Crystal-momentum-resolved electronic structure of solids using resonant soft-X-ray fluorescence spectroscopy

Journal of Electron Spectroscopy and Related Phenomena 110–111 (2000) 323–334 www.elsevier.nl / locate / elspec

Crystal-momentum-resolved electronic structure of solids using resonant soft-X-ray fluorescence spectroscopy a, a b c c J.A. Carlisle *, S.R. Blankenship , L.J. Terminello , J.J. Jia , T.A. Callcott , D.L. Ederer d , R.C.C. Perera e , F.J. Himpsel f a

Virginia Commonwealth University, Richmond, VA 23284, USA Lawrence Livermore National Laboratory, Livermore, CA 94551, USA c University of Tennessee, Knoxville, TN 37996, USA d Tulane University, New Orleans, LA 70118, USA e Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA f University of Wisconsin-Madison, Madison, WI 53706, USA b

Abstract Resonant inelastic X-ray scattering (RIXS) has been observed in graphite and hexagonal boron nitride (hBN) above and below their K edges. Below the core threshold, inelastic-loss features are observed, which disperse linearly with excitation energy, but as the excitation goes above the core binding energy, nonlinear dispersive effects are observed in graphite but not in hBN. We show that these two effects, which have previously been thought of as separate processes, i.e. resonant X-ray Raman scattering (below threshold) and RIXS (above threshold), are in fact described by the same physics of coherent fluorescence. Very good agreement between experiment and simulated RIXS is achieved using a simple one-electron framework. The role core-excitons play in the RIXS process is examined in finer detail, by using narrow-band excitation. Our results indicate that core-hole effects play a minor role in the RIXS observed from graphite but are more pronounced in hBN.  2000 Elsevier Science B.V. All rights reserved. Keywords: X-ray emission spectra; Resonant X-ray scattering; Band structure; Excitons; Graphite; Hexagonal boron nitride

1. Introduction Recently, much interest has been focused on extending our understanding of resonant inelastic X-ray scattering (RIXS) processes in the soft-X-ray regime. There are two primary reasons for this renewed interest. First, over the past 5 years, several third-generation synchrotron light sources have been commissioned, which now deliver light with much greater brightness than previous sources. This, along *Corresponding author. E-mail address: [email protected] (J.A. Carlisle).

with advances in grating spectrometers, have dramatically reduced the time needed for photoncounting techniques to acquire photon emission spectra. This reduction has in turn allowed detailed studies of the variation of emission features as the excitation energy is finely tuned through a core-level absorption threshold. The second reason centers on the increasing complexity of material systems that are of interest in both technology and basic research. In particular, layered materials (e.g. magnetic mutlilayers and semiconductor superlattices) have long been intractable to direct probes of electronic structure (such as

0368-2048 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 00 )00171-7

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electron-yield techniques). Thus, there is a critical need for techniques which are intrinsically bulk (as opposed to surface) sensitive. Soft-X-ray fluorescence spectroscopy (SXF) has long been recognized as a technique with unique capabilities as a probe of electronic structure [1,2]. The technique is illustrated in Figs. 1 and 2. SXF is a bulk sensitive, element selective probe of the bonding structure within a material. Resonant soft-X-ray fluorescence spectroscopy (RSXF), the primary subject of this work, refers to the study of the changes in X-ray emission spectra as the excitation energy is varied near a core-level absorption threshold (Fig. 2). It has been the application of RSXF to solids in the soft-X-ray regime, that has garnered most of the interest in the past decade [3–13]. In addition to probing the local density of states (DOS), RSXF has allowed, in numerous cases, the crystal-momentum-resolved (k-resolved) electronic structure to be studied. As first shown by Gel’mukhanov et al. [3], and more recently by Ma et al. [4], in addition to energy and angular momentum, crystal momentum (k) may be conserved during the scattering process. Such effects have been observed in many systems: diamond [4–6], silicon [7], silicon

Fig. 1. Schematic of the experimental set-up. The sample, grating and photon detector all lie in the horizontal plane, which also ¢ contains the incident light’s polarization vector E.

