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Metals with kagome lattice provide bulk materials to host both the flat-band and Dirac electronic dispersions. A new family of kagome metals is recently discovered in AV6Sn6. The Dirac electronic structures of this material need more experimental evidence to confirm. In the manuscript, we investigate this problem by resolving the quantum oscillations in both electrical transport and magnetization in ScV6Sn6. The revealed orbits are consistent with the electronic band structure models. Furthermore, the Berry phase of a dominating orbit is revealed to be around $\pi$, providing direct evidence for the topological band structure, which is consistent with calculations. Our results demonstrate a rich physics and shed light on the correlated topological ground state of this kagome metal., Comment: 5 figures, accepted version

Kagome materials with magnetic frustration in two-dimensional networks are known for their exotic properties, such as the anomalous Hall effect (AHE) with non-collinear spin textures. However, the effects of one-dimensional (1D) spin chains within these networks are less understood. Here, we report a distinctive AHE in the bilayer-distorted kagome material GdTi$_3$Bi$_4$, featuring 1D Gd zigzag spin chains, a one-third magnetization plateau, and two successive metamagnetic transitions. At these metamagnetic transitions, Hall resistivity shows abrupt jumps linked to the formation of stripe domain walls, while within the plateau, the absence of detectable domain walls suggests possible presence of skyrmion phase. Reducing the sample size to a few microns reveals additional Hall resistivity spikes, indicating domain wall skew scattering contributions. Magnetic atomistic spin dynamics simulations reveal that the magnetic textures at these transitions have reverse chirality, explaining the evolution of AHE and domain walls with fields. These results underscore the potential of magnetic and crystal symmetry interplay, and magnetic field-engineered spin chirality, for controlling domain walls and tuning transverse properties, advancing spintronic applications.

Two-dimensional (2D) moir\'e materials have emerged as a highly tunable platform for investigating novel quantum states of matter arising from strong electronic correlations and nontrivial band topology. Recently, topological flat bands formed in 2D semiconducting moir\'e superlattices have attracted great interests. In particular, a series of topological quantum phases, including the long-sought fractional quantum anomalous Hall (FQAH) effect, have recently been experimentally observed in twisted bilayer MoTe2 (tMoTe2). However, the microscopic information of tMoTe2 moir\'e superlattice and its electronic structure is still lacking. Here, we present scanning tunneling microscopy and spectroscopy (STM/STS) studies of the tMoTe2 moir\'e superlattice, with twist angles ranging from about 2.3{\deg} to 2.8{\deg}. We developed a contact-STM mode to apply pressure on tMoTe2 and observed a phase transition from band insulator to metal of tMoTe2 under pressure at the charge neutrality point. STM imaging reveals a pronounced in-plane lattice reconstruction with periodic strain redistribution in the tMoTe2, which serves as gauge fields for generating topological moir\'e bands. Importantly, the electronic states of the low-energy moir\'e flat bands primarily concentrate at the XM and MX regions as revealed by STS imaging. Such spatial distributions are nicely reproduced by our first principal calculations with a large-scale basis, suggesting the low-energy moir\'e flat bands are formed through the hybridization of K valley bands of the top layer and K' valley bands of the bottom layer. Overall, our findings provide compelling real-space evidence of electronic structure under pressure and topological flat bands of tMoTe2, paving the way for further STM/STS investigations of correlated topological states within the topological flat band in gate-tunable tMoTe2 devices.

