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We investigate the magnetic orders in a mixture of Boson (exciton) and Fermion (electron or hole) trapped in transition-metal dichalcogenides moir\'e superlattices. A sizable antiferromagnetic exchange interaction is found between a carrier and an interlayer exciton trapped at different high symmetry points of the moir\'e supercell. This interaction at a distance much shorter than the carrier-carrier separation dominates the magnetic order in the Bose-Fermi mixture, where the carrier sublattice develops ferromagnetism opposite to that in the exciton sublattice. We demonstrate the possibility of increasing the Curie temperature of moir\'e carriers through electrical tuning of the exciton density in the ground state. In a trilayer moir\'e system with a p-n-p type band alignment, the exciton-carrier interplay can establish a layered antiferromagnetism for holes confined in the two outer layers. We further reveal a spontaneous nematic order in the Bose-Fermi mixture, arising from the interference between the Coulomb interaction and p-wave interlayer tunneling dictated by the stacking registry., Comment: 6 pages, 4 figures

In the search of fractional quantum anomalous Hall (FQAH) effect, the conventional wisdom is to start from a flat Chern band isolated from the rest of the Hilbert space by band gaps, so that many-body interaction can be projected to a landscape that mimics a Landau level. Singular flat bands (SFB), which share protected touching points with other dispersive bands, represent another type of flat landscapes differing from Landau levels and Chern bands in topological and geometric properties. Here we report the finding of FQAH phases in a SFB, which emerges in the bipartite limit of the nearest-neighbor tight-binding model of twisted bilayer MoTe$_2$. At 1/3 and 2/3 filling of the SFB, FQAH effects are demonstrated using density matrix renormalisation group calculations with all bands, as well as exact diagonalization calculations with the two touching bands. Gapping the band touching can turn the SFB into a nearly flat Chern band, but counter-intuitively this suppresses the FQAH effect, as the gap opening introduces strong inhomogeneity to the quantum geometry. An optical scheme to realize such SFB for cold atoms is provided. Our findings uncover a new arena for the exploration of fractional quantum Hall physics beyond the Landau level and Chern insulator paradigms., Comment: Added discussions of singular flat bands, results of exact diagonalization, and updated mean-field results

We discover an intrinsic dipole Hall effect in a variety of magnetic insulating states at integer fillings of twisted MoTe$_2$ moir\'e superlattice, including topologically trivial and nontrivial ferro-, antiferro-, and ferri-magnetic configurations. The dipole Hall current, in linear response to in-plane electric field, generates an in-plane orbital magnetization $M_{\parallel}$ along the field, through which an AC field can drive magnetization oscillation up to THz range. Upon the continuous topological phase transitions from trivial to quantum anomalous Hall states in both ferromagnetic and antiferromagnetic configurations, the dipole Hall current and $M_{\parallel}$ have an abrupt sign change, enabling contact free detection of the transitions through the magnetic stray field. In configurations where the linear response is forbidden by symmetry, the dipole Hall current and $M_{\parallel}$ appear as a crossed nonlinear response to both in-plane and out-of-plane electric fields. These magnetoelectric phenomena showcase novel functionalities of insulators from the interplay between magnetism, topology and electrical polarization., Comment: 6 pages, 4 figures

The potential for low-threshold optical nonlinearity has received significant attention in the fields of photonics and conceptual optical neuron networks. Excitons in two-dimensional (2D) semiconductors are particularly promising in this regard as reduced screening and dimensional confinement foster their pronounced many-body interactions towards nonlinearity. However, experimental determination of the interactions remains ambiguous, as optical pumping in general creates a mixture of excitons and unbound carriers, where the impacts of band gap renormalization and carrier screening on exciton energy counteract each other. Here by comparing the influences on exciton ground and excited states energies in the photoluminescence spectroscopy of monolayer MoSe$_2$, we are able to identify separately the screening of Coulomb binding by the neutral excitons and by charge carriers. The energy difference between exciton ground state (A-1s) and excited state (A-2s) red-shifts by 5.5 meV when the neutral exciton density increases from 0 to $4\times 10^{11}$ cm$^{-2}$, in contrast to the blue shifts with the increase of either electron or hole density. This energy difference change is attributed to the mutual screening of Coulomb binding of neutral excitons, from which we extract an exciton polarizability of $\alpha_{2D}^{\rm exciton} = 2.55\times 10^{-17}$ eV(m/V)$^2$. Our finding uncovers a new mechanism that dominates the repulsive part of many-body interaction between neutral excitons.