carbide [8], hexagonal boron nitride (hBN) [9,10], cubic boron nitride [11], gallium nitride [12], poly(phenylenevinylene) [13], and, most clearly, in graphite [14]. In graphite, a nonlinear dispersion of the emission features is observed which can only be the result of crystal momentum conservation and the coherent participation of delocalized intermediate states in the scattering. RSXF data obtained above threshold in graphite is shown in Fig. 3 [14]. Although the description of the scattering in terms of purely delocalized states [4–6,14,15], as supported by the data of Fig. 3 showing a clear dispersion of emission features with energy, is appealing in its simplicity, serious questions arose concerning the validity of this picture [16–18]. For instance, in core-level absorption spectroscopy (XAS or NEXAFS), core-hole effects (core excitons) are clearly observed and have long been know to dramatically affect the interpretation of absorption spectra. Since the final states in XAS are the intermediate states in RSXF, it has been argued that the omission of these effects from the interpretation and / or modeling of the scattering observed in RSXF renders an interpretation in terms of a one-electron or non-interacting picture in doubt [16,17]. It has been asserted in at least one work that, in fact, the inclusion of such effects is necessary in order to correctly account for the experimental data shown in Fig. 3 [18]. In this work, we will have two primary focuses. First, we wish to illustrate, by combined experiment and simple one-electron theory based on the Kramers–Heisenberg rule, how k-resolved information can be obtained both above and below the core threshold in a prototypical delocalized system, graphite (HOPG). We also wish to illustrate how the non-interacting picture fails when the bonding structure becomes inherently delocalized in hexagonal boron nitride (hBN). Second, we wish to focus on the possible effect core-excitons have on the experimental data by examining, at higher resolution than previously attainable, the changes in the scattering near the s* and p* absorption thresholds in graphite. Our conclusion is that core-excitons have only minor effects on the emission features, even though they clearly have a pronounced effect on the total fluorescence yield. However, other spectral features are not fully accounted for by the inclusion

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Fig. 2. Energy level diagrams appropriate for the non-resonant (left) and resonant (middle and right) modes of soft-X-ray fluorescence spectroscopy. In the non-resonant form of the technique, the excitation energies are far above the core-level threshold, so that the absorption / emission events are effectively ‘decoupled.’ In resonant fluorescence, the excitation energies are within a few eV of the core binding energy, and crystal momentum (in addition to energy and angular momentum) is conserved during the scattering event. In the non-interacting picture, the states that participate in the process are the stationary ground states (band states), whereas in the interacting picture they are perturbed by the presence of a core hole in the intermediate state and a valence hole in the final state. These effects and others change the subspace of k-space that is probed by the technique.

of core excitons in the scattering. This leads us to speculate that valence excitons (the RIXS final state) may play an important role in the scattering process.

2. Experimental The fluorescence experiments were conducted on Beamline 8.0 at the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory [19]. The beamline and the fluorescence spectrometer used in this work are described in detail elsewhere [20,21]. Emitted radiation was measured with a Rowland circle type spectrometer utilizing large spherical gratings and a photon-counting area detector. Total instrumental resolution in the C 1s emission region

was 0.3 eV FWHM. The bandwidth of the incident photons used was varied between 60 and 500 meV, as described below. The incident flux was monitored by measuring the current from a gold foil located immediately upstream from the spectrometer. The incident photon energy was calibrated to the known graphite (p* and s*) and hBN (p*) absorption features [22,23]. The spectrometer energy calibration was accomplished by identifying the elastic peak with the incident photon energy. A typical emission spectrum in this work was acquired in 10 min. The graphite sample used was highly-oriented pyrolytic graphite (HOPG), which was freshly cleaved immediately prior to insertion into the spectrometer. The crushed-powder hexagonal boron nitride (hBN) sample was obtained from a commercial source. The simulated fluorescence spectra were modeled

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Fig. 3. Resonant fluorescence data from (HOPG) graphite (from Ref. [14]). The excitation energies are given to the left of each emission spectrum. The width of the incident radiation is approximately Dhn (300 meV The band structure of graphite is plotted above the RSXF data, with the binding energy axis rotated and aligned to the emitted photon energy axis below. The emission features 1–7 can be easily identified with different branches of the graphite band structure (see text).

by Dr. Eric Shirley (NIST), and the details concerning the stimulation will be found elsewhere [24].

