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In flat-band materials, the strong Coulomb interaction between electrons can lead to exotic physical phenomena. Recently, $\alpha$-In$_2$Se$_3$ thin films were found to possess ferroelectricity and flat bands. In this work, using first-principles calculations, we find that for the monolayer, there is a Weyl point at $\Gamma$ in the flat band, where the inclusion of the spin-orbit coupling opens a gap. Shifting the Fermi level into the spin-orbit gap gives rise to nontrivial band topology, which is preserved for the bilayer regardless of the interlayer polarization couplings. We further calculate the Chern number and edge states for both the monolayer and bilayer, for which the results suggest that they become quantum anomalous Hall insulators under appropriate dopings. Moreover, we find that the doping-induced magnetism for In$_2$Se$_3$ bilayer is strongly dependent on the interlayer polarization coupling. Therefore, doping the flat bands in In$_2$Se$_3$ bilayer can also yield multiferroicity, where the magnetism is electrically tunable as the system transforms between different polarization states. Our study thus reveals that multiferroicity and nontrivial band topology can be unified into one material for designing multifunctional electronic devices., Comment: 6 pages, 4 figures

In order to study the novel gas detection or sensing applications of gallium nitride monolayer (GaN-ML), we mainly focused on the structural, energetic, electronic and magnetic properties of toxic gas molecules (CO, NO) adsorbed on pristine, single vacancy (N-vacancy, Ga-vacancy) defected, and metals (Al, Fe, Pd and Pt) doped GaN-ML using density functional theory (DFT-D2 method) in this work. The calculations demonstrate that pristine GaN-ML is extremely insensitive to CO and NO together with the existence of a weak physisorption nature due to small adsorption energy, charge transfer, and long adsorption distance. It is found that both N-vacancy defected GaN-ML and Fe-doped GaN-ML can significantly increase the adsorption energy and charge transfer for CO. The CO adsorption induces the metallic characteristics of N-vacancy GaN-ML to be converted to the half-metallic characteristics together with 100% spin polarization, and it also drastically changes the magnetic moment, implying that N-vacancy GaN-ML exhibits excellent sensitivity to CO. However, Fe-doped GaN-ML is not conducive to CO detection. Moreover, N-vacancy defected and Pt-doped GaN-ML greatly improve the adsorption ability for NO compared to other substrates, and the presence of stronger orbital hybridization suggests that the interaction between them is chemisorption. Therefore, N-vacancy defected GaN-ML and Pt-doped GaN-ML can serve as potential materials in future NO sensing devices., Comment: 24 pages, 2 tables, 8 figures

Unconventional topological quasiparticles have recently garnered significant attention in the realm of condensed matter physics. Here, based on first-principles calculations and symmetry analysis, we reveal the coexistence of multiple types of interesting unconventional topological quasiparticles in the phonon spectrum of the chiral crystal CsBe$_2$F$_5$. Specifically, we identified eight entangled phonon bands in CsBe$_2$F$_5$, which give rise to various unconventional topological quasiparticles, including the spin-1 Weyl point, the charge-2 Dirac point, the nodal surface, and the hourglass nodal loop. We demonstrate that these unconventional topological quasiparticles are protected by crystal symmetry. We show that there are two large Fermi arcs connecting projections of the bulk spin-1 Weyl point and charge-2 Dirac point on the (001) surface and across the entire surface Brillouin zone. Our work not only elucidates the intriguing topological properties of chiral crystals but also provides an excellent material platform for exploring the fascinating physics associated with multiple types of unconventional topological quasiparticles., Comment: 5 pages, 4 figures

Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band complex. We show that in principle a band complex can have no finite upper bound for certain space groups. It means infinitely many bands can entangle together, forming a connected pattern stable against symmetry-preserving perturbations. This is demonstrated by our developed inductive construction procedure, through which a given band complex can always be grown into a larger one by gluing a basic building block to it. As a by-product, we demonstrate the existence of arbitrarily large accordion type band structures containing $N_C=4n$ bands, with $n\in\mathbb{N}$., Comment: 6 pages, 4 figures

Recent experiments have demonstrated interesting physics in a family of two-dimensional (2D) composition-tunable materials Nb$_{2n+1}$Si$_n$Te$_{4n+2}$. Here, we show that owing to its intrinsic low symmetry, metallic nature, tunable composition, and ambient stability, these materials offer a good platform for studying Berry curvature dipole (BCD) and nonlinear Hall effect. Using first-principles calculations, we find that BCD exhibits pronounced peaks in monolayer Nb$_{3}$SiTe$_{6}$ ($n=1$ case). Its magnitude decreases monotonically with $n$ and completely vanishes in the $n\rightarrow\infty$ limit. This variation manifests a special hidden dimensional crossover of the low-energy electronic states in this system. The resulting nonlinear Hall response from BCD in these materials is discussed. Our work reveals pronounced geometric quantities and nonlinear transport physics in Nb$_{2n+1}$Si$_n$Te$_{4n+2}$ family materials, which should be readily detected in experiment., Comment: 8 pages, 7 figures and 1 table