In twisted MoTe$_{2}$, latest transport measurement has reported observation of quantum anomalous Hall effect at hole filling $\nu=-1$, which undergoes a topological phase transition to a trivial ferromagnet as layer hybridization gets suppressed by interlayer bias $D$. Here we show that this underlies the existence of an orbital Chern insulating state with gate ($D$) switchable sign in an antiferromagtic spin background at hole filling $\nu=-2$. From momentum-space Hartree Fock calculations, we find this state has a topological phase diagram complementary to that of the $\nu=-1$ one: by sweeping $D$ from negative to positive, the Chern number of this $\nu=-2$ state can be switched between $+1$, $0$, and $-1$, accompanied by a sign change of a sizable orbital magnetization. In range of $D$ where this antiferronagnet is the ground state, the orbital magnetization allows magnetic field initialization of the spin antiferromagnetic order and the Chern number., Comment: 6 pages, 4 figures

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.

Understanding quantum many-body systems is at the heart of condensed matter physics. The ability to control the underlying lattice geometry of a system, and thus its many-body interactions, would enable the realization of and transition between emergent quantum ground states. Here, we report in-situ gate switching between honeycomb and triangular lattice geometries of an electron many-body Hamiltonian in R-stacked MoTe2 moir\'e bilayers, resulting in switchable magnetic exchange interactions. At zero electric field, we observe a correlated ferromagnetic insulator near one hole per moir\'e unit cell ({\nu}=-1), i.e., a quarter-filled honeycomb lattice, with a widely tunable Curie temperature up to 14K. Fully polarizing layer pseudospin via electric field switches the system into a half-filled triangular lattice with antiferromagnetic interactions. Further doping this layer-polarized superlattice introduces carriers into the empty layer, tuning the antiferromagnetic exchange interaction back to ferromagnetic. Our work demonstrates R-stacked MoTe2 moir\'es to be a new laboratory for engineering correlated states with nontrivial topology., Comment: 13 pages, 4 figures, plus supplementary material

We thank G.P. Mikitik and Yu.V. Sharlai for contributing this note and the cordial exchange about it. First and foremost, we note that the aim of our paper is to report a methodology to diagnose topological (semi)metals using magnetic quantum oscillations. Thus far, such diagnosis has been based on the phase offset of quantum oscillations, which is extracted from a "Landau fan plot". A thorough analysis of the Onsager-Lifshitz-Roth quantization rules has shown that the famous $\pi$-phase shift can equally well arise from orbital- or spin magnetic moments in topologically trivial systems with strong spin-orbit coupling or small effective masses. Therefore, the "Landau fan plot" does not by itself constitute a proof of a topologically nontrivial Fermi surface. In the paper at hand, we report an improved analysis method that exploits the strong energy-dependence of the effective mass in linearly dispersing bands. This leads to a characteristic temperature dependence of the oscillation frequency which is a strong indicator of nontrivial topology, even for multi-band metals with complex Fermi surfaces. Three materials, Cd$_3$As$_2$, Bi$_2$O$_2$Se and LaRhIn$_5$ served as test cases for this method. Linear band dispersions were detected for Cd$_3$As$_2$, as well as the $F$ $\approx$ 7 T pocket in LaRhIn$_5$., Comment: Response to Matter arising for Nature Communications 12, 6213 (2021)

