Bulk electronic structure of ${\mathrm{K}}_3{\mathrm{C}}_{60}$ as revealed by soft x-rays

We present $\mathrm{C}1s$ x-ray absorption, x-ray emission, and resonant inelastic x-ray scattering (RIXS) spectra of single-phase crystalline ${\mathrm{K}}_3{\mathrm{C}}_{60}$. The comparison to valence-band photoelectron spectra from the same sample facilitates identification of the contribution from surface and bulk electronic states in the latter. Bulk-sensitive techniques show that the valence bands of ${\mathrm{K}}_3{\mathrm{C}}_{60}$ and pure ${\mathrm{C}}_{60}$ are characterized by spectral features of similar width, in agreement with the predictions of band-structure calculations. Symmetry selectivity in the RIXS process allows us to assign peaks in the $\mathrm{C}1s$ absorption spectrum, demonstrating a close correspondence with pure ${\mathrm{C}}_{60}$ also in the conduction band. The symmetry selectivity is as pronounced in ${\mathrm{K}}_3{\mathrm{C}}_{60}$ as in pure ${\mathrm{C}}_{60}$, indicating that the local ${\mathrm{C}}_{60}$ symmetry is not appreciably affected by the K doping, either in the ground state or intermediate state, on the time scale of $6\mathrm{fs}$.

Figure 1

A schematic of the techniques employed. In each case, the final state of the indicated process is shown, along with the associated excitation and/or deexcitation transitions and associated particles (photon and/or electron) for both photon-in–photon-out techniques. Core-level and valence-level PES provide a starting point, creating hole states. For XES, core photoionization first creates the same state as in PES as shown, followed by a transfer of the hole to the valence states and simultaneous emission of a photon that is detected, which in a single-particle picture creates the same final state as valence PES. In RIXS, which is analogous to XES, the intermediate state corresponds to an XAS excitation, which then decays similarly to XES, but with an extra electron in the initially unoccupied valence levels. RIXS leaves the molecule in a valence-excited state, which leads to different emitted photon energies than in XES, as discussed in detail in the text. The two steps are usually measurably coherent in RIXS, which further differentiates it from XES, as discussed in the text.

Figure 2

$\mathrm{C}1s$ XAS of ${\mathrm{C}}_{60}$ and ${\mathrm{K}}_3{\mathrm{C}}_{60}$ measured via Auger electron yield, with the first three resonances of solid ${\mathrm{C}}_{60}$ labeled according to the unoccupied molecular orbitals from which they are derived. The arrows indicate the excitation energies for the spectra in Fig. 3.

Figure 3

Photon-in–photon-out spectra for ${\mathrm{K}}_3{\mathrm{C}}_{60}$ recorded at the indicated excitations of Fig. 2 (RIXS) and at $306\mathrm{eV}$ $\left(g\right)$, which are taken to correspond to off-resonant excitation, i.e., XES. Peak $e$ in the spectra is due to elastic (Rayleigh) scattering at the excitation energy.

Figure 4

Valence band PES, XES, and RIXS data of the indicated samples, measured with the excitation energies $110\mathrm{eV}$ (PES), $306\mathrm{eV}$ (XES), and as indicated by arrows $a$ and $A$ in Fig. 2 for RIXS. The positions of bulk contributions to the PES spectrum in (b) are marked by dashed lines.

Figure 5

Resonant inelastic scattering via the two lowest-energy absorption resonances. Excitation energies as marked in Fig. 2 by $a$ and $b$ (${\mathrm{K}}_3{\mathrm{C}}_{60}$, lower panel), and $A$ and $B$ (${\mathrm{C}}_{60}$, upper panel). (The $e$ in each spectrum marks the elastic-scattering peak.)