The hourglass fermions in solid-state materials have been attracting significant interest recently. However, realistic two-dimensional (2D) materials with hourglass-shaped band structures are still very scarce. Here, through the first-principles calculations, we identify the monolayer Pb(ClO$_{2}$)$_{2}$ and Sr(ClO$_{2}$)$_{2}$ materials as the new realistic materials platform to realize 2D hourglass Weyl nodal loop. We show that these monolayer materials possess an hourglass Weyl nodal loop circling around the $\Gamma$ point and Weyl nodal line on the Brillouin zone (BZ) boundary in the absence of spin-orbit coupling (SOC). Through the symmetry analysis, we demonstrate that the hourglass Weyl nodal loop and Weyl nodal line are protected by the nonsymmorphic symmetries, and are robust under the biaxial strains. When we include the SOC, a tiny gap will be opened in the hourglass nodal loop and nodal line, and the nodal line can be transformed into the spin-orbit Dirac points. Our results provide a new realistic material platform for studying the intriguing physics associated with the 2D hourglass Weyl nodal loop and spin-orbit Dirac points., Comment: 10 pages, 7 figures, Accepted for publication in New Journal of Physics

Extensive investigations on topological phase transition (TPT) in three-dimensional compounds have been done. whereas, rare in two-dimensional systems, let alone noncentrosymmetric materials. In this work, based on first-principles calculations, we explore an inversion symmetry broken structural ReC2H monolayer. We reveal that it undergoes two TPTs, namely from normal insulator to Z2 topological insulator and back to normal insulator, at the critical biaxial strain of 2.3% and 7.8%, respectively. The band inversion occurs at the generic momentum in the first TPT, while at high symmetric K point in the second one. Usually, band inversion is identified by the exchange in the components or irreducible representations of the wavefunctions. These quantities can be easily obtained in theoretical calculation but hard to be detected in experimental techniques like Angle-resolved photoemission spectroscopy. It is well known that nonlinear optical (NLO) response is very sensitive to the components and symmetries of the engaged bands, which also incorporates information of band topology. Therefore, we study the shift current, one of the widely explored NLO responses in noncentrosymmetric systems, during the two TPTs. We find that in both cases band inversion leads to the sign change of shift vectors around the momenta where the bandgap closes and reopens. Whereas the shift current, as the overall contribution of shift vectors weighted by the absorption rate in the whole Brillouin zone, may keep its direction. This work offers insight that a scrutinized examination is highly demanded in utilizing shift current to detect TPT.

Graphene quantum dots (GQDs) not only have potential applications on spin qubit,but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron-electron (e-e) interaction. The tip induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimentional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes., Comment: https://rdcu.be/cBFYq

Chiral phonons were initially proposed and further verified experimentally in two-dimensional (2D) hexagonal crystal lattices. Many intriguing features brought about by chiral phonons are attributed to the pseudo-angular momenta which are associated with the threefold rotational symmetry of hexagonal lattices. Here, we go beyond the hexagonal crystals and investigate the chiral phonons in systems with fourfold rotational symmetry. We clarify the symmetry requirements for the emergence of chiral phonons in both 2D square lattices and 3D tetragonal lattices. For 2D, the realization of $C_4$ chiral phonons requires the breaking of time-reversal symmetry; while for 3D, they can exist on the $C_4$-invariant path in a chiral tetragonal lattice. These phonons have the advantage that they can be more readily coupled with optical transitions, which facilitates their experimental detection. We demonstrate our idea via model analysis and first-principles calculations of concrete materials, including the MnAs monolayer and the $\alpha$-cristobalite. Our work reveals chiral phonons beyond the hexagonal lattices and paves the way for further exploration of chiral phonon physics in square/tetragonal materials and metamaterials., Comment: 8 pages, 6 figures

A variety of exotic quantum phases of matter have been created by Van der Waals heterostructures. Moreover, these twisted heterostructures provide a feasible way of braiding correlation effect and nontrivial band topology together. Here, through a comprehensive spectrum study, we report the discovery of topological torus lattice in twisted mono-bilayer graphene. The strong Coulomb correlations give rise to an unusual charge localization behavior within the moir\'e supercell, leading to an electron crystal. The nontrivial band topology is encoded into the electron crystal, which would result in spatial modulated Chern numbers, and is evidenced by an emergent topological torus lattice state. Our result illustrates an efficient strategy for entwining and engineering topological physics with a strong electron correlation.

Electronic correlations could have significant impact on the material properties. They are typically pronounced for localized orbitals and enhanced in low-dimensional systems, so two-dimensional (2D) transition metal compounds could be a good platform to study their effects. Recently, a new class of 2D transition metal compounds, the MoSi$_2$N$_4$-family materials, have been discovered, and some of them exhibit intrinsic magnetism. Here, taking monolayer VSi$_{2}$P$_{4}$ as an example from the family, we investigate the impact of correlation effects on its physical properties, based on the first-principles calculations. We find that different correlation strength can drive the system into a variety of interesting ground states, with rich magnetic, topological and valley features. With increasing correlation strength, while the system favors a ferromagnetic semiconductor state for most cases, the magnetic anisotropy and the band gap type undergo multiple transitions, and in the process, the band edges can form single, two or three valleys for electrons or holes. Remarkably, there is a quantum anomalous Hall (QAH) insulator phase, which has a unit Chern number. The boundary of the QAH phase correspond to the half-valley semimetal state with fully valley polarized bulk carriers. We further show that for phases with the out-of-plane magnetic anisotropy, the interplay between spin-orbit coupling and orbital character of valleys enable an intrinsic valley polarization for electrons but not for holes. This electron valley polarization can be switched by reversing the magnetization direction, providing a new route of magnetic control of valleytronics. Our result sheds light on the possible role of correlation effects in the 2D transition metal compounds, and it will open new perspectives for spintronic, valleytronic and topological nanoelectronic applications based on these materials., Comment: 8 pages, 8 figures

