# C05

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

#### Summary

The materials platform of SFB 1170 is broad, ranging from honeycomb monolayers made of heavy elements to oxides of late transition metals. The “leitmotiv” is large spin-orbit interaction in confined geometries and their combination with electronic correlation. As witnessed by its publication list, in the first funding period C05 has been playing the role of the backbone of materials’ investigations for the whole Collaborative Research Center, contributing realistic calculations to experimental/theory joint collaborations of particular breadth. The strong interconnection of the various activities within such a large but at the same time geographically localized SFB 1170 leads to an increase of the number of projects of this kind. Hence, the presence of a “nerve centre” for realistic electronic band structure calculations including spin-orbit and many-body correlations is essential. As in the first funding period, we are going to work hand in hand with most of the experimental groups involved. By no means is this going to be a mere a posteriori description of the outcome of the measurements. Our cross-linking ability of identifying directions based on both theory and experimental evidences, has already yielded a number of important results – like for example the synergy with A08 – and will doubtlessly continue to be fruitful in the second funding period too.

The topics that we are going to address can be grouped in four big areas: spin-orbit interaction and electronic correlations on the heavy side of the transition metals, quasi-freestanding Kane-Mele-like monolayers on substrates, realistic description of Landau levels for quantum oscillations in HgTe and heavy adatoms on Ag(111) and Au(111) as well as step edges in topological crystalline insulators (TCI). To the first category belongs our planned activity on the iridates, ruthenates and osmates, in cooperation with C08. This will become possible thanks to the huge effort made in the course of the first funding period, closely collaborating with project Z03. We have developed and published our code package “w2dynamics”, which allows now for an unbiased treatment of local many-body correlations and spin-orbit interaction. As we have analyzed in our joint publication, the thickness is a relevant parameter in the iridates, as it induces metal-to-insulator transition, structural as well as magnetic reconstructions and quantum confinement. In the second funding period we are going to make a step forward, namely to ruthenate/iridate heterostructures, at the moment under the spot for their possible relation to the topological Hall effect.

The dimensionality reduction is the common denominator that brings us to study topological phases down at the monolayer level. How can we sustain a tin honeycomb layer on a substrate that does not spoil its Kane-Mele-type of band inversion at the K-point? We gave an answer to this central ques- tion at the end of the first funding period and we will use the second one to make our prediction even more reliable and at the same time more easily realizable in the lab. Here, our experimental partners are the colleagues from project A08. Further, we are going to analyze the band structure of HgTe and of its quantum wells with state-of-the-art Density Functional Theory (DFT) approaches. The precise shape of the bands around the Γ point is important for the interpretation of the transport experiments done in A03 and A04. We pursue a realistic description of Landau levels that will be particularly valuable at high magnetic fields, where the corrections beyond k·p are sizeable. The simi- larities between the ultra-thin limit of HgTe (111) and heavy adatoms on noble metal surfaces (e.g. Ag or Au) inspired us, in conjunction with A01, to investigate alternative scenarios to engineer topological band inversions. Another exciting research line that C05 is going to explore is the interpretation of the one-dimensional mid-gap states found together with A02 on the surface of the TCI (Pb,Sn)Se as a hallmark of the dimensional hierarchy of topological states. Finally, the recent algorithmic develop- ments on w2dynamics will prove indispensable to investigate the effect of replacing tin with thulium, a metal close to the right end of the 4f -series. This fascinating route towards topological heavy-fermion compounds is experimentally realized within C06 and is going to play a special role in our C05.