray probing [20]. We employ a unique ombination of preision x- ray measurements of the eletroni and ioni struture. The frequeny shift of the inelastially sattered x-rays enodes the optial properties and, thus, the behavior of the band gap in the sample [21]. We observe an inreasing diret band gap in diamond in well-haraterized ompression states from simultaneous x-ray diffration. The sattering spetra show a lear signature of olletive plasmon exitations that harateristially shifts to higher frequeny losses with the inreasing pressure. Combining these data with ab initio simulations reveals an opening of the band gap up to the highest observed pressures. Moreover, we an learly rule out pressureindued hanges as a soures of the observed red shift of the optial absorption edge. Our experiment was performed at the end station for Matter in Extreme Conditions (MEC) in the LCLS at the This material is based upon work supported by the U.S. Department of Energy, Offie of Siene, Offie of Basi Energy Sienes, under Contrat No. DE-AC02-76SF00515.

2 2 Figure 1. Configuration for dynami-ompression experiment. (a) The diamond foils are ompressed with a high-energy optial laser and probed with the high-photon flux x-ray beam from LCLS. The sattered x-rays are resolved in spetrum and angle. (b) Hydrodynami simulations predit a density of 5 gm 3 when the ompression waves ollide. ) Data for the inelasti sattering spetrum showing a distint plasmon resonane. d) The Debye-Sherrer rings in the diffration images are sensitive to the density of the sample. SLAC National Aelerator Laboratory [22]. Fig. 1(a) gives a shemati of the experimental setup. Thin foils of diamond, reated by hemial vapor deposition, were heated and ompressed by driving two ounterpropagating pressure waves with intense optial lasers inident on eah surfae. Hydrodynami simulations with the HELIOS ode using the PROPACEOS equation of state tables [23] predit densities of up to 5 g/m 3 at the ollision of the two ompression waves several nanoseonds after the start of the laser drive (see Fig. 1(b)). The diamond foils were prepared by hemial vapor deposition onto a silion substrate seeded with a diamond powder. The samples were 3 x 3 mm at a thikness of 40 µm. The foil surfaes were analyzed using a profilometer showing an average grain size of 100 nm. The rystal grains show a typial preferene to the orientation of the substrate planes [24]. The average density of the foils was measured using the profilometer and a mirobalane as 3.45 g/. This is slightly less than the bulk density (3.51 g/) as measured by x-ray diffration, whih is explained by the formation of amorphous arbon at the boundaries of the rystal grains. The main impurity was hydrogen adsorbed on the surfaes of the grains at a ontent of 0.1% by mass as estimated by eletron energy loss spetrosopy. Compression of the sample was ahieved by two optial lasers eah delivered up to 4 J of light at 527 nm in a 4 ns long ramp pulse. The laser spots were smoothed with ontinuous phase plates giving a foal spot of 60 µm FWHM and a peak intensity of 70 TW/m 2. The ompressed samples were probed by 8 kev x-rays from the LCLS. The FEL beam provided a typial pulse energy of 0.3 mj of x-rays on target and was foused to a spot size of 10 µm Thus, the entral, most uniformly ompressed region of the diamond sample was probed. Forward sattering spetra from the ompressed diamond were reorded at a fixed angle of 25±0.26 using a highly oriented pyrolyti graphite rystal spetrometer. A Cornell-SLAC Pixel Array Detetor observed Debye-Sherrer rings from x-ray diffration over an angular range of 2θ = 17-55, suffiient to observe the (111) and (220) diffration peaks. For eah shot, we reorded inelasti spetra using a graphite rystal spetrometer as well as powder diffration rings with an area detetor in

