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Abstract The quantum limit in a Fermi liquid, realized when a single Landau level is occupied in strong magnetic fields, gives rise to unconventional states, including the fractional quantum Hall effect and excitonic insulators. Stronger interactions in metals with nearly localizedf-electron degrees of freedom increase the likelihood of these unconventional states. However, access to the quantum limit is typically impeded by the tendency off-electrons to polarize in a strong magnetic field, consequently weakening the interactions. In this study, we propose that the quantum limit in such systems must be approached in reverse, starting from an insulating state at zero magnetic field. In this scenario, Landau levels fill in the reverse order compared to regular metals and are closely linked to a field-induced insulator-to-metal transition. We identify YbB₁₂as a prime candidate for observing this effect and propose the presence of an excitonic insulator state near this transition. 

Building on discoveries in graphene and two-dimensional (2D) transition metal dichalcogenides, van der Waals (VdW) layered heterostructures—stacks of such 2D materials—are being extensively explored with resulting new discoveries of novel electronic and magnetic properties in the ultrathin limit. Here, we review a class of naturally occurring heterostructures—the so-called misfits—that combine disparate VdW layers with complex stacking. Exhibiting remarkable structural complexity and diversity of phenomena, misfits provide a platform on which to systematically explore the energetics and local bonding constraints of heterostructures and how they can be used to engineer novel quantum fabrics, electronic responsiveness, and magnetic phenomena. Like traditional classes of layered materials, they are often exfoliatable and thus also incorporatable as units in manually or robotically stacked heterostructures. Here, we review the known classes of misfit structures, the tools for their single crystal and thin film synthesis, the physical properties they exhibit, and the computational and characterization tools available to unravel their complexity. Directions for future research are also discussed. 

Abstract While ∼30% of materials are reported to be topological, topological insulators are rare. Magnetic topological insulators (MTI) are even harder to find. Identifying crystallographic features that can host the coexistence of a topological insulating phase with magnetic order is vital for finding intrinsic MTI materials. Thus far, most materials that are investigated for the determination of an MTI are some combination of known topological insulators with a magnetic ion such as MnBi₂Te₄. Motivated by the recent success of EuIn₂As₂, the role of chemical pressure on topologically trivial insulator is investigated, Eu₅In₂Sb₆via Ga substitution. Eu₅Ga₂Sb₆is predicted to be topological but is synthetically difficult to stabilize. The intermediate compositions between Eu₅In₂Sb₆and Eu₅Ga₂Sb₆are observed through theoretical works to explore a topological phase transition and band inversion mechanism. The band inversion mechanism is attributed to changes in Eu–Sb hybridization as Ga is substituted for In due to chemical pressure. Eu₅In_4/3Ga_2/3Sb₆is also synthesized, the highest Ga concentration in Eu₅In_2‐xGa_xSb₆, and report the thermodynamic, magnetic, transport, and Hall properties. Overall, the work paints a picture of a possible MTI via band engineering and explains why Eu‐based Zintl compounds are suitable for the co‐existence of magnetism and topology.