Universität zu Köln

Jayakumar, Vaishnavi (2025). Building blocks for cluster Mott insulators: from elementary models to potential realizations. PhD thesis, Universität zu Köln.

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Abstract

The Hubbard model is a paradigmatic model in condensed matter physics, which provides a rich playground for investigating the physics of a wide range of strongly correlated electronic systems. The core principle of the Hubbard model is the competition between Coulomb repulsions and hoppings. An important limit in the model is the Mott insulating regime, which is realized in the strong interaction limit. As a result, electrons get localized on single atomic sites at half-filling. In this thesis, we investigate extensions of this idea to cluster Mott insulators. These are special materials where electrons are now localized on clusters of sites. We use the theoretical framework that we develop to explore the physics of real cluster Mott materials. To that end, in a first study, we construct and study the cluster Hubbard model on a plethora of different clusters. We propose a new selection rule, called the cluster Hund's rule, which provides guidelines as to which states qualify as ground states in the pure interaction limit of the cluster Hubbard Hamiltonian. Using a combination of analytical insights and exact diagonalization, we conducted a comprehensive investigation of the emergent degrees of freedom in clusters of different geometries and fillings. This study helped us understand how these cluster Mott degrees of freedom respond to the interplay of strong correlations and hopping. In a second study, we investigated the cause of the observed magnetic signatures in $\mathrm{Ba_4LiIr_3O_{12}}$. This material hosts iridium dimers, and was expected to be non-magnetic since it possesses completely filled shells. Using insights from our previous study, we were able to detect non-trivial ground state degeneracies called non-Kramers doublets as the reason behind the observed magnetism of the material. Hence, we established $\mathrm{Ba_4LiIr_3O_{12}}$as the first cluster Mott material whose physics is driven by non-Kramers doublets. Having constructed this theoretical framework so far, we used it in our third study to investigate real materials which host trimer clusters – hexagonal perovskites of the form $\mathrm{A_4BM_3O_{12}}$, and considered different fillings of $3d$ to $5d$transition-metal “M” ions. Through a systematic treatment, we verified the observed magnetic moments for a wide variety of trimer materials. In addition, we also obtained the composition of magnetic moments in different directions. We use this study to propose ground state properties and phase diagrams for materials that are likely to be synthesized in the future.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Jayakumar, Vaishnavi vj@thp.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-783612
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Mott insulators UNSPECIFIED cluster Hubbard model UNSPECIFIED cluster materials UNSPECIFIED
Date of oral exam:	5 September 2024
Referee:	Name Academic Title Trebst, Simon Prof. Dr. Bulla, Ralf apl. Prof. Dr. Hickey, Ciarán Prof.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78361