3 3 Figure 2. Sattered spetra from ompressed diamond. The experimental data (blak lines) preeding (5.5 ns) and at oalesene (6.5 ns) are ompared to the syntheti spetra (red lines). The ompressed shots show a downshift in the plasmon peak as ompared to the undriven ontrol sample. The blue dashed lines show the relative ontributions to the sattering for the undriven spetrum, while the dashed line onnets the enters of the plasmon peaks. Inset: the spetrum at 6.5 ns is ompared to a 95% onfidene interval for the fitted plasmon shift. the forward diretion [25]. Examples for these two kinds of spetra are shown in Fig. 1() and (d). The angular shift of the Bragg peaks in the ompressed samples diretly provides the density; the spetral shift of the plasmon peak is sensitive to the hanges in the eletroni struture. Figure 2 shows examples of inelasti sattering spetra measured at times near the oalesene of the ramp waves, thus sampling different density states. For omparison, we also show a ontrol spetrum from undriven diamond. A larger density from the ompression leads to an inrease in the plasmon loss. These hanges are refleted in the experimental spetra by a greater shift of the inelasti feature away from the elasti peak. We determine the plasmon frequeny shift by fitting a theoretial spetrum to the data, with the total plasmon loss as a free parameter. The plasmon peak is shifted by up to 10 ± 1 ev from the position of the unompressed diamond. Observing the energy-loss of sattered x-rays is a wellestablished tehnique in dynami ompression experiments whih an yield the material properties of warm dense matter or plasma states [20, 26]. In this regime, inelasti sattering omes primarily from free eletrons that have been ionized or reside in the ondution band. Under ertain onditions, the response of the eletrons beomes olletive and plasmons are observed [21]. In stati ompressions experiments, suh plasmons have also been measured with reent results from sodium at pressures up to 100 GPa [27]. A similar olletive resonane an also be exited in insulators and semiondutors. Previous studies on nonmetals have almost exlusively haraterized thin membranes using eletron energy loss spetrosopy [28]. For dynamially ompressed matter, where the high pressure and density state is maintained for only several nanoseonds, eletron sattering will be insuffiient. Here, only the advent of reord-brightness LCLS x-ray free eletron laser provides a near ideal probe, permitting single-shot measurements of the inelasti x-ray sattering spetrum. Valene eletrons loalized within hemial bonds in insulators an be olletively exited into an available ondution band. For diamond, the four sigma bonds then osillate between bonding and anti-bonding states. The plasmon and average separation between these two bands, the Penn gap, form a system of oupled osillators. The resonane frequeny for a sattered wave vetor k may be modeled as ω(k) = ω2b 2 + ω2penn + α k 2. (1) m e Here, ω b = n b e 2 /m e ɛ 0 is the plasma frequeny assoiated with the valene eletrons with density n b, and ω Penn is the Penn gap frequeny [29] between the valene and ondution bands. The additional quadrati dispersion term goes beyond the usual Drude model and is introdued following the behavior of the random phase approximation for free eletrons. We have measured the empirial dispersion onstant α to be Taking ω b = 31.1 ev from the valane eletron density and ω Penn = 13.8 ev gives a plasmon loss of 34 ev for diamond under standard onditions [30, 31]. Under ompression, the plasmon loss will shift to lower energies from both the densifiation and band gap opening. Thus, by independently onstraining the density, we an experimentally determine the behavior of the band gap. We ompare the measured plasmon shift to preditions in Fig. 3(a). Here, we first assumed a onstant Penn energy. The inrease of the eletron density due to the ompression is not suffiient to explain the data. The remaining inrease of the plasmon energy must be attributed to an inrease of the Penn gap. To improve our modeling, we also use Penn gaps that have been extrated from density funtional theory (DFT) simulations. The DFT alulations predit an inrease in the Penn gap under ompression whih, when inserted into Eq. (1), gives an exellent agreement with the measured plasmon shift. The experimental data indiate an inrease in the Penn gap from 13.8 ev at normal density to 20.5 ev at the maximum ompression of 5.3 gm 3. Conomitant with the inreasing Penn gap, the DFT simulations reveal a widening optial band gap. The alulated pressure oeffiient is approximately 5 mev/gpa for pressures up to 80 GPa, 3meV/GPa up to 250 Pa, and then 2meV/GPa