Topological flat bands formed in two-dimensional lattice systems offer unique opportunity to study the fractional phases of matter in the absence of an external magnetic field. Celebrated examples include fractional quantum anomalous Hall (FQAH) effects and fractional topological insulators. Recently, FQAH effects have been experimentally realized in both the twisted bilayer MoTe2 (tMoTe2) system and the rhombohedral stacked multilayer graphene/hBN moir\'e systems. To date, experimental studies mainly focus on the first moir\'e flat band, except a very recent work that reported the evidence of the integer and fractional quantum spin Hall effects in higher moir\'e bands of a 2.1{\deg} tMoTe2 device. Here, we present the systematical transport study of approximately 3{\deg} tMoTe2 devices, especially for the second moir\'e band. At {\nu} = -2 and -4, time-reversal-symmetric single and double quantum spin Hall states formed, consistent with the previous observation in 2.1{\deg} tMoTe2 device. On the other hand, we observed ferromagnetism in the second moir\'e band, and a Chern insulator state driven by out-of-plane magnetic fields at {\nu} = -3. At {\nu} = -2.5, nonmonotonic temperature dependence of resistivity and large out-of-plane negative magnetoresistance have been observed, which likely arises from the frustrated liquid-like ground state and weak effective Ruderman-Kittel-Kasuya-Yosida interactions. Applying out-of-plane electric field can induce quantum phase transitions at both integer and fractional filling factors. Our studies pave the way for realizing tunable topological states and other unexpected magnetic phases beyond the first moir\'e flat band based on twisted MoTe2 platform.

Kagome metals are known to host Dirac fermions and saddle point Van Hove singularities near Fermi level. With the minimal two-pocket model (Dirac cone + Van Hove singularity), we propose a semiclassical theory to explain the experimentally observed sublinear resistivity in Ni$_3$In and other Kagome metals. We derive the full semiclassical description of kinetic phenomena using Boltzmann equation, and demonstrate that internode electron-electron interaction leads to sublinear in $T$ scaling for both electrical and thermal transport at low temperatures. At higher temperatures above the Dirac node chemical potential, thermal and electric current dissipate through distinct scattering channels, making a ground for Wiedemann-Franz law violation., Comment: 4.5 + 4 pages, 4 + 4 figures

Recent advances in manipulation of orbital angular momentum (OAM) within the paradigm of orbitronics present a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi$_2$Te$_4$ as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work we open up new possibilities for innovative applications in topological spintronics and orbitronics., Comment: 4 figures

We investigate the moir\'e band structures and possible even denominator fractional quantum Hall state in small angle twisted bilayer MoTe$_2$, using combined large-scale local basis density functional theory calculation and continuum model exact diagonalization. Via large-scale first principles calculations at $\theta=1.89^{\circ}$, we find a sequence of $C=1$(Chern number in K valley)moir\'e Chern bands, in analogy to Landau levels. By constructing the continuum model with multiple Chern bands, we undertake band-projected exact diagonalization using unscreened Coulomb repulsion to identify possible non-Abelian states near twist angle $\theta=1.89^{\circ}$ at the half filling of second moir\'e band., Comment: 5+4 pages, 4+6 figures. added results about PES,n(k),and many-body Chern number

Most of previously reported dark-bright solitons admit identical width for the two components in both theoretical and experimental studies. We report dark-bright solitons can admit strikingly different widths, and derive a family of analytical solutions for them by Lagrangian variational method. The existence regimes for these solitons become much more widespread in the space of nonlinear parameters, than the ones for the previously known dark-bright solitons with identical width. Our analysis indicates that the effective quantum wells are quite different in the two components, in sharp contrast to the ones for all previously known vector solitons. Especially, the particle number of bright soliton can be used to control the generation of dark-bright solitons with varied ratios of solitons' widths. Based on the current experimental technologies, we propose an experimental scheme for observing these novel dark-bright solitons. The results suggest that abundant vector solitons with difference widths exist in multi-components coupled systems, and would inspire experiments to observe them in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