3. Results and discussion Resonant fluorescence spectra obtained from graphite are shown in Fig. 4. The stack-plot of the emission spectra show the C K emission region as the incident photon energy (hn ) is varied below and

Fig. 4. Resonant fluorescence data obtained from HOPG for incident excitation energies hn varied from 281 eV (below the C 1s threshold) to 320 eV (a much broader range than in Fig. 3). The intensity of each spectrum has been normalized to the incident photon flux. Note that the spacing between the excitation energies is non-uniform. The width of the incident radiation is now Dhn (150 meV. The dashed lines mark the location of the RIXS peaks. Note the linear dispersion of the Raman features below the Fermi level, compared to the generally non-linear dispersion above the core threshold.

above the C K edge, which is assumed to be located at hn 5284.5 eV [22,23]. The photon energies are given to the left of each spectrum. The intensities of each emission spectrum have been normalized to the incident photon flux, so that absolute intensity comparisons between spectra may be made in Fig. 4. Note that the energy separation between successive spectra in the stack-plots is non-uniform. The choice

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of emission geometry (a 5 358; see Fig. 1) allows emission from p-bands as well as s-bands [14,25]. The emission spectrum obtained for hn 5320 eV is sufficiently far from the C K edge, so it represents the normal or non-resonant C K emission spectra for graphite. Radiative recombinations with the corehole obey the normal dipole selection rules, so that this spectrum represents the p (l51) partial DOS. As expected for the non-resonant fluorescence process, spectral features in this valence emission spectrum correspond to regions with a large DOS in the graphite band structure (Fig. 2). In contrast, the resonant emission spectra, obtained when the incident photon energies are near the C K edge, exhibit many interesting spectral features, which appear to change in a systematic way with excitation energy. The two regimes for scattering below and above the core threshold are qualitatively quite different, and can be characterized by the types of dispersive features present. Below threshold, the spectra consist of features which move linearly with the excitation energy. These ‘loss’ features (borrowing the nomenclature of optical Raman spectroscopy), which occur at a constant energy displacement from the elastic peaks, are labeled A, B and C, and their displacements from the elastic peak are approximately 16, 12 and 10 eV, respectively. As hn moves above the K edge, the nature of the emission changes dramatically. Instead of linear dispersion, the peaks move in a nonlinear fashion. These features are highlighted by the dashed lines in Fig. 4. In fact, some of the features move in a manner opposite to the (increasing) excitation energy. The movement of these features can be directly related to the band structure [14]. Of particular interest in this work is the behavior of emission spectra as the excitation is tuned so that a core electron is favorably excited near the M- and G-points in the Brillouin zone. This point will be discussed in detail below, in regard to the possible effects of core-excitons have on the interpretation of the scattering. It is interesting now to compare the RIXS in graphite with its structural analog, hBN. Whereas graphite is a semimetal, with an intrinsically delocalized electronic structure, hBN is a wide band-gap semiconductor (Eg | 5.5 eV); a III–V material wherein the bonding interaction involves significant charge

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transfer from boron to nitrogen. The empty states in the lowest-lying conduction bands are physically localized near the boron atoms. It is natural then to expect the RIXS to be fundamentally changed owing to the participation of localized intermediate and final states in the scattering. This material also has a well-known p* core-hole exciton, with a binding energy of |1.1 eV [22,23]. Fig. 5 shows the B K resonant emission spectra from hBN. Again, all spectra have been normalized to the incident photon flux, and labeled by the excitation energy. The elastic peak exhibits a very strong intensity enhancement for hn 5192 eV, when B 1s electrons are excited into the exciton state involving the B p* orbital. This feature is detected whenever boron is p-bonded in a material, and has

Fig. 5. Resonant fluorescence data obtained from hexagonal boron nitride (hBN). The excitation energies are given to the left of each spectrum. Again, note that the spacing between the excitation energies is non-uniform. Features A, B and C are discussed in the text.