In a recent work, new two-dimensional materials, the monolayer MoSi$_{2}$N$_{4}$ and WSi$_{2}$N$_{4}$, have been successfully synthesized in experiment, and several other monolayer materials with the similar structure, such as MoSi$_{2}$As$_{4}$, have been predicted [{\color{blue}Science 369, 670-674 (2020)}]. Here, based on first-principles calculations and theoretical analysis, we investigate the electronic and optical properties of monolayer MoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and MoSi$_{2}$As$_{4}$. We show that these materials are semiconductors, with a pair of Dirac-type valleys located at the corners of the hexagonal Brillouin zone. Due to the broken inversion symmetry and the effect of spin-orbit coupling, the valley fermions manifest spin-valley coupling, valley-contrasting Berry curvature, and valley-selective optical circular dichroism. We also construct the low-energy effective model for the valleys, calculate the spin Hall conductivity and the permittivity, and investigate the strain effect on the band structure. Our result reveals interesting valley physics in monolayer MoSi$_{2}$N$_{4}$, WSi$_{2}$N$_{4}$ and MoSi$_{2}$As$_{4}$, suggesting their great potential for valleytronics and spintronics applications., Comment: 10 pages,10 figures

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle {\theta}c. Experimentally, the {\theta}c is demonstrated to be very close to the magic angle ({\theta} ~ 1.05{\deg}). In this work, we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunnelling microscopy (STM). Our experiment demonstrates that both the two structures are stable in the TBG around the magic angle. By applying a STM tip pulse, we show that the two structures can be switched to each other and the bandwidth of the flat bands, which plays a vital role in the emergent strongly correlated states in the magic-angle TBG, can be tuned. The observed tunable lattice reconstruction and bandwidth of the flat bands provide an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle., Comment: 4 figures in main text

Layered materials with robust magnetic ordering have been attracting significant research interest. In recent experiments, a new layered material 1$T$-CrTe$_{2}$ has been synthesized and exhibits ferromagnetism above the room temperature. Here, based on first-principles calculations, we investigate the electronic, magnetic, and transport properties of 1$T$-CrTe$_{2}$, both in the bulk and in the two-dimensional (2D) limit. We show that 1$T$-CrTe$_{2}$ can be stable in the monolayer form, and has a low exfoliation energy. The monolayer structure is an intrinsic ferromagnetic metal, which maintains a high Curie temperature above the room temperature. Particularly, we reveal interesting features in the anomalous Hall transport. We show that in the ground state, both bulk and monolayer 1$T$-CrTe$_{2}$ possess vanishing anomalous Hall effect, because the magnetization preserves one vertical mirror symmetry. The anomalous Hall conductivity can be made sizable by tuning the magnetization direction or by uniaxial strains that break the mirror symmetry. The room-temperature 2D ferromagnetism and the tunable anomalous Hall effect make the material a promising platform for nanoscale device applications., Comment: 8 pages, 9 figures

We predict a new family of two-dimensional (2D) rare earth monochalcogenide materials MX (M = Sc, Y; X = S, Se, Te). Based on first-principles calculations, we confirm their stability and systematically investigate their mechanical properties. We find that these materials are metallic and interestingly, they possess nodal lines in the low-energy band structure surrounding the whole Brillouin zone, protected by nonsymmorphic crystal symmetries in the absence of spin-orbit coupling (SOC). SOC opens small energy gaps at the nodal line, except for two high-symmetry points, at which fourfold degenerate 2D spin-orbit Dirac points are obtained. We show that these topological band features are robust under uniaxial and biaxial strains, but can be lifted by the shear strain. We also investigate the optical conductivities of these materials, and show that the transformation of the band structure under strain can be inferred from the optical absorption spectrum. Our work reveals a new family of 2D topological metal materials with interesting mechanical and electronic properties, which will facilitate the study of nonsymmorphic symmetry enabled nodal features in 2D., Comment: 15 pages, 4 figures

Topological metals (TMs) are a kind of special metallic materials, which feature nontrivial band crossings near the Fermi energy, giving rise to peculiar quasiparticle excitations. TMs can be classified based on the characteristics of these band crossings. For example, according to the dimensionality of the crossing, TMs can be classified into nodal-point, nodal-line, and nodal-surface metals. Another important property is the type of dispersion. According to degree of the tilt of the local dispersion around the crossing, we have type-I and type-II dispersions. This leads to significant distinctions in the physical properties of the materials, owing to their contrasting Fermi surface topologies. In this article, we briefly review the recent advances in this research direction, focusing on the concepts, the physical properties, and the material realizations of the type-II nodal-point and nodal-line TMs., Comment: 12 pages, 16 figures

In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially fill the zero-energy flat band, we observe a correlation-induced gap of about 10 meV that splits the flat band. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the emergence of large orbital magnetic moments in the TBG when valley degeneracy of the flat band is lifted by electron-electron interactions. The orbital magnetic moment per moire supercell is measured as about 15 uB in the TBG.

Inherent symmetries of a system lead to multiple degeneracies of its energy spectra. Introducing individual atomic impurities can locally break these symmetries, which is expected to lift the degenerate degrees of freedom around the impurities. Although central to our understanding of the fundamental properties of solids, the broken-symmetry states induced by individual atomic impurities have so far eluded observation. Here, we report nanoscale probing of the broken-symmetry states in graphene induced by two types of individual atomic impurities, i.e., isolated nitrogen dopants and isolated hydrogen atoms chemisorbed on graphene. Our experiments demonstrate that both types of atomic impurities can locally break sublattice symmetry of graphene and generate valley-polarized states, which extends several nanometers around the impurities. For the isolated hydrogen atom chemisorbed on graphene, the enhanced spin-orbit coupling, which arises from the sp3 distortion of graphene due to the hydrogen chemisorption, further lifts the spin degeneracy, resulting in a fully spin and valley polarized states within about 1 nm around the hydrogen atom. Our result paves the way to control various broken-symmetry states at the nanoscale by various atomic impurities.

