Bulk quantum Hall effect of spin-valley-coupled Dirac fermions in a polar antiferromagnet BaMnSb$_2$
H. Sakai, H. Fujimura, S. Sakuragi, M. Ochi, R. Kurihara, A. Miyake, M. Tokunaga, T. Kojima, D. Hashizume, T. Muro, K. Kuroda, T. Kondo, T. Kida, M. Hagiwara, K… 展开作者
H. Sakai, H. Fujimura, S. Sakuragi, M. Ochi, R. Kurihara, A. Miyake, M. Tokunaga, T. Kojima, D. Hashizume, T. Muro, K. Kuroda, T. Kondo, T. Kida, M. Hagiwara, K. Kuroki, M. Kondo, K. Tsuruda, H. Murakawa, N. Hanasaki
备注：
14 pages, 4 figures. Accepted in Phys. Rev. B (Rapid Communication)
Unconventional features of relativistic Dirac/Weyl quasi-particles in topological materials are most evidently manifested in the 2D quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization. Although its extension to three dimensions has been long-sought and inspired theoretical proposals, material candidates have been lacking. Here we have discovered valley-contrasting spin-polarized Dirac fermions in a multilayer form in bulk antiferromagnet BaMnSb$_2$, where the out-of-plane Zeeman-type spin splitting is induced by the in-plane inversion symmetry breaking and spin-orbit coupling (SOC) in the distorted Sb square net. Furthermore, we have observed well-defined quantized Hall plateaus together with vanishing interlayer conductivity at low temperatures as a hallmark of the half-integer QHE in a bulk form. The Hall conductance of each layer is found to be nearly quantized to $2(N+1/2)e^2/h$ with $N$ being the Landau index, which is consistent with two spin-polarized Dirac valleys protected by the strong spin-valley coupling.
The subject of topological materials has attracted immense attention in condensed-matter physics, because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either …
In non-centrosymmetric metals, spin-orbit coupling (SOC) induces momentum-dependent spin polarization at the Fermi surfaces. This is exemplified by the valley-contrasting spin polarization in monolayer transition metal dichalcogenides (TMDCs) with in-plane inversion asymmetry. However, the valley configuration of massive Dirac fermions in TMDCs is fixed by the graphene-like structure, which limits the variety of spin-valley coupling. Here, we show that the layered polar metal BaMn$X_2$ ($X =$Bi, Sb) hosts tunable spin-valley-coupled Dirac fermions, which originate from the distorted $X$ square…
Crystal-symmetry-paired spin-valley locking in a layered room-temperature antiferromagnet
Southern University of Science and Technology（南方科技大学）；The Hong Kong University of Science and Technology（香港科技大学）；Zhejiang University（浙江大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Hiroshima University（广岛大学）；University of Science and Technology of China（中国科学技术大学）；Institute of Advanced Science Facilities, Shenzhen（深圳先进科学设施研究院）
Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)$_{v}\times $SU(2)$_{s}$ symmetric spin-valley model to obtain the correlated insulating state and the p…
Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moiré superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all th…
We reveal that local interactions in graphene allow novel spin liquids between the semi-metal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z$_{2}$ spin liquid, respectively. We argue that the algebraic spin liquid can be regarded as the two dimensional realization of one dimensional spin dynamics, where antiferromagnetic correlations show exactly the same power-law dependence as valence bond correlations. Nature of the Z$_{2}$ spin liquid turns out to be $d + i d'$ singlet pairing, but time reversal symmetry is preserved, taking $d + i d'$ in one vall…
We investigate spin and valley symmetry-broken fractional quantum Hall phases within a formalism that naturally extends the paradigm of quantum Hall ferromagnetism from integer to fractional quantum Hall states, allowing us to construct detailed phase diagrams for a large class of multi-component states. Motivated by recent experiments on Graphene aligned with a Boron Nitride substrate, we predict a sequence of transitions realized by increasing the magnetic field, starting from a sub-lattice polarized state to a valley coherent Kekule charge density wave state and further to an anti-ferromagn…
Hidden antiferromagnetism, persistent valley fluctuations, and $U(6)$ crossovers in triangular-lattice M-point moiré materials via determinantal quantum Monte Carlo
University of Oxford（牛津大学）；Max-Planck-Institut für Physik Komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
For the innovation of spintronic technologies, Dirac materials, in which the low-energy excitation is described as relativistic Dirac fermions, are one of the most promising systems, because of the fascinating magnetotransport associated with the extremely high mobility. To incorporate Dirac fermions into spintronic applications, their quantum transport phenomena are desired to be manipulated to a large extent by magnetic order in a solid. We here report a bulk half-integer quantum Hall effect in a layered antiferromagnet EuMnBi$_2$, in which field-controllable Eu magnetic order significantly …
We report interlayer electronic transport in CaMnBi$_{2}$ single crystals. Quantum oscillations and angular magnetoresistance suggest coherent electronic conduction and valley polarized conduction of Dirac states. Small cyclotron mass, large mobility of carriers and nontrivial Berry's phase are consistent with the presence of Dirac fermions on the side wall of the warped cylindrical Fermi surface. Similar to SrMnBi$_{2}$ that features an anisotropic Dirac cone, our results suggest that magnetic field-induced changes in the interlayer conduction are also present in layered bismuth-based materia…
Optical signatures of antiferromagnetic correlations in a strongly interacting quantum Hall MoSe2 monolayer
Harvard University（哈佛大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；University of Connecticut（康涅狄格大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Columbia University（哥伦比亚大学）；National Institute for Materials Science（国立材料研究所）
Bilayer graphene (BLG) offers a rich platform for broken symmetry states stabilized by interactions. In this work we study the phase diagram of BLG in the quantum Hall regime at filling factor $ν=0$ within the Hartree-Fock approximation. In the simplest non-interacting situation this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) …
Understanding strongly interacting electrons enables the design of materials, nanostructures and devices. Developing this understanding relies on the ability to tune and control electron-electron interactions by, e.g., confining electrons to atomically thin layers of 2D crystals with reduced screening. The interplay of strong interactions on a hexagonal lattice with two nonequivalent valleys, topological moments, and the Ising-like spin-orbit interaction gives rise to a variety of phases of matter corresponding to valley and spin polarized broken symmetry states. In this work we describe a hig…
