In a previous study, we had shown that nodal-line semimetals under inhomogeneous strain give rise to electronic bands that are flat along three independent spatial directions. Due to the flatness of the electronic bands in these materials, interaction effects are enhanced and correlated phases can emerge, such as superconductors or ferromagnets. The flat-band superconductivity arises due to a large geometric contribution to the superfluid weight. However, this study was restricted to clean systems without impurities, but in realistic materials disorder through impurities is unavoidable. To find out how robust flat-band superconductivity is in general, we studied the behavior of the superfluid weight in a topological flat-band model with non-magnetic disorder. In such a model, the superfluid weight is entirely geometrical in the clean limit due to large Berry curvature. Our calculations showed that the superfluid weight shows an unexpected universal decay independent of the quantum geometry and the band dispersion for a variety of models. Most importantly, we found that a flat band superconductor is as resilient to disorder as a conventional one. Our results imply that also the superfluidity in 3D flat bands is robust against the presence of non-magnetic impurities.
In search for new materials as a platform for 3D flat bands, we studied chalcogenide superlattices HgTe/CdTe and HgTe/HgSe. HgTe and HgSe are topological insulators in the bulk, while CdTe is a trivial insulator. We also investigated how the emerging phases could be tuned using hydrostatic pressure and uniaxial strain. We found that HgTe/CdTe superlattices realize isoenergetic nodal lines, which could host strain-induced 3D flat bands at the Fermi level without requiring doping. On the other hand, HgTe/HgSe superlattices feature a rich phase diagram as a function of strain and pressure. We found that they can harbor Weyl semimetal, Dirac semimetal, nodal-line, and topological-insulator phases.
We included a magnetic component into our superlattice setup by studying HgTe/MnTe, where MnTe is an antiferromagnetic insulator in the bulk. Our results show the evolution of the magnetic topological phases with respect to the different possible magnetic configurations in the MnTe layers. Most notably, we found the elusive axion insulator phase for out-of-plane antiferromagnetic order below a critical MnTe thickness. Such a phase gives rise to exotic electromagnetic properties typically dubbed axion electrodynamics. Switching the magnetic orientation into the plane, the superlattice realizes different antiferromagnetic topological insulators depending on the thickness of the MnTe layers. For ferromagnetic order, the system realizes a ferromagnetic Weyl semimetal. Interestingly, we also observed a large anomalous Hall conductivity in this case indicating the presence of large Berry curvature.
We further studied the 2D superlattice of bilayer graphene. In particular, minimally twisted bilayer graphene features 2D quasi-flat bands which lead to the emergence of various exotic correlated phases, such as superconductivity, through the enhancement of electronic interactions. These quasi-flat bands have a substructure and feature a number of so-called van-Hove singularities at which the density of states diverges. These singularities play an important role in the exotic phenomena observed in this material. To better understand how they influence the electronic properties, we studied the correspondence of the conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic, ballistic samples. We found a correspondence between features in the conductance and the presence of van Hove singularities. Moreover, we identified additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with non-singular band crossings, and unusually large conductance oscillations as a function of the system size. Our findings suggest that twisted bilayer graphene close the magic angle could be utilized in high-frequency device applications and sensitive detectors.
We further investigated topological phases in one-dimensional chalcogen superlattices. Specifically, we studied the topological properties of the helical atomic chains occurring in elemental selenium Se and tellurium Te, where the 1D chains are arranged in a 2D array. We derived a realistic model and showed that it realizes a crystalline topological insulator protected by a rotational symmetry.
The results of this project were communicated at various international conferences. Implications of the results were discussed with experts from theory and experiment. Most of the code used in this work was published Open Access on Zenodo following the FAIR principles. Furthermore, the results of the project were communicated in an accessible language to the broader public through social media on Twitter and LinkedIn. The basic physical concepts were further popularized in a number of blog posts on Medium, which were also promoted on Twitter and Facebook.