A remarkable property of twisted bilayer graphene (TBG) with small twist angle is the presence of a well-defined and conserved low-energy valley degrees of freedom1, which can potentially bring about new types of valley-associated spontaneous-symmetry breaking phases. Electron-electron (e-e) interactions in the TBG near the magic angle 1.1 degree can lift the valley degeneracy, allowing for the realization of orbital magnetism and topological phases2-11. However, direct measurement of the orbital-based magnetism in the TBG is still lacking up to now. Here we report evidence for orbital magnetic moment generated by the moire-scale current loops in a TBG with a twist angle {\theta} ~ 1.68 degree. The valley degeneracy of the 1.68 degree TBG is removed by e-e interactions when its low-energy van Hove singularity (VHS) is nearly half filled. A large and linear response of the valley splitting to magnetic fields is observed, attributing to coupling to the large orbital magnetic moment induced by chiral current loops circulating in the moire pattern. According to our experiment, the orbital magnetic moment is about 10.7 uB per moire supercell. Our result paves the way to explore magnetism that is purely orbital in slightly twisted graphene system., Comment: 4 figures in main text

2D materials with nontrivial energy bands are highly desirable for exploring various topological phases of matter, as low dimensionality opens unprecedented opportunities for manipulating the quantum states. Here, it is reported that monolayer (ML) dialkali-metal monoxides, in the well-known 2H-MoS$_2$ type lattice, host multiple symmetry-protected topological phases with emergent fermions, which can be effectively tuned by strain engineering. Based on first-principles calculations, it is found that in the equilibrium state, ML Na$_2$O is a 2D double Weyl semimetal, while ML K$_2$O is a 2D pseudospin-1 metal. These exotic topological states exhibit a range of fascinating effects, including universal optical absorbance, super Klein tunneling, and super collimation effect. By introducing biaxial or uniaxial strain, a series of quantum phase transitions between 2D double Weyl semimetal, 2D Dirac semimetal, 2D pseudospin-1 metal, and semiconductor phases can be realized. The results suggest monolayer dialkali-metal monoxides as a promising platform to explore fascinating physical phenomena associated with novel 2D emergent fermions., Comment: 7 pages, 4 figures

In the magic-angle twisted bilayer graphene (MA-TBG), strong electron-electron (e-e) correlations caused by the band-flattening lead to many exotic quantum phases such as superconductivity, correlated insulator, ferromagnetism, and quantum anomalous Hall effects, when its low-energy van Hove singularities (VHSs) are partially filled. Here our high-resolution scanning tunneling microscope and spectroscopy measurements demonstrate that the e-e correlation in a non-magic-angle TBG with a twist angle {\theta} = 1.49 still plays an important role in determining its electronic properties. Our most interesting observation on that sample is that when one of its VHS is partially filled, the one associated peak in the spectrum splits into four peaks. Our analysis based on the continuum model suggests that such a one-to-four split of the VHS originates from the formation of an interaction-driven spin-valley-polarized metallic state near the VHS, lifting both the spin and valley degeneracies. Our results for this non-magic-angle TBG reveal a new symmetry-breaking phase, which has not been identified in the MA-TBG or in other systems.

Photoluminescence (PL) from excitons serves as a powerful tool to characterize the optoelectronic property and band structure of semiconductors, especially for atomically thin 2D transition metal chalcogenide (TMD) materials. However, PL quenches quickly when the thickness of TMD material increases from monolayer to few-layers, due to the change from direct to indirect band transition. Here we show that PL can be recovered by engineering multilayer heterostructures, with the band transition reserved to be direct type. We report emission from layer engineered interlayer excitons from these multilayer heterostructures. Moreover, as desired for valleytronic devices, the lifetime, valley polarization, and the valley lifetime of the generated interlayer excitons can all be significantly improved as compared with that in the monolayer-monolayer heterostructure. Our results pave the way for controlling the properties of interlayer excitons by layer engineering., Comment: 5 Figures in main text

Dirac point in two-dimensional (2D) materials has been a fascinating subject of research. Recently, it has been theoretically predicted that Dirac point may also be stabilized in 2D magnetic systems. However, it remains a challenge to identify concrete 2D materials which host such magnetic Dirac point. Here, based on first-principles calculations and theoretical analysis, we propose a stable 2D material, the monolayers TaCoTe$_2$, as an antiferromagnetic (AFM) 2D Dirac material. We show that it has an AFM ground state with an out-of-plane N\'{e}el vector. It hosts a pair of 2D AFM Dirac points on the Fermi level in the absence of spin-orbit coupling (SOC). When the SOC is considered, a small gap is opened at the original Dirac points. Meanwhile, another pair of Dirac points appear on the Brillouin zone boundary below the Fermi level, which are robust under SOC and have a type-II dispersion. Such a type-II AFM Dirac point has not been observed before. We further show that the location of this Dirac point as well as its dispersion type can be controlled by tuning the N\'{e}el vector orientation., Comment: 8 pages, 8 figures

Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2pi continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.