The recently synthesized ternary quasi-2D material TaRhTe$_4$ is a bulk Weyl semimetal with an intrinsically layered structure, which poses the question how the topology of its electronic structure depends on layers separations. Experimentally these separations may be changed for instance by intercalation of the bulk, or by exfoliation to reach monolayer or few-layer structures. Here we show that in the monolayer limit a quantum spin Hall insulator (QSHI) state emerges, employing density functional calculations as well as a minimal four-orbital tight-binding model that we develop. Even for weak spin-orbit couplings the QSHI is present, which has an interesting edge state that features Rashba-split bands with quadratic band minima. Further we find that a weak topological insulator (WTI) manifests in the bilayer system due to sizable intralayer hopping, contrary to the common lore that only weak interlayer interactions between stacked QSHIs lead to WTIs. Stacked bilayers give rise to a phase diagram as function of the interlayer separation that comprises a Weyl semimetal, WTI and normal insulator phases. These insights on the evolution of topology with dimension can be transferred to the family of layered ternary transition metal tellurides., Comment: 22 pages, 14 figures

Large-scale moir\'e systems are extraordinarily sensitive, with even minute atomic shifts leading to significant changes in electronic structures. Here, we investigate the lattice relaxation effect on moir\'e band structures in twisted bilayer MoTe$_2$ with two approaches: (a) large-scale plane-wave basis first principle calculation down to $2.88^{\circ}$, (b) transfer learning structure relaxation + local-basis first principles calculation down to $1.1^{\circ}$. We use two types of van der Waals corrections: the D2 method of Grimme and the density-dependent energy correction, and find that the density-dependent energy correction yields a continuous evolution of bandwidth with twist angles. Based on the above results. we develop a more complete continuum model with a single set of parameters for a wide range of twist angles, and perform many-body simulations at $\nu=-1,-2/3, -1/3$., Comment: 6+15 pages, 5+16 figs, updated continuum model fitting, dDsC correction in maintext, D2 correction in the SM

Recent preprints claimed that the copper doped lead apatite Pb$_9$CuP$_6$O$_{25}$ (LK99) might be a high-temperature superconductor because of its strong diamagnetism and transport properties. Motivated by the strongly correlated effects that can arise from a triangular lattice of Cu atoms with narrow bandwidth, we calculated the maximally projected Wannier functions from density functional theory simulations, and constructed a minimal two-orbital triangular model with Cu ($3d_{xz},3d_{yz}$) basis, and a four-orbital buckled honeycomb model with Cu ($3d_{xz},3d_{yz}$), O ($2p_x,2p_y$). Since the Coulomb interaction Ud is much larger than potential energy difference between Cu and O, charge transfer will occur for hole filling fraction $n_h > 1$. We further calculate the interaction parameters, and discuss the possible insulating state and corresponding spin exchange coupling., Comment: 5+4 pages, 3+3 figures

Compounds with kagome lattice structure are known to exhibit Dirac cones, flat bands, and van Hove singularities, which host numerous versatile quantum phenomena. Inspired by these intriguing properties, we investigate the temperature and magnetic field dependent electrical transports along with the theoretical calculations of ScV6Sn6, a nonmagnetic charge density wave (CDW) compound. At low temperatures, the compound exhibits Shubnikov-de Haas quantum oscillations, which help to design the Fermi surface (FS) topology. This analysis reveals the existence of several small FSs in the Brillouin zone, combined with a large FS. Among them, the FS possessing Dirac band is a non-trivial and generates a non-zero Berry phase. In addition, the compound also shows the anomalous Hall-like behaviour up to the CDW with the CDW phase, ScV6Sn6 presents a unique material example of the versatile HfFe6Ge6 family and provides various promising opportunities to explore the series further., Comment: Published version, 19 Pages, 5 figures with supplementary

The interplay between ferroelectricity and band topology can give rise to a wide range of both fundamental and applied research. Here, we map out the emergence of nontrivial corner states in two-dimensional ferroelectrics, and remarkably demonstrate that ferroelectricity and corner states are coupled together by crystallographic symmetry to realize the electric control of higher-order topology. Implemented by density functional theory, we identify a series of experimentally synthesized two-dimensional ferroelectrics, such as In$_2$Se$_3$, BN bilayers, and SnS, as realistic material candidates for the proposed ferroelectric higher-order topological insulators. Our work not only sheds new light on traditional ferroelectric materials but also opens an avenue to bridge the higher-order topology and ferroelectricity that provides a nonvolatile handle to manipulate the topology in next-generation electronic devices.