4 4 a ) b) ) 4. 0g / 6. 5g / Figure 3. Analysis of the inelasti sattering data. (a) Measured plasmon shift versus density. The experimental data is ompared to the two preditions using a onstant band gap (green) and one inferred from DFT alulations of the density of states (blue). The density for the markers showing the experimental data is determined from the (111) diffration peak with error bars inferred from the (220) peak. The dashed blak line shows the plasmon shift of undriven diamond. (b) Density of states from the DFT alulations for different densities showing an opening of the band gap and modifiations of the shape under ompression. The arrows demonstrate the inrease in the Penn gap with density. ) Simulated isosurfaes of the valene eletron density of diamond. Under ompression the bound eletrons move loser to the ions, widening the band gap and stiffening the material. to the highest simulated pressure of 800 GPa. These lowest pressure oeffiients are omparable to previous theoretial and experimental work: 5 mev/gpa from the theoretial alulations by Fahy et al. [11], 6 mev/gpa from the experiments of Onodera et al. [16] to 2.3 GPa, and 6.9 mev/gpa at up to 7 GPa from Trojan et al. [15]. The stiffening of the band struture at high pressures demonstrates that the material properties annot be inferred from extrapolation from low pressure studies. At elevated temperatures, thermal ioni motion an lead to a redution in the band gap [32]. By observing the intensity of the elastially sattered peak, we measured the temperature of the diamond sample through the Debye-Waller fator. The relative inrease in the elasti peak yields a maximum temperature of 2800 K [33], whih has a negligible impat on the DFT results. Under the large anisotropi stresses, typial of diamond anvil ells [34], the band gap of diamond has been predited to ollapse at pressures of 400 GPa [35]. As our maximum inferred pressure is lose to this value, it is important to onsider non-hydrostati effets that ompress the lattie differently along eah diretion and may lead to a disagreement in the lattie onstants, and thus density for different Bragg peaks. By measuring the shifts of the (111) and (220) diffration peaks, we find the largest strain in our experiment results in a 0.03 A anisotropy in the inferred lattie onstants and an error of 5% in the density. Our DFT alulations show that this small amount of strain has only negligible effets on the band struture. These small strains are in strong ontrast to the 10% elongation of the lattie onstant as predited in highly strained diamond anvils [35]. In onlusion, we present the first detailed measurements ombined with DFT simulations of the eletroni struture of diamond at extreme pressures. For that goal, we have transformed eletron loss spetrosopy into the x-ray domain allowing probing of larger samples on muh shorter time sales. By employing wavelengthand angularly-resolved x-ray sattering simultaneously, we show that diamond remains an insulator to densities of at least 5.3 gm 3 and pressures of 370 ± 25 GPa. We have observed the band gap of diamond to inrease under ompression. The stability of diamond under strong hydrostati ompression an have large impliations for arbon-rih planets as a pressure-indued metalli phase has signifiantly different thermodynami properties. Moreover, our results point to anisotropy and impurities as a soure for the losure of the optial window in diamond anvil ells. This work was performed at the Matter at Extreme Conditions (MEC) instrument of LCLS, supported by the DOE Offie of Siene, Fusion Energy Siene under ontrat No. SF This work was supported by DOE Offie of Siene, Fusion Energy Siene under FWP The target work was supported by a Laboratory Direted Researh and Development grant. UZ was supported by the Peter Paul Ewald Fellowship of the VolkswagenStiftung.

