# C05

## Topological states in materials with highly entangled spin, orbital and charge degrees of freedom

#### Summary

Unconventional physics emerging from the synergy and competition of spin, charge and orbital degrees of freedom is one of the central topics of this Collaborative Research Center. In modern condensed matter physics, the term “unconventional” is often used to indicate a physical phenomenon that emerges not only from one of the active degrees of freedom, but rather from their interplay. Two of the most prominent known examples involve strong electronic correlations: high-T_{c} superconductivity on the one hand and fractional topological insulators on the other hand. These unconventional phenomena force us to reexamine some of the fundamental building blocks of condensed matter physics, such as the Landau Fermi liquid/quasi-particle picture and the connection between spin and statistics.

Our understanding of spontaneous symmetry-breaking and phase transitions has also been recently challenged by the discovery of topological insulators (TI) and topological superconductors (TSC). At the basis of these new states of matter, there is another “teamwork” between two fundamental degrees of freedom: the spin-orbit coupling (SOC). A rather unexplored area of the SOC physics is the case where the SOC cohabits with strong electronic correlation. In that case, unconventional physics is expected to appear. From experiments and theoretical studies, we know that charge and spin fluctuations originating from many-body effects of electronic correlation and relativistic effects from SOC play fundamental roles for various electronic properties. Analyzing specific examples and developing theories which are able to predict at least some of these mutual interchange effects will eventually lead us to a deeper understanding of the cooperative and competitive nature of these different degrees of freedom.

In this project, we plan to investigate the electronic correlations and band topology of specific classes of materials. One of these classes is, e.g. epitaxially grown 2D adatom systems on semiconductor surfaces. The enhanced electronic correlations from the reduced dimensionality has been observed in many adatom systems. Compared to their bulk phases, Coulomb repulsion between electrons becomes more pronounced when they are grown in fractions of one monolayer (ML) on semiconductor surfaces. If the electronic structure of these adatoms further displays a non-trivial band topology, the interplay of electron correlation and the band topology will govern the low-energy physics of the system, which is of prime interest to this project. In TIs, the bulk energy gap coexists with metallic edge/surface states. The bulk-gap opening mechanism can be rather general, e.g. it can be the spin-orbit coupling in TIs and the pairing in topological superconductors. As another important driving force leading to a charge gap, namely the electron-electron interaction, has not been fully explored hitherto. This is partly due to the fact that, when electronic interactions come into play, the energy scales get strongly renormalized. As a result, it becomes, in most cases, difficult to find an appropriate “single-particle” description within band-structure theory.

In this project, we will focus on four classes of target systems (labeled as T1 - T4):

- T1: heavy adatoms on semiconductor surfaces e.g. Pb/Si(111).

- T2: nontrivial edge states of 2D TIs on semiconductor surfaces, e.g. Bi/SiC(0001) and Stanene/SiC(0001).

- T3: bulk TIs with strong spin-orbit coupling, such as Iridates or SmB6.

- T4: Bismuth-Oxide and Tin-Telluride compounds.

We will address material-specific aspects, including the search for novel topological systems, from the combination of ab-initio methods and many-body approaches. The availability of these necessary and powerful theoretical methods and, especially, the prime interest of this project defines its special and distinct role in the whole SFB “ToCoTronics". The four target material systems are carefully chosen to be of interest to both theoretical and experimental groups inside this SFB. In particular, our experience with density-functional theory (DFT) calculations will provide important insights and valuable theoretical support to other projects. Furthermore, all materials in T1 - T4 are characterized by a reduced dimensionality and strong spin-orbit interactions. Therefore, the many-body calculations based on the results of the density-functional theory will further help to uncover the essential role of interactions in these systems, which will be also investigated by the experimental projects within this SFB initiative.

#### References

[C05.1] G. Li, P. Hoepfner , J. Schäfer, C. Blumenstein, S. Meyer, A. Bostwick, E. Rotenberg, R. Claessen, and W. Hanke, Magnetic order in a frustrated two-dimensional atom lattice at a semiconductor surface. Nat. Comm. 4, 1620 (2013)