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been utilized to probe the bonding structure of BN monolayers deeply buried in a C–BN–C multilayer [26]. Below the core threshold (192 eV), the spectra show two inelastic peaks, labeled A and B, separated by 5 eV, along with the elastic peak. As was the case in graphite above, these features exactly track the excitation energy, so that the higher-energy feature B maintains a constant energy separation of about 11 eV from the elastic peak. At threshold, a new feature appears in the spectrum, labeled C, about 2.5 eV above peak B. At higher incident photon energies, peak C is again absent. In sharp contrast to graphite, for excitation above the core threshold (hn $ 193.7 eV), the emission features abruptly become broadened and fixed in energy position, resembling ordinary B 1s fluorescence for hBN. In Fig. 5, note also the continuation of the Raman peaks for excitation energies immediately above the B 1s threshold (i.e. the data from hn 5192.0 eV to hn 5193.7 eV). Whereas in graphite we have both Raman and non-Raman features for excitation energies corresponding to the core threshold, in hBN the Raman features are the only dispersive ones observed. We now discuss our interpretation of the above data in terms of a simple one-electron picture. Figs. 6 and 7 show simulated RIXS spectra for HOPG and hBN, based on the following model. The scattering process is given by the Kramers–Heisenberg formula, which results quite generally from the application of time-dependent perturbation theory in second order [3,4,13,14] kfup ? Aumlkmup ? Auil ]]]]]] Gm m E 2 E 2 hn 2 i ] m i 2 ? dsEf 1 hn 9 2 Ei 2 hnd

ds ]~ dV

*O

*

2

(1)

In this expression uil is the initial (ground state) of the system with energy Ei , humlj is the ensemble of intermediate states to be summed over, with lifetimes hGm j, and ufl sums over the final states. Electron– electron interactions, related excitonic effects, and vibrational effects all complicate the absorption– emission process, so that its description within an independent-electron framework must be regarded as

Fig. 6. Simulated RIXS data for graphite, for the same energies as the experimental data shown in Fig. 4, based on a non-interacting (one-electron) picture. XES denotes ordinary fluorescence, which mimics the spectrum acquired at hn 5 320 eV in Fig. 4.

approximate. However, the simplicity afforded by that framework motivates its use at the outset, and the framework permits description of emission features (for graphite) remarkably well. The states humlj have a core hole and an electron in a conductionband state with energy Em $ EB , the core-level binding energy. For scattering involving valence electrons, ufl contains an electron in the conduction band state and a hole in a valence band state. Energy conservation requires that the energies of the incident and emitted photons be related to the energies of the electron and hole by

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incoherent emission due to energy conservation between the core-hole and the photoelectron. The finite emission observed then is purely coherent. The sum over intermediate states humlj is over all states with photoelectrons being promoted from the corelevel to the unoccupied conduction electron states whose energies Em $ EB . The observed emission energies, hn 9, are solely those allowed by conservation of energy (Eq. (2)) hn 9 2 hn 5 Ee (k e ) 2 Eh (k h )

Fig. 7. Simulated RIXS for hBN, for the same energies as the experimental data in Fig. 6.

hn 9 2 hn 5 Ee (k e ) 2 Eh (k h )

(2)

where the equality is approximate because of effects neglected. If the appropriate wave functions are substituted into the Kramers–Heisenberg formula above, the following conservation rule results, which connects the momenta of the photons q and q9 to the crystal momentum of the electron and hole [4–6] q–q9 5 k e –k h 1 G

(3)

This equation implies that inelastic scattering features track with the excitation energy, and the magnitude of the energy loss is the energy difference between the bands with the (nearly) same crystal momentum (i.e. k e (k h ). The observed intensities are modified by the matrix elements and the energy denominator in Eq. (1) above, so that the profile of the emission is a (partial) joint density of states (p-JDOS). The energy denominators weigh the overall yields for each huml, uflj channel. Thus, the emission profiles observed in graphite and hBN for excitation below the core threshold are the p-JDOS in each system tracking hn, as predicted by Eq. (4). We note the agreement between experiment and the simulated spectra is quite good in this regime for both systems. For excitation above the core binding energy, the Kramers–Heisenberg formula suggests a very different scattering regime compared with excitation below threshold. First, the energy denominator, which possesses no minima below the core threshold, now resonantly enhances intermediate states which have energies Em (hn, so that intermediate states for which Ee (k e )(hn –EB