Exotic properties in single or few layers of van der Waals materials carry great promise for applications in nanoscaled electronics, optoelectronics and flexible devices. The established, distinct examples include extremely high mobility and superior thermal conductivity in graphene, a large direct band gap in monolayer MoS2 and quantum spin Hall effect in WTe2 monolayer, etc. All these exotic properties arise from the electron quantum confinement effect in the two-dimensional limit. Here we report a novel phenomenon due to one-dimensional (1D) confinement of carriers in a layered van der Waals material NbSi0.45Te2 revealed by angle-resolved photoemission spectroscopy, i.e. directional massless Dirac fermions. The 1D behavior of the carriers is directly related to a stripe-like structural modulation with the long-range translational symmetry only along the stripe direction, as perceived by scanning tunneling microscopy experiment. The four-fold degenerated node of 1D Dirac dispersion is essential and independent on band inversion, because of the protection by nonsymmorphic symmetry of the stripe structure. Our study not only provides a playground for investigating the striking properties of the essential directional massless Dirac fermions, but also introduces a unique monomer with 1D long-range order for engineering nano-electronic devices based on heterostructures of layered van der Waals materials., Comment: A revised version published in Nature Materials (2019); 20 pages, 4 figures

Using low-temperature high-magnetic-field scanning tunneling microscopy and spectroscopy (STM/STS), we systematically study a graphene quantum dot (GQD) defined by a circular graphene p-p junction. Inside the GQD, we observe a series of quasi-bound states arising from whispering-gallery-mode (WGM) confinement of the circular junction and directly visualize these quasi-bound states down to atomic dimensions. By applying a strong magnetic field, a large jump in energy of the quasi-bound states, which is about one-half the energy spacing between the quasi-bound states, is observed. Such a behavior results from turning on a {\pi} Berry phase of massless Dirac fermions in graphene by a magnetic field. Moreover, our experiment demonstrates that a quasi-bound state splits into two peaks with an energy separation of about 26 meV when the Fermi level crosses the quasi-bound state, indicating that there are strong electron-electron interactions in the GQD.

A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the relativistic zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor v = 0 of charge-neutral graphene, have been extensively explored in experiment. To date, identification of these high-field broken-symmetry states has mostly relied on macroscopic transport techniques. Here, we study splitting of the zero LL of graphene at partial filling and demonstrate a direct approach by imaging the QHIFM states at atomic scale with a scanning tunneling microscope. At half filling of the zero LL (v = 0), the system is in a spin unpolarized state and we observe a linear magnetic-field-scaling of valley splitting. Simultaneously, the spin degeneracy in the two valleys is also lifted by the magnetic fields. When the Fermi level lies inside the spin-polarized states (at v = 1 or -1), the spin splitting is dramatically enhanced because of the strong many-body effects. At v = 0, we direct image the wavefunctions of the QHIFM states at atomic scale and observe an interaction-driven density wave featuring a Kekule distortion, which is responsible for the large gap at charge neutrality point in high magnetic fields., Comment: 3 figures in main text

Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops. These materials host a single hourglass Weyl loop circling around a high-symmetry point. Interestingly, there is also a spin-orbit Dirac point enabled by an additional screw axis. We show that the hourglass Weyl loop and the Dirac point are robust under a variety of applied strains. By breaking the screw axis, the Dirac point can be transformed into a second Weyl loop. Furthermore, by breaking the glide mirror, the hourglass Weyl loop and the spin-orbit Dirac point can both be transformed into a pair of spin-orbit Weyl points. Our work offers guidance and realistic material candidates for exploring fascinating physics of several novel 2D emergent fermions., Comment: 11 pages, 10 figures

It is quite easy to control spin polarization and spin direction of a system via magnetic fields. However, there is no such a direct and efficient way to manipulate valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. The pseudomagnetic fields, which are quite different from real magnetic fields, pointing in opposite directions at the two distinct valleys of graphene. Therefore, coexistence of the pseudomagnetic fields and the real magnetic fields leads to imbalanced effective magnetic fields at two distinct valleys of graphene. This allows us to control the valley in graphene as convenient as the electron spin. In this work, we report consistent observation of valley polarization and inversion in strained graphene via pseudo-Landau levels, splitting of real Landau levels and valley splitting of confined states using scanning tunneling spectroscopy. Our results highlight a pathway to valleytronics in strained graphene-based platforms., Comment: 4 figures in main text, accepted by Phys. Rev. Lett

ABC-stacked trilayer graphene (TLG) are predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat-band structures near the charge neutrality point (CNP). Here, using high magnetic field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG. We observe an approximately linear magnetic-field-scaling of the valley splitting and orbital splitting in the ABC-stacked TLG. Our experiment indicates that the valley splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the orbital splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlation effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields., Comment: 4 Figures in main text

Nodal-line metals and semimetals, as interesting topological states of matter, have been mostly studied in nonmagnetic materials. Here, based on first-principles calculations and symmetry analysis, we predict that fully spin-polarized Weyl loops can be realized in the half metal state for the three-dimensional material Li$_3$(FeO$_3$)$_2$. We show that this material has a ferromagnetic ground state, and it is a half metal with only a single spin channel present near the Fermi level. The spin-up bands form two separate Weyl loops close to the Fermi level, which arise from band inversions and are protected by the glide mirror symmetry. One loop is of type-I, whereas the other loop is of hybrid type. Corresponding to these two loops in the bulk, on the (100) surface, there exist two fully spin-polarized drumheads of surface states within the surface projections of the loops. The effects of the electron correlation and the spin-orbit coupling, as well as the possible hourglass Weyl chains in the nonmagnetic state have been discussed. The realization of fully spin-polarized Weyl-loop fermions in the bulk and drumhead fermions on the surface for a half metal may generate promising applications in spintronics., Comment: 8 pages, 9 figures