5 5 [1] Nazare, M. H. & Neves (Eds.), A. J. Properties, Growth and Appliations of Diamond (Institution of Engineering and Tehnology, 2000). [2] Jayaraman, A. Diamond anvil ell and high-pressure physial investigations. Rev. Mod. Phys. 55, (1983). URL RevModPhys [3] Mao, W. L. et al. Bonding hanges in ompressed superhard graphite. Siene 302, (2003). [4] Hubbard, W. et al. Interior struture of neptune: omparison with uranus. Siene 253, (1991). [5] Fortney, J. et al. Frontiers of the physis of dense plasmas and planetary interiors: Experiments, theory, and appliations. Physis of Plasmas (1994-present) 16, (2009). [6] Lindl, J. D. et al. The physis basis for ignition using indiret-drive targets on the national ignition faility. Physis of Plasmas (1994-present) 11, (2004). [7] Lindl, J. et al. Review of the national ignition ampaign Physis of Plasmas (1994-present) 21, (2014). [8] MaKinnon, A. et al. High-density arbon ablator experiments on the national ignition failitya). Physis of Plasmas (1994-present) 21, (2014). [9] Kremp, D., Shlanges, M. & Kraeft, W.-D. Quantum statistis of nonideal plasmas, vol. 25 (Springer Siene & Business Media, 2006). [10] Goñi, A. R. & Syassen, K. Optial properties of semiondutors under pressure. Semiondt. Semimet. 54, (1998). [11] Fahy, S., Chang, K. J., Louie, S. G. & Cohen, M. L. Pressure oeffiients of band gaps of diamond. Phys. Rev. B 35, 5856 (1987). [12] Yin, M. T. & Cohen, M. L. Will diamond transform under megabar pressures? Phys. Rev. Lett. 50, (1983). URL PhysRevLett [13] Yin, M. T. Si-iii (b-8) rystal phase of si and : Strutural properties, phase stabilities, and phase transitions. Phys. Rev. B 30, (1984). URL http: //link.aps.org/doi/ /physrevb [14] Nielsen, O. H. Optial phonons and elastiity of diamond at megabar stresses. Phys. Rev. B 34, (1986). URL PhysRevB [15] Trojan, I. A., Eremets, M. I., Korolik, M. Y., Struzhkin, V. V. & Utjuzh, A. N. Fundamental gap of diamond under hydrostati pressure. Jpn. J. Appl. Phys. 32, 282 (1993). URL i=s1/a=282. [16] Onodera, A. et al. Pressure dependene of the optialabsorption edge of diamond. Phys. Rev. B 44, (1991). URL /PhysRevB [17] Vohra, Y. K., Xia, H., Luo, H. & Ruoff, A. L. Optial properties of diamond at pressures of the enter of earth. Appl. Phys. Lett. 57, (1990). [18] Mao, H.-K. & Hemley, R. Optial transitions in diamond at ultrahigh pressures. Nature 351, (1991). [19] Bradley, D. K. et al. Shok ompressing diamond to a onduting fluid. Phys. Rev. Lett. 93, (2004). URL /PhysRevLett [20] Flether, L. et al. Ultrabright x-ray laser sattering for dynami warm dense matter physis. Nature Photonis 9, (2015). [21] Glenzer, S. H. & Redmer, R. X-ray thomson sattering in high energy density plasmas. Rev. Modern Phys. 81, 1625 (2009). [22] Glenzer, S. et al. Matter under extreme onditions experiments at the lina oherent light soure. Journal of Physis B: Atomi, Moleular and Optial Physis 49, (2016). [23] MaFarlane, J. J., Golovkin, I. E. & Woodruff, P. R. Helios-r a 1-d radiation-magnetohydrodynamis ode with inline atomi kinetis modeling. J. Quant. Spetros. Radiat. Transfer 99, (2006). [24] Dawedeit, C. et al. Grain size dependent physial and hemial properties of thik vd diamond films for high energy density physis experiments. Diamond Relat. Mater. 40, (2013). [25] Gauthier, M. et al. New experimental platform to study high density laser-ompressed matter. Rev. Si. Instrum. (2014). [26] Glenzer, S. H. et al. Observations of plasmons in warm dense matter. Phys. Rev. Lett. 98, (2007). [27] Mao, H. K. et al. Eletroni dynamis and plasmons of sodium under ompression. Pro. Natl. Aad. Si. U.S.A. 108, (2011). [28] Egerton, R. F. Eletron energy-loss spetrosopy in the tem. Reports on Progress in Physis 72, (2009). URL i=1/a= [29] Penn, D. R. Wave-number-dependent dieletri funtion of semiondutors. Phys. Rev. 128, 2093 (1962). [30] Ferrari, A. C. et al. Density, sp 3 fration, and rosssetional struture of amorphous arbon films determined by x-ray refletivity and eletron energy-loss spetrosopy. Phys. Rev. B 62, (2000). [31] Robertson, J. Diamond-like amorphous arbon. Mater. Si. Eng. R 37, (2002). [32] Romero, N. A. & Mattson, W. D. Density-funtional alulation of the shok hugoniot for diamond. Phys. Rev. B 76, (2007). [33] Gamboa, E. J. et al. Single-shot measurements of plasmons in ompressed diamond with an x-ray lasera). Physis of Plasmas 22, (2015). URL pop/22/5/ / [34] Ruoff, A. L., Luo, H. & Vohra, Y. K. The losing diamond anvil optial window in multimegabar researh. J. Appl. Phys. 69, (1991). [35] Surh, M. P., Louie, S. G. & Cohen, M. L. Band gaps of diamond under anisotropi stress. Phys. Rev. B 45, 8239 (1992).