(5)

over an energy range comparable to Gm , will be predominant in the absorption–emission process. This leads to crystal momentum selectivity, in addition to conservation of total momentum for coherent processes above threshold. When Eq. (5) holds, the coherent emission energies are given by substitution of the above equation into Eq. (2) hn 9 ( Eh (k h )–EB

The scattering below and above threshold may be described as follows. For hn , EB , there is no

(4)

(6)

Again, k e (k h , but the favored values of crystal

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momentum do not span the entire zone, but are limited to isoenergy contours. Crystal momentumresolved information may be inferred from the observed, nonlinear dispersion of emission features, which follow the E(k) dependence of the band structure. This is what is observed in Fig. 3. It is apparent that the experimental spectra differ more significantly from the theoretical ones in the above threshold regime, especially for hBN. This is caused by, in part, the second interesting difference between excitation above compared with below threshold. The decoupling of absorption and emission energetics, i.e. the possibility of real transitions to a state, uml, permits incoherent emission, too. However, our simplified theory does not address the relative amounts of coherent and incoherent emission. In addition, the independent-electron approximation precludes broadening of fluorescence features, which is seen in experimental spectra. Nonetheless, unnaturally sharp features in theoretical spectra correspond otherwise well, frequently, with their broadened counterparts in experimental spectra. The disagreement between theory and experiment is greater for excitation above threshold in hBN compared to graphite. The resemblance of the spectra to the calculated incoherent spectrum possibly indicates that incoherent processes dominate coherent ones in hBN compared to graphite. This point is discussed further in more detail below. We now turn our attention to core excitons and their possible influence on the RIXS process. One way to address this issue is to incorporate the corehole into the theory directly, and then regenerate the simulated spectra shown in Figs. 6 and 7. Shirley (NIST) has been working in this direction, and his results and discussion can be found elsewhere [15,24]. Based on Shirley’s preliminary findings, core-excitons result in only minor changes to the simulated spectra. However, recent work by Gel˚ ’mukhanov and Agren [27] has shown that the RIXS emission is split into two qualitatively different sidebands, the first one caused by transitions to localized states while the second is connected with the participation of delocalized states in the scattering. Another way to address this issue is through experiment. If the core-hole perturbs the scattering, we may expect to observe the effects of such a

perturbation in several ways. (1) The exciton changes the momentum selectivity, by changing the portion of BZ projected out of the band structure. This would lead to spectra which look qualitatively very different from what one might expect based on the non-interacting picture alone. (2) The participation of the exciton dominates the scattering by virtue of its strong localization. The exciton becomes effectively the only intermediate state participating in the RIXS scattering, leading to a partial or total breakdown in momentum selectivity and the observation of only ‘Raman-like’ scattering both above and below threshold. Excitonic effects are quite strong in graphite. Fig. 8 shows the HOPG band structure [15] and Fig. 9 shows an experimental XAS spectrum obtained from graphite, which shows clear p* and s* absorption features at 285.5 and 291.6 eV, respectively. Below this experimental spectrum are the plotted the density of unoccupied states and a simulated XAS spectrum determined with the core-hole potential included

Fig. 8. Band structure of graphite, transposed to facilitate comparison to the experimental and simulated RIXS. The band energies are plotted horizontally with crystal momentum on the vertical axis.

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Fig. 9. Experimental and simulated X-ray absorption spectrum for graphite. Solid lines correspond to calculations made with corehole effects included, whereas dashed lines give the results of calculations based on a non-interacting (one-electron) picture.

[15,24]. Clearly, the core-hole has a dramatic effect on the experiment in this technique. Due to recent advances in the storage ring at the ALS, Beamline 8.0 now delivers roughly an order of magnitude more flux in the 100–1000 eV range. This affords us the opportunity to examine, with much higher resolution that in previous studies, the crystal momentum conservation and selectivity during RIXS, for intermediate state energies near wellknown core-excitons, while retaining data acquisition times at around 10 min. This can be accomplished by narrowing the bandwidth of the excitation energy Dhn down to |60 meV. This reduction of the bandwidth narrows the widths of the isoenergy contours in the BZ that are summed over during the RIXS process (i.e. the spread of crystal momenta in the BZ is reduced). Figs. 10 and 11 show the RSXF data collected near the p* (Fig. 10) and s* Fig. 11A and B absorption edges in graphite, using Dhn ¯ 60 meV. Through comparison of Fig. 3 (Dhn ¯ 500 meV) and Fig. 10 (Dhn ¯ 60 meV), it is clear that narrowband excitation has an marked effect on the mea-

