Exciton spectroscopy of hexagonal boron nitride using nonresonant x-ray Raman scattering

Abstract

We report non-resonant x-ray Raman scattering (XRS) measurements from hexagonal boron nitride for transferred momentum from 2 to 9Å −1 along directions both in and out of the basal plane. A symmetry-based argument, together with real-space full multiple scattering calculations of the projected density of states in the spherical harmonics basis, reveals that a strong pre-edge feature is a dominantly Y10-type Frenkel exciton with no other s-, p-, or d -components. This conclusion is supported by a second, independent calculation of the q-dependent XRS cross-section based on the Bethe-Salpeter equation. The physics of low-energy photoelectrons in solids is a complex, many body problem 1 . All aspects of the electronic structure of the material must be taken into account 2,3 , including the interaction between the photoelectron and the complementary hole 3,4,5,6 . This latter effect allows for similar long-lived bound states in metals (generally called Fermi-edge singularities) 7 and in insulators (called excitons) 8 . As a canonical example of a many body problem in condensed matter physics, core-excitons are a topic of continuing interest 4,5,6 .The present synergy between steadily progressing ab initio theoretical treatments 2,3,9,10 and on-going improvements in instrumentation 11 in studies of nonresonant x-ray Raman scattering (XRS) shows a strong potential for rapid progress on this old problem 5,6 . XRS is the inelastic scattering of hard x-rays from bound electrons, and XRS studies have seen a recent explosion in the number and range of applications 5,6,11,12,13,14,15,16,17 . In comparison with q-resolved electron energy loss spectroscopy (EELS) 18 , XRS is more suited for bulk condensed matter systems 13 due to the large penetration length afforded by the relative high-energy incident and scattered photons. The measured q-dependent XRS provides direct information about multipole contributions to the dynamic structure factor S(q, ω) 5,6,14,15,16 . It can be directly compared with theoretical calculations of S(q, ω) 6,14,15,16 , and can in some cases be inverted to provide an experimental measure of the perturbed projected density of states (l -DOS) 10,19 , which can again be compared to theory.XRS has shown itself to be especially suitable for spectroscopy of the angular characteristics of core excitons at the near edge region. For example, XRS studies 5,6 on LiF and icosahedral B 4 C convincingly demonstrated s-, and p-type excitons at the F and B K-edges, respectively, which can be attributed to atoms located at a center of inversion symmetry of the unit cell with parity a good quantum number for the final states 6 . Here, we demonstrate that for some systems one can learn not only the ∆l selection rule for the exciton but also a full description of its angular characteristics in terms of spherical harmonics, Y lm .We present measurements of the q-dependent XRS of hexagonal boron nitride (h-BN), an anisotropic system with all atoms sitting at positions with reflection symmetry to the basal plane (Figure 1,...

Angle-resolved electron energy loss spectroscopy in hexagonal boron nitride

“…Actually, the presence of a core hole is important here, and the single-electron description should be improved. For instance, the authors of reference [38] calculated the full dielectric constant using the Bethe-Salpeter formalism [41] and found good agreement with the experimental data.…”

“…The different peaks are sharp and related to well-known transitions with typical symmetries between the deep 1s level and the first unoccupied π * states (192 eV) and σ * states (199 eV) [32][33][34][35][36][37][38][39]. Energy-filtered scattering patterns have been recorded in the 185-215 eV range for the three samples.…”

“…3. We have a clear illustration here of the anisotropy of the losses in the 1s → π * transition, which can simply be explained as follows [32,38].…”

Core and shallow-cored- tof-shell excitations in rare-earth metals

“…At low momentum transfer, as is the case for the EELS experiments reported here, the exponential operator can be approximated by the dipole operator, a r q ⋅ i , and the excitation structure probed is identical to that of x-ray absorption (with linearly polarized photons), where q plays the role of the x-ray polarization vector in XAS [20,31,[36][37][38][39][40][41][42].…”

Structure and dynamics in liquid water from x-ray absorption spectroscopy

“…X-ray Raman scattering is a bulk sensitive technique as is uses hard x-ray radiation of several keV photons and, under certain circumstances, the Raman scattering intensity is proportional to the x-ray absorption cross section at the respective edges of the elements in the sample [62,63,61,29,64].…”