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications., Comment: Nat. Phys. (2022)

A Weyl semimetal with strong electron-phonon interaction can show axionic coupling in its insulator state at low temperatures, owing to the formation of a charge density wave (CDW). Such a CDW emerges in the linear chain compound Weyl semimetal Ta$_2$Se$_8$I below 263 K, resulting in the appearance of the dynamical condensed-matter axion quasiparticle. In this study, we demonstrate that the interchain coupling in Ta$_2$Se$_8$I can be varied to suppress the CDW formation with pressure, while retaining the Weyl semimetal phase at high temperatures. Above 17 GPa, the Weyl semimetal phase does not survive and we induce superconductivity, due to the amorphization of the iodine sub-lattice. Structurally, the one-dimensional Ta-Se-chains remain intact and provide a superconducting channel in one dimension. We highlight that our results show a near-complete suppression of the gap induced by the axionic charge-density wave at pressures inaccessible to previous studies. Including this CDW phase, our experiments and theoretical predictions and analysis reveal the complete topological phase diagram of Ta$_2$Se$_8$I and its relationship to the nearby superconducting state. The results demonstrate Ta$_2$Se$_8$I to be a distinctively versatile platform for exploring correlated topological states., Comment: 8 pages, 4 figures

It has recently been proposed that combining chirality with topological band theory may result in a totally new class of fermions. These particles have distinct properties: they appear at high symmetry points of the reciprocal lattice, they are connected by helicoidal surface Fermi arcs spanning the entire Brillouin zone, and they are expected to exist over a large energy range. Additionally, they are expected to give rise to totally new effects forbidden in other topological classes. Understanding how these unconventional quasiparticles propagate and interact is crucial for exploiting their potential in innovative chirality-driven device architectures. These aspects necessarily rely on the detection of handedness-dependent effects in the two enantiomers and remain largely unexplored so far. Here, we use scanning tunnelling microscopy to visualize the electronic properties of both enantiomers of the prototypical chiral topological semimetal PdGa at the atomic scale. We reveal that the surface-bulk connectivity goes beyond ensuring the existence of topological Fermi arcs, but also determines how quasiparticles propagate and scatter at impurities, giving rise to chiral quantum interference patterns of opposite handedness and opposite spiralling direction for the two different enantiomers, a direct manifestation of the change of sign of their Chern number. Additionally, we demonstrate that PdGa remains topologically non-trivial over a large energy range, experimentally detecting Fermi arcs in an energy window of more than 1.6 eV symmetrically centerd around the Fermi level. These results are rationalized in terms of the deep connection between chirality in real and reciprocal space in this class of materials, and they allow to identify PdGa as an ideal topological chiral semimetal.

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically non-trivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where $\pi$-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a $T^2$-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd$_3$As$_2$ and the multiband Dirac metal LaRhIn$_5$. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi$_2$O$_2$Se, no frequency shift associated to linear bands is observed as expected. However, the $\pi$-phase shift in Bi$_2$O$_2$Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.

Magnetic insulators are often antiferromagnetic (AFM) and layered AFM compounds usually show low ordering temperature. On the other hand, layered ferromagnetic (FM) insulators with high-TC are very rare although they could be quite useful for spintronic applications. Here, using crystal field level analysis in combination with density functional theory calculations as well as Monte Carlo simulations, we predict that the layered insulator Sr2NiRuO4 would have a strong FM coupling with TC as high as 240 K. The tetragonal crystal field in the Ni-O-Ru square plane stabilizes the S=1/2 Ni+ and S=3/2 Ru3+ states. The unique level ordering and occupation optimize the FM Ni-Ru superexchange interactions in the checkerboard arrangement, thus suggesting Sr2NiRuO4 as an unusual high-TC layered FM insulator. This work highlights the potential of charge-spin-orbital degrees of freedom for stabilizing strong FM coupling in layered oxides., Comment: 17 pages, 7 figures, 1 table