# C07

## Topological states with d-electrons: the playground of oxide-heterostructures

#### Summary

In Project C07 we pursue a theoretical insight into the characterization and the fabrication of topological phases induced by electronic correlation. Despite the progress made in the investigation of topological insulators beyond the independent-electron picture valid for semiconductors, we still lack concrete realizations as well as clear and experimentally sensible ways to pinpoint genuine correlation effects in the formation of topological insulators. The focus will be on the correlation-induced quantum spin Hall (QSH) phase. The QSH effect has been predicted by Kane and Mele in graphene [1] and then observed in HgTe/CdTe heterostructures [2]. Bernevig, Hughes and Zhang have modeled it via an effective 4×4 Hamiltonian derived from the s- and p-electrons in the quantum well. This describes the topological phase transition to the QSH state when the thickness of the HgTe is increased beyond a critical value for which the gap in the band structure vanishes [3].

Yet, many-body mechanisms for inducing the QSH state can also be envisaged. The interest in studying them comes from the properties of the other correlation-driven phase transitions, such as the one between a topologically trivial band insulator and a Mott insulator [4] [5]. The Bloch nature of uncorrelated electrons and the localized properties of atomic-like interacting electrons compete in such a transition. These two opposing mechanisms give rise, respectively, to the band and the Mott gaps and, as a result, the transition between these two states is strongly of first order, with a thermodynamic instability associated to the orbital occupations and to the local spin degrees of freedom. In this project we want to see how this physics emerges in the correlation-driven transition from a topologically trivial to a non-trivial band insulator and eventually to the Mott insulator. The energy splitting between the relevant bands has therefore to be of atomic origin, e.g. local multiplets in materials with partially filled d- or f-shells, or it must come from the energy mismatch between two layers in a heterostructure. Inter-layer hopping processes or intrinsic spin-orbit coupling give then rise to a hybridization gap. In such a situation, the interplay between atomic Hund’s rule and kinetic energy effects directly influences occupations and orbital character and can drive the system into a topologically non-trivial phase. Recently, some proposals to induce the QSH by electronic correlation have been discussed in the context of oxide heterostructures [6] [7] [8]. Particularly promising seem to be heterostructures of Ni or other transition metal oxides, grown in the [111] direction, where a “particle-hole”-symmetric band structure naturally arises.

So far, no experimental realization has however been reported. The difficulty is twofold: on the one hand the candidate systems are either unavailable or not easy to grow. On the other hand, an experimental characterization of the fluctuation-induced QSH effect is far from being straightforward. The obvious way would be to use transport, as in HgTe/CdTe quantum wells. However, even imagining to have access to an experimental determination of the ℤ2 topological invariant in these materials, the key observation to discriminate whether or not the topological transition is actually driven by many-body effects would still be missing. In this project we are going to examine novel heterostructures of transition metal oxides, trying to find new candidates for the correlation-induced QSH effect. In this search we will closely collaborate and exchange ideas with Project C08, where new classes of interfaces will be experimentally investigated. Our aim is not only to add more and more promising heterostructures to the list of potential interaction-induced QSH systems, but also to give the experimental groups working in this new exciting direction, very clear and discernible signatures needed to claim that the transition mechanism is of many-body nature rather than the conventional one.

#### References

[1] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005), ibid. 95, 226801 (2005).

[2] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2007).

[3] B. A. Bernevig, T. L. Hughes and S.-C. Zhang, Science 314, 1757 (2006).

[4] M. Sentef, J. Kuneš, P. Werner and A. P. Kampf, Phys. Rev. B 80, 155116 (2009).

[5] P. Werner and A. J. Millis, Phys. Rev. Lett. 99, 126405 (2007).

[6] D. Xiao, W. Zhu, Y. Ran, N. Nagaosa and S. Okamoto, Nat. Comm. 2, 596 (2011).

[7] A. Rüegg, C. Mitra, A. A. Demkov and G. A. Fiete, Phys. Rev. B 88, 115146 (2013).

[8] S. Okamoto, W. Zhu, Y. Nomura, R. Arita, D. Xiao and N. Nagaosa, Phys. Rev. B 89, 195121 (2014).

[C07.1] J. C. Budich, B. Trauzettel and G. Sangiovanni, Fluctuation-driven topological Hund insulators, Phys. Rev. B 87, 235104 (2013).