We propose boundary obstructed topological phases caused by Wannier orbital shift between ordinary atomic sites, which, however, cannot be indicated by symmetry eigenvalues at high symmetry momenta (symmetry indicators) in bulk. On the open boundary, Wannier charge centers can shift to different atoms from those in bulk, leading to in-gap surface states, higher-order hinge states or corner states. To demonstrate such orbital-shift-induced boundary obstructed topological insulators, we predict eight material candidates, all of which were overlooked in present topological databases. Metallic surface states, hinge states, or corner states cover the large bulk energy gap (for example, more than 1 eV in TlGaTe$_2$) at related boundary, which are ready for experimental detection. Additionally, we find these materials are also fragile topological insulators with hourglass like surface states.

The discovery of quantum spin Hall effect has ignited the field of topological physics with vast variety of exotic properties. Here, we present the emergence of doubled quantum spin Hall effect in two dimensions characterized with a high spin Chern number of ${\mathcal C_S}=2$ and two pairs of helical edge states. Although is overlooked and invisible in topological quantum chemistry and symmetry indicator theory, the already experimentally synthesized $\alpha$-antimonene and $\alpha$-bismuthene are revealed as realistic material candidates of predicted topological states with band inversions emerging at generic $k$-points, rather than the high-symmetry momenta. Remarkably, the nontrivial energy gap can be as large as 464 meV for $\alpha$-bismuthene, indicating the high possibility of room-temperature observation of the doubled quantum spin Hall effect. Moreover, a four-band effective model is constructed to demonstrate further the feasibility of attaining this type of nontrivial topology. Our results not only uncover a novel topological character of antimony and bismuth, but will also facilitate the experimental characterization of the previously overlooked hidden topology., Comment: 4 figures

Nonsymmorphic symmetry can induce exotic wallpaper fermions, e.g., hourglass fermion, fourfold-degenerate Dirac fermion, and M\"obius fermion, as commonly believed only in nonsymmorphic wallpaper groups. Here, we extend the notion of wallpaper fermions to symmorphic wallpaper groups, and remarkably uncover the emergence of long-awaited third-order topological insulators. The symmetry analysis and k $\cdot$ p models reveal that nonessential symmetries play an essential role for obtaining the previously overlooked hidden surface spectrum. Based on this, we present the hourglass fermion, fourfold-degenerate Dirac fermion, and M\"obius fermion in the (001) surface of Tl$_4$XTe$_3$ (X = Pb/Sn) with a symmorphic wallpaper group $p4m$. Remarkably, 16 helical corner states reside on eight corners in Kramers pair, rendering the first real electronic material of third-order topological insulator. A time-reversal polarized octupole polarization is defined to uncover the nontrivial third-order topology, as is implemented by the 2$^{nd}$ and 3$^{rd}$ order Wilson loop calculations. Our results could considerably broaden the range of wallpaper fermions and lay the foundation for future experimental investigations of third-order topological insulators.

The intertwined ferroelectricity and band topology will enable the non-volatile control of the topological states, which is of importance for nanoelectrics with low energy costing and high response speed. Nonetheless, the principle to design the novel system is unclear and the feasible approach to achieve the coexistence of two parameter orders is absent. Here, we propose a general paradigm to design 2D ferroelectric topological insulators by sliding topological multilayers on the basis of first-principles calculations. Taking trilayer Bi2Te3 as a model system, we show that in the van der Waals multilayer based 2D topological insulators, the in-plane and out-of-plane ferroelectricity can be induced through a specific interlayer sliding, to enable the coexistence of ferroelectric and topological orders. The strong coupling of the order parameters renders the topological states sensitive to polarization flip, realizing non-volatile ferroelectric control of topological properties. The revealed design-guideline and ferroelectric-topological coupling not only are useful for the fundamental research of the coupled ferroelectric and topological physics in 2D lattices, but also enable novel applications in nanodevices.