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Fig. 10. Experimental RIXS spectra for HOPG collected for excitation energies near the p* absorption threshold of 284.5 eV. The excitation energies are given to the left of each emission spectrum. The width of the incident radiation has been reduced to Dhn 5 60 meV (compare these spectra with Fig. 3, obtained using 300 meV bandwidth excitation). Note the abrupt onset of emission at hn 9 5 276 eV.

sured spectra. Note carefully that the range of excitation energies in Fig. 10. is narrower than in Fig. 3. Features in Fig. 10 are sharper than in Fig. 3, and the transition from emission around the K point to emission around M (referred to as the K-to-M crossover in earlier work [14]), as the excitation energy increases, is much sharper. Note carefully features 2 and 3 in Fig. 3, and compare them to their counterparts in Fig. 10. Whereas in Fig. 3 there is a range of energies for which emissions from both the K and M branches of the upper p bands are observed simultaneously, reduction of the excitation bandwidth leads to a much more smooth transition in Fig. 10. Clearly, momentum conservation and selectivity are very much in force for all the excitation energies above, equal to, and below the p* energy. In fact, careful comparison with the simulated spectra in Fig. 6 shows that using the narrower bandwidth enhances the agreement between theory and experiment in the

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Fig. 11. Experimental RIXS spectra for HOPG collected for excitation energies near the s* absorption threshold of 291.6 eV. The excitation energies are given to the left of each emission spectrum. (A) Data acquired using Dhn ¯ 60 meV. Note that the spacing between successive spectra is 0.25 eV. This emission near 281 eV (dotted line) is consistent with final states corresponding to a p→s* promotion near M. Note that this feature does not move with the excitation energy. (B) Spectra obtained in the same energy range as in (A), but with very broad-band excitation (Dhn ¯ 500 meV). Note the absence of the emission feature at 281 eV.

K-to-M transition region. Note also, in Fig. 4, that the absorption cross-section strongly modulates the fluorescence yield, without apparently having a large effect on features of that yield. Our explanation for the above behavior can be qualitatively described as follows. Core-hole effects have such a large effect on the experimental XAS data since the core-hole is the final state in this measurement. However, in RIXS, the core-hole is an intermediate state. Although the exciton is more localized in real space, and thus more delocalized in momentum space, the final momenta which participate in the scattering is determined by the projection of the excitonic state onto the RIXS final state, which contains an electron in the conduction band and a hole in the valence band. These final states are almost certainly not as localized as the core excitonic states. Thus, momentum selectivity is for the most part the same as one would expect based on a one-electron or non-interaction picture.

The above explanation is sensible for excitons whose binding energies lie within the continuum of conduction band states. At the s* edge, however, there is an exciton that is disjointed from the bottom of the s* bands at M (see Figs. 8 and 9), with a binding energy estimated to be 0.1–0.2 eV [15,28]. Fig. 11A shows RSXF spectra obtained near the s* absorption edge using Dhn ¯ 60 meV, and Fig. 11B show similar spectra obtained using Dhn ¯ 300 meV. As opposed to data taken near the p*-edge, the spectra obtained using the narrower bandwidth have several addition features, highlighted by the dotted line and arrows in Fig. 11A. The feature located at |281 eV, does not move with excitation energy, and is detectable over a narrow energy range (|0.5 eV). Note that its appearance and disappearance corresponds exactly with the s* absorption energy (|291.6 eV). Two other, weaker, features also rise and fall with the appearance of the 281 eV feature, located at roughly 276 and 269 eV.

