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Abstract The experimental discovery of fractional Chern insulators (FCIs) in moiré materials raises the question of whether their time-reversal invariant analogs, fractional topological insulators (FTIs), can also be realized in these platforms. We address this via exact diagonalization calculations in both a Landau level (LL) model and continuum model for twisted MoTe₂, and extract principles for engineering FTIs in realistic conditions. For the spinful LL model at filling$$\nu =\frac{1}{3}+\frac{1}{3}$$ $\nu =\frac{1}{3}+\frac{1}{3}$, we show that a suppression of the short-range component of the interaction is important to stabilize the FTI. For twisted MoTe₂at$$\nu =-\frac{4}{3}$$ $\nu =-\frac{4}{3}$, we find that a short-range attractiongon top of the screened Coulomb interaction is needed to realize an FTI. We discuss how this threshold value ofgcould be reduced by examining larger system sizes, incorporating band-mixing effects, exploiting Landau level character, and engineering the dielectric environment. While our study highlights the challenges, at least for the fillings considered, for obtaining FTIs, we also provide potential sample-engineering routes to improve the stability of FTI phases. 

The discovery of a charge density wave in FeGe extends the discussion of the nature of charge order in kagome metals to a magnetic compound. Motivated by this observation, we combine density functional theory (DFT) and functional-renormalization-group calculations to study interaction-induced Fermi-surface instabilities of the magnetic state of FeGe. We argue that the leading intra-band contribution to electronic correlations are approximately two-dimensional (2D) and come from Van Hove points at the projected $M$points. By varying parameters around DFT values, we determine a phase diagram for the quasi-2D scenario as function of on-site and nearest-neighbor interactions. We discuss universal aspects in the electronic mechanisms for the resulting phases, as well as the role of SU(2) symmetry breaking. We find FeGe to be in a regime of strong competition between $p$-wave charge density wave, $f$-wave pairing, and $d$-wave spin Pomeranchuk instabilities. This interplay can be influenced in favor of superconducting pairing for slightly increased nearest-neighbor interaction, suggesting a potential to induce superconductivity in FeGe. 

We conducted a high-throughput search for topological magnetic materials across 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. This brings up to date the previous studies. For each material, we performed first-principles electronic calculations and diagnosed the topology as a function of the HubbardUparameter. Our high-throughput calculation led us to the prediction of 250 experimentally relevant topologically nontrivial materials, which represent 47.89% of the newly analyzed materials. We present five remarkable examples of these materials, each showcasing a different topological phase: Mn₂AlB₂(BCSID 1.508), which exhibits a nodal line semimetal to topological insulator transition as a function of SOC; CaMnSi (BCSID 0.599), a narrow gap axion insulator; UAsS (BCSID 0.594), a 5f-orbital Weyl semimetal; CsMnF₄(BCSID 0.327), a material presenting a new type of quasi-symmetry protected closed nodal surface; and FeCr₂S₄(BCSID 0.613), a symmetry-enforced semimetal with double Weyls and spin-polarized surface states.