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Abstract Lattice geometry continues providing exotic topological phases in condensed matter physics. Exciting recent examples are the higher-order topological phases, manifesting via localized lower-dimensional boundary states. Moreover, flat electronic bands with a non-trivial topology arise in various lattices and can hold a finite superfluid density, bounded by the Chern number C. Here we consider attractive interaction in the dice lattice that hosts flat bands with C = ± 2 and show that the induced superconducting state exhibits a second-order topological phase with mixed singlet-triplet pairing. The second-order nature of the topological superconducting phase is revealed by the zero-energy Majorana bound states at the lattice corners. Hence, the topology of the normal state dictates the nature of the Majorana localization. These findings suggest that flat bands with a higher Chern number provide feasible platforms for inducing higher-order topological superconductivity.

Abstract Searching for topological superconductors with non-Abelian states has been attracting broad interest. The most commonly used recipe for building topological superconductors utilizes the proximity effect, which significantly limits the working temperature. Here, we propose a mechanism to attain topological superconductivity via forward phonon scatterings. Our crucial observation is that electron-phonon interactions with small momentum transfers favor spin-triplet Cooper pairing under an applied magnetic field. This process facilitates the formation of chiral topological superconductivity even without Rashba spin-orbit coupling. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbit coupling, pairing symmetries, and the topological property of the superconducting state. This theory not only deepens our understanding of the superconductivity induced by the electron-phonon interaction but also sheds light on the critical role of the electron-phonon coupling in pursuing non-Abelian Majorana quasiparticles.

Flat bands are dispersionless electronic structures with increased electron–electron correlations and can coexist with the non-trivial topological features of a Kagome lattice. Here, the authors theoretically explore the interplay between band topology and electronic correlations in a multiorbital model on a Kagome lattice demonstrating that fractional filling can give rise to fractional Chern insulating states.

Majorana fermions are elusive particles which have proven extremely tricky to observe experimentally, with current efforts focused on hybrid superconducting devices. Here, the authors theoretically propose a set up combining a Josephson junction and a skyrmion crystal to create and control the Majorana bound states.

Understanding the spin-wave excitations of chiral magnetism is important to confirm such exotic magnetic order. Here, the authors obtain the spin wave spectrum for a given magnetic structure from Monte Carlo simulations and analyse the signatures when a ferromagnetic film undergoes a transition from a skyrmion crystal to a helical phase.