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Inspection of the graphite band structure, shown in Fig. 8, indicates that these features are derived from states at the M-point in the BZ. Apparently in this range of excitation energies, k-selectivity is present to a significant degree, and the portion of the BZ selected is near M. This data strongly suggests that a highly localized intermediate state exists near the bottom of the s*-bands at M, and that this state slightly influences the scattering for a narrow range of energies centered on the M-point. The key is that these emission features do not move in energy as the excitation energy is varied. If the detected features were part of the ‘normal’ RIXS involving delocalized states, then they should have some measurable dispersion (either the non-linear RIXS or the linear Raman-like behavior). Based on a non-interacting picture, we should observe an M-toG crossover, similar to the K-to-M crossover shown in Fig. 10 and discussed above. For instance, we should observe a very rapid dispersion, to lower emission energy, of the 281 eV feature, as hn varies from roughly 291–292.5 eV. The fact that they do not move is suggestive that an highly localized, excitonic state (comprised of a narrow range of k-values near M) dominates the RIXS in this narrow intermediate state energy range. Conclusive proof of the excitonic character discussed above awaits the completion of the incorporation of core-hole effects into the theory. Calculations are underway, and preliminary results support the above scenario. Thus, based on the experiments and the comparison with simulated spectra generated without core-hole effects, we conclude that excitons have only minor effects on the detailed line-shape of the resonant emission spectra in graphite. This conclusion can be extended to a number of other systems [4–14]. The RIXS in hBN is harder to reconcile within a one-electron picture. The RSXF data from this system deviates significantly from the simulation in three main ways: (1) The Raman-like scattering continues above the core-level threshold, (2) This Raman-like mode abruptly ends at 193.6 eV, with the spectrum transforming into one which looks identical to the non-resonant spectrum, and (3) The feature labeled C in Fig. 5 is unaccounted for in the simulation. As mentioned above, hBN has a very strong core

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exciton, with a binding energy of |1 eV. The most likely explanation for (1) above is that this state dominates the RIXS to the point that it is effectively the only intermediate state participating in the summation of Eq. (1). Conservation of crystal momentum still occurs, but the k-selectivity is suppressed by the dominance of this state in the scattering. This does not explain point (2) above. However, all the work to date on various systems show that, as the excitation energy increases several eV above the core threshold, the spectra increasingly resemble the nonresonant emission. Apparently, for hBN, once hn reaches the conduction band minimum, the RIXS is abruptly shut down. Feature C cannot be explained either in the noninteracting picture or by evoking core excitonic effects. Preliminary calculations which include corehole effects do not reproduce this feature either. It is possible that it is derived from a scattering which has a valence exciton in the final state. Work is currently underway to incorporating valence excitons into the theory.

4. Conclusions To summarize, we have demonstrated that the inelastic resonant X-ray scattering present in resonant fluorescence spectra obtained below and above a core-level absorption threshold may be utilized to probe the band structure of a material. The scattering regimes below and above threshold are described by the same scattering physics of coherent fluorescence for delocalized intermediate and final states, as put forward by Gel’mukhanov et al. [3] and Ma et al. [4], based on the quasiparticle band structures, without inclusion of excitonic or vibrational effects. We have probed, using narrow-band excitation, the role core-excitons play in the RIXS process. In graphite, core-hole effects result in only minor changes to the resonant emission spectra, but in hBN these effects or more pronounced. The ability of RIXS to examine the k-resolved electronic structure, coupled with the intrinsic strengths of soft-X-ray fluorescence for probing the bulk-sensitive and element-resolved electronic structure of materials, demonstrates the great potential of this technique for probing the electronic structure of novel materials

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systems which are generally inaccessible to other techniques.

Acknowledgements This work was supported at VCU by a Research Corporation Cottrell College Science Award No. CC4526, a Jeffress Trust Memorial foundation No. J-424, and by a Faculty Grant-in-Aid at Virginia Commonwealth University. The work is also supported by the Division of Materials Science, Office of Basic Energy Sciences, and performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48, by National Science Foundation Grant No. DMR-9017996 and DMR9017997, by a Science Alliance Center for Excellence Grant from the University of Tennessee, by the U.S. Department of Energy (DOE) Contract No. DE-AC05-84OR21400 with Oak Ridge National Laboratory and by the Louisiana Educational Quality Support Fund and DOE-EPSCOR Grant LEQSF (9395)-03 at Tulane University. This work was performed at the Advanced Light Source, which is also supported by the Office of Basic Energy Scienes, US Department of Energy, under contract No. DEAC03-76SF00098.

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