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It was recently argued that Bernal stacked bilayer graphene (BLG) exposed to a two-dimensional superlattice (SL) potential exhibits a variety of intriguing behaviors [Ghorashi et al., Phys. Rev. Lett. 130, 196201 (2023)]. Chief among them is the appearance of flat Chern bands that are favorable to the appearance of fractional Chern insulator states. Here, we explore the application of spatially periodic out-of-plane orbital magnetic fields to the model of Ghorashi et al. to find additional means of inducing flat Chern bands. We focus on fields that vary on length scales much larger than the atomic spacing in BLG, generating what we refer to as magnetic SLs. The magnetic SLs we investigate either introduce no net magnetic flux to the SL unit cell or a single quantum of flux. We find that magnetic SLs acting on their own can induce topological flat bands, but richer behavior, such as the appearance of flat and generic bands with high Chern numbers, can be observed when the magnetic SLs act in conjunction with commensurate electric SLs. Finally, we propose a method of generating unit-flux-quantum magnetic SLs along with concomitant electric SLs. The magnetic SL is generated by periodic arrays of flux vortices originating from type II superconductors, while the electric SL arises due to a magnetic SL-induced charge density on the surface of a magnetoelectric material. Tuning the vortex lattice and the magnetoelectric coupling permits control of both SLs, and we study their effects on the band structure of BLG. 

One of the most striking signatures of Weyl fermions in solid-state systems is their surface Fermi arcs. Fermi arcs can also be localized at internal twin boundaries where two Weyl materials of opposite chirality meet. In this work, we derive constraints on the topology and connectivity of these “internal Fermi arcs.” We show that internal Fermi arcs can exhibit transport signatures, and we propose two probes: quantum oscillations and a quantized chiral magnetic current. We propose merohedrally twinned B20 materials as candidates to host internal Fermi arcs, verified through both model and calculations. Our theoretical investigation sheds light on the topological features and motivates experimental studies on the intriguing physics of internal Fermi arcs. 

Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in d-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz. d-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond.