Ground state wave function of the strongly correlated topological insulator SmB₆

SmB₆ is a material under intensive investigation, motivated by indications that it may be the first topological insulator that is also strongly correlated. Different from semi-conductor based topological insulators, strongly correlated systems which are topologically non-trivial may exhibit not only a metallic state at the surface but alternatively a ferromagnetic or other more surprising and exotic surface states.

SmB₆ is an intermediate valent system that opens a gap only at low temperatures due to correlation effects at the Sm 4f orbitals together with the hybridization with the conduction band states. Strikingly, it always exhibits conducting properties at the surface no matter how the surface was prepared. It is therefore tempting to take this observation as evidence for the topological nature of SmB₆. With the topological properties of the surface being fully determined by the bulk, it is crucial to understand the electronic structure of the bulk and the symmetries of the states involved. Attempts are being made to adiabatically connect the many body electronic structure with that of an effective band structure. In this respect, it is surprising that the ground state wave function of the Sm³⁺ ions in the bulk is not even known so far, despite attempts in the past using e.g. neutron scattering. Whether it is the so-called Γ₈ quartet or Γ₇ doublet makes a crucial difference for e.g. the spin texture of the topological surface states.

Recently, scientists from the Max-Planck Institute for Chemical Physics of Solids and the University of Cologne could clarify this issue by applying a new technique, namely core-level non-resonant inelastic x-ray scattering (NIXS), see Sundermann et al., Phys. Rev. Letter (2018). In NIXS the core hole excitation 4d→ 4f (N-edge) probes directly the 4f states and the direction dependence of the scattering function S(q,ω) gives insight into the ground state symmetry in analogy to the a linear polarized x-ray absorption experiment. However, in a NIXS experiment the core hole excitation is measured at such large momentum transfers that higher multipoles contribute to S(q,ω). As a result, asymmetries can be detected even in a cubic environment. In the recent past the same two teams have shown at the example of several Ce compounds that the principle works.   

Figure 1 shows the main result of the NIXS experiment: the experimental dichroic spectrum (black dots) and simulated dichroic spectra for the Γ₈ quartet (orange) and Γ₇ doublet (light blue) scaled with the factor of 0.6 to account for the Sm³⁺ component of the ground state; dashed lines with energy independent broadening, solid lines with extra broadening in the dipole region. We can clearly conclude from the good quantitative agreement that the ground state is the Γ₈ quartet. In fact, the opposite dichroism at 125 and 140 eV (see red arrows) reduces the experimental challenge to a simple yes-no experiment and makes the determination of ground state wave function of the Sm³⁺ in SmB₆ straightforward. The finding that the ground state is the Γ₈ quartet and not the Γ₇ doublet, contradicts all existing band structure calculations and illustrates in a sobering manner the difficulties in making reliable predictions for the properties of correlated systems.  Our experimental results point out that future calculations of the low energy properties of SmB₆ should be performed within a reduced basis of only Γ₈ states.

The NIXS experiment was possible thanks to the high brilliance of modern synchrotrons and major advances in x-ray instrumentation since the non-resonant scattering process is very photon hungry.  The experiment was carried out at the P01 beamline at DESY/PETRA-III in Hamburg, which is presently being upgraded with contributions from MPI-CPfS in Dresden and the MPI-FKP in Stuttgart. Figure 2 shows the non-resonant x-ray scattering end station at P01 in its present form together with a cartoon of the scattering configuration.