Twisted graphene bilayers (TGBs) have low-energy van Hove singularities (VHSs) that are strongly localized around AA-stacked regions of the moire pattern. Therefore, they exhibit novel many-body electronic states, such as Mott-like insulator and unconventional superconductivity. Unfortunately, these strongly correlated states were only observed in magic angle TGBs with the twist angle theta~1.1{\deg}, requiring a precisely tuned structure. Is it possible to realize exotic quantum phases in the TGBs not limited at the magic angle? Here we studied electronic properties of a TGB with theta~1.64{\deg} and demonstrated that a VHS splits into two spin-polarized states flanking the Fermi energy when the VHS is close to the Fermi level. Such a result indicates that localized magnetic moments emerge in the AA-stacked regions of the TGB. Since the low-energy VHSs are quite easy to be reached in slightly TGBs, our result therefore provides a facile direction to realize novel quantum phases in graphene system., Comment: 4 figures

Measuring degeneracy and broken-symmetry states of a system at nanoscale requires extremely high energy and spatial resolution, which has so far eluded direct observation. Here, we realize measurement of the degeneracy and subtle broken-symmetry states of graphene at nanoscale for the first time. By using edge-free graphene quantum dots, we are able to measure valley splitting and valley-contrasting spin splitting of graphene at the single-electron level. Our experiments detect large valley splitting around atomic defects of graphene due to the coexistence of sublattice symmetry breaking and time reversal symmetry breaking. Large valley-contrasting spin splitting induced by enhanced spin-orbit coupling around the defects is also observed. These results reveal unexplored exotic electronic states in graphene at nanoscale induced by the atomic defects., Comment: 4 figures in main text

Nodal-loop semimetals are materials in which the conduction and valence bands cross on a one-dimensional loop in the reciprocal space. For the nodal-loop character to manifest in physical properties, it is desired that the loop is close to the Fermi level, relatively flat in energy, simple in its shape, and not coexisting with other extraneous bands. Here, based on the first-principles calculations, we show that the monoclinic CuTeO$_3$ is a realistic nodal-loop semimetal that satisfies all these requirements. The material features only a single nodal loop around the Fermi level, protected by either of the two independent symmetries: the $\mathcal{PT}$ symmetry and the glide mirror symmetry. The size of the loop can be effectively tuned by strain, and the loop can even be annihilated under stain, making a topological phase transition to a trivial insulator phase. Including the spin-orbit coupling opens a tiny gap at the loop, and the system becomes a $\mathbb{Z}_2$ topological semimetal with a nontrivial bulk $\mathbb{Z}_2$ invariant but no global bandgap. The corresponding topological surface states have been identified. We also construct a low-energy effective model to describe the nodal loop and the effect of spin-orbit coupling., Comment: 8 pages, 10 figures

We have investigated the critical behavior of a shandite-type half-metal ferromagnet Co3Sn2S2. It exhibits a second-order paramagnetic-ferromagnetic phase transition with TC = 174 K. To investigate the nature of the magnetic phase transition, a detailed critical exponent study has been performed. The critical components beta, gamma, and delta determined using the modified Arrott plot, the Kouvel-Fisher method as well as the critical isotherm analysis are match reasonably well and follow the scaling equation, confirming that the exponents are unambiguous and intrinsic to the material. The determined exponents of Co3Sn2S2 deviates from theoretical estimated short-range universal models. Instead, Co3Sn2S2 exhibits long-range order in the nature of magnetic interaction with the spin decay as J(r) ~ 1/r^[-(d + sigma)] with sigma = 1.28., Comment: 5 pages, 5 figures

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by spacetime inversion symmetry and sublattice symmetry and characterized by a $\mathbb{Z}_2$ index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic two-fold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group symmetry requirements are satisfied. Several concrete nodal-surface material examples are predicted via the first-principles calculations. The possibility of multi-nodal-surface materials is discussed., Comment: 13 pages, 12 figures

Negative differential conductance (NDC), characterized by the decreasing current with increasing voltage, has attracted continuous attention for its various novel applications. The NDC typically exists in a certain range of bias voltages for a selected system and controlling the regions of NDC in curves of current versus voltage (I-V) is experimentally challenging. Here, we demonstrate an unusual magnetic-field-controlled NDC in graphene npn junction resonators. The magnetic field not only can switch on and off the NDC, but also can continuously tune the regions of the NDC in the I-V curves. In the graphene npn junction resonators, magnetic fields generate sharp and pronounced Landau-level peaks with the help of the Klein tunneling of massless Dirac fermions. A tip of scanning tunneling microscope induces a relatively shift of the Landau levels in graphene beneath the tip. Tunneling between the misaligned Landau levels results in the magnetic-field-controlled NDC that may have potential applications for future graphene-based technology., Comment: 4 figures in main text

Nonsymmorphic space group symmetries can generate exotic band-crossings in topological metals and semimetals. Here, based on symmetry analysis and first-principles calculations, we reveal rich band-crossing features in the existing layered compounds Ta$_3$SiTe$_6$ and Nb$_3$SiTe$_6$, enabled by nonsymmorphic symmetries. We show that in the absence of spin-orbit coupling (SOC), these three-dimensional (3D) bulk materials possess accidental Dirac loops and essential fourfold nodal lines. In the presence of SOC, there emerges an hourglass Dirac loop---a fourfold degenerate nodal loop, on which each point is a neck-point of an hourglass-type dispersion. We show that this interesting type of band-crossing is protected and dictated by the nonsymmorphic space group symmetries, and it gives rise to drumhead-like surface states. Furthermore, we also investigate these materials in the monolayer form. We show that these two-dimensional (2D) monolayers host nodal lines in the absence of SOC, and the nodal lines transform to essential spin-orbit Dirac points when SOC is included. Our work suggests a realistic material platform for exploring the fascinating physics associated with nonsymmorphic band-crossings in both 3D and 2D systems., Comment: 12 pages, 12 figures

