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Utilizing the realistic continuum description of twisted bilayer MoTe2 and many-body exact diagonalization calculation, we establish that the second moir\'e band of twisted bilayer MoTe2, at a small twist angle of approximately 2{\deg}, serves as an optimal platform for achieving the long-sought non-Abelian fractional quantum anomalous Hall states without the need for external magnetic fields. Across a wide parameter range, our exact diagonalization calculations reveal that the half-filled second moir\'e band demonstrates the ground state degeneracy and spectral flows, which are consistent with the pfaffian state in the first Landau level. We further elucidate that the emergence of the non-Abelian state is deeply connected to the remarkable similarity between the second moir\'e band and the first Landau level. Essentially, the band not only exhibits characteristics akin to the first Landau level, $\frac{1}{2\pi}\int_\mathrm{BZ}\mathrm{d}^2\mathbf{k}\:\mathrm{tr}\:\eta(\mathbf{k}) \approx 3$ where $\eta_{ab}(\mathbf{k})$ is the Fubini-Study metric of the band, but also that its projected Coulomb interaction closely mirrors the Haldane pseudopotentials of the first Landau level. Motivated from this observation, we introduce a novel metric of "first Landau level"-ness of a band, which quantitatively measures the alignment of the projected Coulomb interaction with the Haldane pseudopotentials in Landau levels. This metric is then compared with the global phase diagram of the half-filled second moir\'e band, revealing its utility in predicting the parameter region of the non-Abelian state. In addition, we uncover that the first and third moir\'e bands closely resemble the lowest and second Landau levels, revealing a remarkable sequential equivalence between the moir\'e bands and Landau levels. We finally discuss the potential implications on experiments., Comment: 4.5+5.5 pages, 4+9 figures

Imposing incommensurable periodicity on the periodic atomic lattice can lead to complex structural phases consisting of locally periodic structure bounded by topological defects. Twisted trilayer graphene (TTG) is an ideal material platform to study the interplay between different atomic periodicities, which can be tuned by twist angles between the layers, leading to moir\'e-of-moir\'e lattices. Interlayer and intralayer interactions between two interfaces in TTG transform this moir\'e-of-moir\'e lattice into an intricate network of domain structures at small twist angles, which can harbor exotic electronic behaviors. Here we report a complete structural phase diagram of TTG with atomic scale lattice reconstruction. Using transmission electron microscopy combined with a new interatomic potential simulation, we show that a cornucopia of large-scale moir\'e lattices, ranging from triangular, kagome, and a corner-shared hexagram-shaped domain pattern, are present. For small twist angles below 0.1{\deg}, all domains are bounded by a network of two-dimensional domain wall lattices. In particular, in the limit of small twist angles, the competition between interlayer stacking energy and the formation of discommensurate domain walls leads to unique spontaneous symmetry breaking structures with nematic orders, suggesting the pivotal role of long-range interactions across entire layers. The diverse tessellation of distinct domains, whose topological network can be tuned by the adjustment of the twist angles, establishes TTG as a platform for exploring the interplay between emerging quantum properties and controllable nontrivial lattices.

We study the magneto-optical Kerr effect (MOKE) of the two-dimensional heterostructure CrI3/In2Se3/CrI3 by using density functional theory calculations and symmetry analysis. The spontaneous polarization in the In2Se3 ferroelectric layer and the antiferromagnetic ordering in CrI3 layers break the mirror symmetry and the timereversal symmetry, thus activating MOKE. We show that the Kerr angle can be switched by either the polarization or the antiferromagnetic order parameter. Our results suggest that ferroelectric and antiferromagnetic 2D heterostructures could be exploited for ultra-compact information storage devices, where the information is encoded by the two ferroelectric or the two time-reversed antiferromagnetic states, and the read-out performed optically by MOKE.

Twisting in bilayers introduces structural chirality with two enantiomers, i.e., left- and right-hand bilayers, depending on the oriented twist angle. The interplay between this global chirality and additional degrees of freedom, such as magnetic ordering and the local octahedral chirality arising from the geometry of the bonds, can yield striking phenomena. In this work, we focus on collinear antiferromagnetic CrI$_3$ twisted homo-bilayers, which are characterized by a staggered octahedral chirality in each monolayer. Using symmetry analysis, density functional theory and tight-binding model calculations we show that layers twisting can lower the structural and magnetic point-group symmetries, thus activating pyroelectricity and the magneto-optical Kerr effect, which would otherwise be absent in untwisted antiferromagnetic homo-bilayers. Interestingly, both electric polarization and Kerr angle are controllable by the twist angle and their sign is reversed when switching from left- to right-twisted bilayers. We further unveil the occurrence of unconventional vortices with spin textures that alternate opposite chiralities in momentum space. These findings demonstrate that the interplay between twisting and octahedral chirality in magnetic bilayers and related van der Waals heterostructures represents an extraordinary resource for tailoring their physical properties for spintronic and optoelectronic applications., Comment: Accepted by PRB; 15 pages, 9 figures, and 4 tables in main text; 10 pages, 8 figures, and 1 table in supplemental material

Metal-organic frameworks (MOFs) possess a hybrid nature, combining the inorganic properties from the metal ions and the organic properties from the molecular linkers. Stroppa, \textit{et al.}, showed that the perovskite-type MOF [C(NH$_2$)$_3$]M[(HCOO)$_3$] (M = Cr, Cu) exhibits the magneto-electric coupled multiferroicity [Angew. Chem. Int. Ed. 50, 5847 (2011) and Adv. Mater. 25, 2284 (2013)]. Moreover, their ferroelectricity arises from the hybrid improper mechanism, which also explains the magneto-electric coupling. In this work, we further examine the electric and magnetic properties of [C(NH$_2$)$_3$]M[(HCOO)$_3$]. We find that the hybrid mode composed of non-polar modes induces purely electronic polarization even without the polar mode. The polar mode compensates for the purely electronic polarization. It leads to a counter-intuitive argument that the inversion of the polar mode rather enhances the polarization. We provide microscopic origin and macroscopic analysis for this polarization property. In addition, we find that the orbital magnetic moment is comparable to the spin contribution in the Cu-based MOF. Finally, we establish the model for the orbital magnetic moment based on the perturbation theory., Comment: 19 pages, 9 figures, An extended version by collaboration with experiments is under preparation

The interlayer van der Waals interaction in twisted bilayer graphene (tBLG) induces both in-plane and out-of-plane atomic displacements showing complex patterns that depend on the twist angle. In particular, for small twist angles, within each graphene layer, the relaxations give rise to a vortex-like displacement pattern which is known to affect the dispersion of the flat bands. Here, we focus on yet another structural property, the chirality of the twisted bilayer. We perform first-principles calculations based on density functional theory to investigate the properties induced by twist chirality in both real and momentum space. In real space, we study the interplay between twist chirality and atomic relaxation patterns. In momentum space, we investigate the spin textures around the $K$ points of the Brillouin zone, showing that alternating vortex-like textures are correlated with the chirality of tBLG. Interestingly, the helicity of each vortex is inverted by changing the chirality while the different twist angles also modify the spin textures. We discuss the origin of the spin textures by calculating the layer weights and using plot regression models., Comment: 12 pages and 7 figures in main text, 11 pages and 12 figures in supplemental material; revised according to referees' suggestions; Accepted in Phys. Rev. B