Driving Spin Orbit Coupling to the Extreme (exSOC)

What is spin-orbit coupling and why is it so important in condensed matter? Generally, an electron orbiting the nucleus in an atom creates a small magnetic field (which is the larger the heavier the atom). As the electron also possesses an intrinsic magnetic bar called spin, this spin now interacts with the induced magnetic field of the orbital motion. We call this interaction spin-orbit coupling (SOC). The result is that, depending on the orientation of the spin with respect to the induced magnetic field, the electron experiences an additional energy boost or a small energy decrease. SOC is also present when electrons move through a crystal lattice. Some materials do not conduct a current, like glass or wood these are insulators. The physical origin of this non-conductivity lies in the fact that, in an insulator, the energy bands the electron travels in are separated by a gap. And here it becomes interesting: Only recently it was found that in some insulators, SOC is strong enough to lead to the phenomenon of band inversion, with dramatic consequences. The inversion creates robust surface states within the gap, turning the materials surface into a metal while the interior remains insulating. Such materials are named topological insulators. The Austrian-Czech Bilateral Project exSOC concentrates on Ce- and U-based Kondo insulators (KI). An example material is Ce3Bi4Pt3. The name KI refers to the fact that in these intermetallic compounds the gap between the valence and the conduction bands is created by strong correlations (Kondo effect of the f electron from Ce and conduction electrons from Bi and Pt). Due to the heavy elements constituting them, these materials also exhibit a large SOC. As before, sufficiently strong SOC may lead to band inversion, potentially turning the material into a topological Kondo insulator (TKI). Yet, in a strongly correlated setting, the role of SOC is poorly understood. In fact, entirely new states of matter may result from the interplay of strong SOC and strong correlations, making this a vastly open new field. Questions we address are: Can a KI be driven into a TKI state upon enhancing SOC? Do Ce- or U-based TKIs exist? Which SOC is more relevant, the SOC related to the f electrons from Ce or U or the SOC originating from the Bi and Pt electrons? We intend to answer these questions by a series of chemical substitutions which tune the SOC strength (for example, replacing Ce by much heavier U), and a series of experiments to detect and characterize the new emerging states.

Solid materials are classified as metals (copper, gold), semimetals or semiconductors (silicon), and insulators (wood, glass) depending on their capacity to conduct electricity. In metals, the speed of the moving electrons is influenced by their interaction with the ions that constitute the structure of the material and with other nearby electrons, and by the interaction of the electron's magnetic moment (spin) with its own orbital motion (spin-orbit coupling, SOC). In typical insulators and semiconductors, these interactions collude to restrict the moving electric charges to a forbidden energy zone and therefore cannot conduct electricity freely. In other words, the energy bands characterizing the motion of charges are separated by a gap. Recently, a novel class of insulators and semimetals has been discovered, the topological insulators and Weyl or Dirac semimetals. Here, specific symmetry constraints imposed by the crystal structure, together with the effect of SOC, produce "symmetry-protected" states that circumvent the gap restriction. These novel states act as exotic particles that could transport electric and magnetic information in a highly efficient way, and have attracted a great deal of interest due to their potential use for applications in spintronics and quantum computation. So far, much progress has been made on non- and weakly-interacting systems. Within our project, Driving Spin-Orbit Coupling to the Extreme (exSOC), we collaborated with the team at Charles University in Prague to connect the physics of topology and strong electronic correlations. Our playground has been a series of so-called Kondo materials, in which large electronic interactions arise from the presence of both localized 4f or 5f electron states and conduction bands (from s, p, d electrons). Starting from the novel Weyl-Kondo semimetal state recently discovered in Ce3Bi4Pd3, we set out to explore other selected materials using different combinations of atoms as tuning knobs of their correlated and topological properties. For example, by replacing the 4d Pd by the 3d Ni or 5d Pt atoms, or the 4f Ce by the 5f U atoms, the previously unknown compounds Ce3Bi4Ni3 and U3Bi4Pt3 were synthesized as bulk single crystals. For Ce3Bi4Ni3 we found that a large insulating gap develops, suppressing the topological Weyl-Kondo semimetal properties. Our results with these and other newly discovered materials are of key importance for fundamental physics research, and contribute to bridge the gap between material science and quantum applications.