Correlated phases of matter in Hopf insulators

• Applicant: Dr. Konstantinos Ladovrechis
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567023139

A recently proposed topological phase of matter beyond the tenfold-way paradigm is the Hopf insulator, which is a genuinely three-dimensional, time-reversal-broken, topological insulating phase characterized by a nontrivial third homotopy group of spheres. The existence of Hopf insulators has been linked to several novel ideas in topological band theory, exemplified by the notions of delicate topology, quantized dipolar charge and returning Thouless pump. On the experimental side, Hopf insulating phases have already been realized in circuit systems as well as in solid-state quantum simulators. Those attempts, however, are featuring Hopf insulators in the absence of interactions and disorder or, at least, in a parameter regime where these effects can be considered negligible. On the other hand, for topological insulators classified within the tenfold-way paradigm, it has long been established that the role of correlations has been fundamental in unraveling and exploring the richness of certain phenomenological aspects. Such past experience naturally poses the question for the fate of the Hopf insulators away from the clean and noninteracting limit. The aim of this project is to theoretically investigate the robustness of Hopf insulators against relevant perturbations. So far in the corresponding literature, little progress has been made in addressing the impact of interactions and disorder in static conditions. The importance of accounting for those effects is particularly transparent in the case of experimental realizations of the Hopf insulators. I shall hence begin the current project by studying both quantitatively and qualitatively the fate of the Hopf insulating phase in the presence of long-range Coulomb interaction at zero temperature. In order to maintain control over the interplay between the band topology and electronic correlations, the corresponding analysis is carried out in the vicinity of the topological quantum critical point (TQCP) separating a Hopf insulating phase from a trivial insulator. The next step is to enrich the predictability regarding the phase diagram around the TQCP by considering, on one hand, short- and long-range interactions in the time-reversal-symmetric analog of the Hopf insulator (’spin Hopf insulator’), and on the other hand, short-range disorder. The ever-growing accessibility of the Hopf insulating phases in the laboratory allows for direct experimental test of any potential prediction. Therefore, such a setting furnishes an ideal sandbox for the Hopf insulators problems I wish to solve subsequently in this project.

• DFG Programme: WBP Position