With considering the great success of scanning tunnelling microscopy (STM) studies of graphene in the past few years, it is quite surprising to notice that there is still a fundamental contradiction about the reported tunnelling spectra of quasi-free-standing graphene monolayer. Many groups observed V-shape spectra with linearly vanishing density-of-state (DOS) at the Dirac point, whereas, the others reported spectra with a gap of 60 meV pinned to the Fermi level in the quasi-free-standing graphene monolayer. Here we systematically studied the two contradicted tunnelling spectra of the quasi-free-standing graphene monolayer on several different substrates and provided a consistent interpretation about the result. The gap in the spectra arises from the out-of-plane phonons in graphene, which mix the Dirac electrons at the Brillouin zone corners with the nearly free-electron states at the zone center. Our experiment indicated that interactions with substrates could effectively suppress effects of the out-of-plane phonons in graphene and enable us to detect only the DOS of the Dirac electrons in the spectra. We also show that it is possible to switch on and off the out-of-plane phonons of graphene at the nanoscale, i.e., the tunnelling spectra show switching between the two distinct features, through voltage pulses applied to the STM tip., Comment: 4 Figures

Nanoscale twisted bilayer graphene (TBG) is quite instable and will change its structure to Bernal (or AB-stacking) bilayer with a much lower energy. Therefore, the lack of nanoscale TBG makes its electronic properties not accessible in experiment up to now. In this work, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 nm to 0 nm. By using scanning tunnelling microscopy, we studied carefully the structure and the electronic properties of the nanoscale TBG. Our results indicate that the low-energy electronic properties, including twist-induced van Hove singularities (VHSs) and spatial modulation of local density-of-state, are strongly affected by the translational symmetry breaking of the nanoscale TBG. Whereas, the electronic properties above the energy of the VHSs are almost not influenced by the quantum confinement even when the width of the TBG is reduced to only a single moire spot., Comment: 4 Figures

Nitrogen vacancy (NV) centres in diamond are attractive as quantum sensors owing to their superb coherence under ambient conditions. However, the NV centre spin resonances are relatively insensitive to some important parameters such as temperature. Here we design and experimentally demonstrate a hybrid nano-thermometer composed of NV centres and a magnetic nanoparticle (MNP), in which the temperature sensitivity is enhanced by the critical magnetization of the MNP near the ferromagnetic-paramagnetic transition temperature. The temperature susceptibility of the NV center spin resonance reached 14 MHz/K, enhanced from the value without the MNP by two orders of magnitude. The sensitivity of a hybrid nano-thermometer composed of a Cu_{1-x}Ni_{x} MNP and a nanodiamond was measured to be 11 mK/Hz^{1/2} under ambient conditions. With such high-sensitivity, we monitored nanometer-scale temperature variation of 0.3 degree with a time resolution of 60 msec. This hybrid nano-thermometer provides a novel approach to studying a broad range of thermal processes at nanoscales such as nano-plasmonics, sub-cellular heat-stimulated processes, thermodynamics of nanostructures, and thermal remanent magnetization of nanoparticles., Comment: 21 pages, 6 figures

Nodal loop appears when two bands, typically one electron-like and one hole-like, are crossing each other linearly along a one-dimensional manifold in the reciprocal space. Here we propose a new type of nodal loop which emerges from crossing between two bands which are both electron-like (or hole-like) along certain direction. Close to any point on such loop (dubbed as a type-II nodal loop), the linear spectrum is strongly tilted and tipped over along one transverse direction, leading to marked differences in magnetic, optical, and transport responses compared with the conventional (type-I) nodal loops. We show that the compound K4P3 is an example that hosts a pair of type-II nodal loops close to the Fermi level. Each loop traverses the whole Brillouin zone, hence can only be annihilated in pair when symmetry is preserved. The symmetry and topological protections of the loops as well as the associated surface states are discussed.

When electrons are confined in a two dimensional (2D) system, typical quantum mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy(STM) and scanning tunneling spectroscopy(STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

The interlayer gallery between two adjacent sheets of van der Waals materials is expected to modify properties of atoms and molecules confined at the atomic interfaces. Here, we directly image individual hydrogen atom intercalated between two graphene sheets and investigate its dynamics by scanning tunnelling microscope (STM). The intercalated hydrogen atom is found to be remarkably different from atomic hydrogen chemisorbed on external surface of graphene. Our STM measurements, complemented by first-principles calculations, show that the hydrogen atom intercalated between two graphene sheets has dramatically reduced potential barriers for elementary migration steps. Especially, the confined atomic hydrogen dissociation energy from graphene is reduced to 0.34 eV, which is only about a third of a hydrogen atom chemisorbed on graphene. This offers a unique platform for direct imaging of the atomic dynamics of confined atoms. Our results suggest that the atomic interfaces of van der Waals materials may provide a confined environment to tune the interfacial chemical reactions., Comment: 5 figures

A variety of new and interesting correlated states have been predicted in graphene monolayer doped to Van Hove singularities (VHSs) of its density-of-state (DOS). However, tuning the Fermi energy to reach a VHS of graphene by either gating or chemical doping is prohibitively difficult, owning to their large energy distance (3 eV). Therefore, these correlated states, which arise from effects of strong electron-electron interactions at the VHSs, have remained experimentally elusive. Here, we report experimental evidences of electron-electron interactions around the VHSs of a twisted bilayer graphene (TBG) through scanning tunneling microscopy measurements. By introducing a small twisted angle between two adjacent graphene sheets, we are able to generate low-energy VHSs arbitrarily approaching the Fermi energy. The split of the VHSs are observed and the symmetry breaking of electronic states around the VHSs are directly visualized. These results experimentally demonstrate the important effects of electron-electron interactions on electronic properties around the VHSs of the TBG, therefore providing motivation for further theoretical and experimental studies in graphene systems with considering many-body interactions., Comment: 4 Figures in main text

Graphene, as an atomic-thick ultrasoft membrane, almost has no resistance against out-of-plane deformations and, therefore, it is always wrinkled to a certain degree. Recently, corrugated structures and their effects on the electronic properties of monolayer graphene have been studied extensively. However, similar experimental studies in bilayer graphene have yet to be reported. Here, we show that corrugations in bilayer graphene can generate incommensurate stacking solitons (domain walls) between commensurate Bernal-stacked domains. By using scanning tunneling microscopy, we microscopically study electronic structures of a corrugation-induced stacking soliton that separates two adjacent AB and BA stacked bilayer regions with a uniform interlayer potential difference. Both topological gapless edge states and quasi-localized gapped quantum-well-like states are observed in the nanoscale corrugation. Atomic resolution mapping of the topological edge states along the stacking soliton reveals the existence of intervalley scattering between them, which could explain recent experiments where the conductance along domain walls of gapped graphene bilayer is smaller than a quantized value 4e2 h., Comment: 4 figures

Chirally stacked $N$-layer graphene is a semimetal with $\pm p^N$ band-touching at two nonequivalent corners in its Brillioun zone. We predict that an off-resonant circularly polarized light (CPL) drives chirally stacked $N$-layer graphene into a Floquet Chern Insulators (FCIs), a.k.a. quantum anomalous Hall insulators, with tunable high Chern number $C_F=\pm N$ and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number $C_v=\pm N$ induced by a voltage gate can be engineered by the parameters of the CPL and voltage gate. We propose a topological domain wall between the FCI and VH phases, along which perfectly valley-polarized $N$-channel edge states propagate unidirectionally without backscattering.

The pristine graphene is strongly diamagnetic. However, graphene with single carbon atom defects could exhibit paramagnetism with local magnetic moments ~ 1.5 per vacancy1-6. Theoretically, both the electrons and electrons of graphene contribute to the magnetic moment of the defects, and the pi magnetism is characterizing of two spin-split DOS (density-of-states) peaks close to the Dirac point1,6. Since its prediction, many experiments attempt to study this pi magnetism in graphene, whereas, only a notable resonance peak has been observed around the atomic defects6-9, leaving the pi magnetism experimentally so elusive. Here, we report direct experimental evidence of the pi magnetism by using scanning tunnelling microscope. We demonstrate that the localized state of the atomic defects is split into two DOS peaks with energy separations of several tens meV and the two spin-polarized states degenerate into a profound peak at positions with distance of ~ 1 nm away from the monovacancy. Strong magnetic fields further increase the energy separations of the two spin-polarized peaks and lead to a Zeeman-like splitting. The effective g-factors geff around the atomic defect is measured to be about 40. Such a giant enhancement of the g-factor is attributed to the strong spin polarization of electron density and large electron-electron interactions near the atomic vacancy., Comment: 4 Figures in main text

Graphene nanoribbons (GNRs) are one-dimensional (1D) structures that exhibit a rich variety of electronic properties1-17. Therefore, they are predicted to be the building blocks in next-generation nanoelectronic devices. Theoretically, it has been demonstrated that armchair GNRs can be divided into three families, i.e., Na = 3p, Na = 3p + 1, and Na = 3p + 2 (here Na is the number of dimer lines across the ribbon width and p is an integer), according to their electronic structures, and the energy gaps for the three families are quite different even with the same p1,3-6. However, a systematic experimental verification of this fundamental prediction is still lacking, owing to very limited atomic-level control of the width of the armchair GNRs investigated7,9,10,13,17. Here, we studied electronic structures of the armchair GNRs with atomically well-defined widths ranging from Na = 6 to Na = 26 by using scanning tunnelling microscope (STM). Our result demonstrated explicitly that all the studied armchair GNRs exhibit semiconducting gaps due to quantum confinement and, more importantly, the observed gaps as a function of Na are well grouped into the three categories, as predicted by density-functional theory calculations3. Such a result indicated that we can tune the electronic properties of the armchair GNRs dramatically by simply adding or cutting one carbon dimer line along the ribbon width., Comment: 5 figures

The light-like dispersion of graphene monolayer results in many novel electronic properties in it1, however, this gapless feature also limits the applications of graphene monolayer in digital electronics2. A rare working solution to generate a moderate bandgap in graphene monolayer is to cut it into one-dimensional (1D) nanometre-wide ribbons3-13. Here we show that a wide bandgap can be created in a unique 1D strained structure, i.e., graphene-nanoribbon-like (GNR-like) structure, of a continuous graphene sheet via strong interaction between graphene and the metal substrate, instead of cutting graphene monolayer. The GNR-like structures with width of only a few nanometers are observed in a continuous graphene sheet grown on Rh foil by using thermal strain engineering. Spatially-resolved scanning tunnelling spectroscopy revealed bandgap opening of a few hundreds meV in the GNR-like structure in an otherwise continuous metallic graphene sheet, directly demonstrating the realization of a metallic-semiconducting-metallic junction entirely in a graphene monolayer. We also show that it is possible to tailor the structure and electronic properties of the GNR-like structure by using scanning tunnelling microscope., Comment: 4 Figures in main text and 6 Figures in SI