Because of its large density-of-states and the 2π Berry phase near its low-energy band-contact points, neutral bilayer graphene (BLG) at zero magnetic field (B) is susceptible to chiral-symmetry breaking, leading to a variety of gapped spontaneous quantum Hall states distinguished by valley and spin-dependent quantized Hall conductivities. Among these, the layer antiferromagnetic state, which has quantum valley Hall (QVH) effects of opposite sign for opposite spins, appears to be the thermodynamic ground state. Though other gapped states have not been observed experimentally at B=0, they can b…
Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG) which observed spin-valley symmetry-breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry breaking orders. We find that interactions select the inter-valley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole and electron doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both inter-valley supercon…
The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattic…
We investigate the optical properties in a minimal model of spin-orbit coupled systems on honeycomb lattice at half-filling. The absorption of the circularly polarized light in the charge and antiferromagnetic ordered states is particularly studied, and the spin-valley selective excitation depending on the handedness of the light is found. It is shown that the optical selection rules plainly differ with the type of broken symmetries and topological properties of the electronic states. Consequently, the abrupt change of spin-valley selectivity in the optical absorption occurs at the topological…
Twisting moiré heterostructures to the flatband regime allows for the formation of strongly correlated quantum states, since the dramatic reduction of the bandwidth can cause the residual electronic interactions to set the principal energy scale. An effective description for such correlated moiré heterostructures, derived in the strong-coupling limit at integer filling, generically leads to spin-valley Heisenberg models. Here we explore the emergence and stability of spin liquid behavior in an SU(2)$^{\mathrm{spin}}\otimes$SU(2)$^{\mathrm{valley}}$ Heisenberg model upon inclusion of Hund's-ind…
We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors $ν_G=-2+n/3$ $(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $SU(4)$ symmetric limit. For all the fractions we study there are two-component states for which the competing phases are generalizations of those occurring at neutrality $ν_G=0$. They…
We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number $\pm 1$ with equal-spin-pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of thre…
Chirally stacked N-layer graphene with N>=2 is susceptible to a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers. In mean-field theory the neutral bilayer ground state is a layer antiferromagnet (LAF) state that has opposite spin-polarizations in opposite layers. In this Letter we analyze how the LAF and other competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using response and edge state signatures to i…
Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants $g_{z}$ and $g_{\perp}$. In this paper we demonstrate that when $g_{z}=-g_{\perp}$ an exact SO(5) symmetry survives which unifies the Néel spin order parameter of…
In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin" models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg" model on…
Recently Chern insulators with Chern number $C=1$ and $C=2$ in zero (or very small) magnetic field have been observed in two moire graphene systems: twisted bilayer graphene and ABC trilayer graphene, both aligned with a hexagonal Boron-Nitride (h-BN) substrate. These Chern insulator states arise due to many body effects in the Chern bands of these systems when they are partially filled to a total integer filling $ν_T = 1,3$ (including spin and valley degrees of freedom). A simple possible explanation is from Hartree-Fock mean field theory which predicts valley and spin polarization in the zer…
Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0<|ν|<1 and 1<|ν|<2. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU(2) valley symmetry, which we find to be important for |ν|<1 but negligible for |ν| >1. The effective absence of valley anisotropy for |ν|>1 means that states with odd numerator, e.g. |ν|=5/3 or 7/5 can accommodate charged excitations in the form of large valley skyrmions, whic…
Motivated by recent non-local transport studies of quantum-Hall-magnet (QHM) states formed in monolayer graphene's $N=0$ Landau level, we study the scattering of QHM magnons by gate-controlled junctions between states with different integer filling factors $ν$. For the $ν=1|-1|1$ geometry we find magnons are weakly scattered by electric potential variation in the junction region, and that the scattering is chiral when the junction lacks a mirror symmetry. For the $ν=1|0|1$ geometry, %in which the scattering region contains a $ν=0$ canted antiferromagnet, we find that kinematic constraints comp…
Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $ν=0,\pm 1$. Notably the ground state at $ν=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $ν=\pm 1,0$ by using exact di…
Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave and Kekul$é$ distortion are smoothly connected to a Kekul$…
Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of artificial Mott insulators where antiferromagnetic correlations between spins and orbitals can be designed. We show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models. We exploit the property that massive Dirac fermions form mid-gap bound stat…
Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless a…
Effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin-orbit coupling and the multi-orbital correlation effect. We show that the model exhibits a Neel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order…
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the corre…
Extended s-wave superconductivity in M-point twisted bilayer SnSe2
University of Würzburg（维尔茨堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马克斯·普朗克研究所）；The Flatiron Institute（平顿研究所）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics, Princeton University（普林斯顿大学物理系）；ITAMP, Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Harvard University
Topological magnon insulators constitute a growing field of research for their potential use as information carriers without heat dissipation. We report an experimental and theoretical study of the magnetic ground-state and excitations in the van der Waals two-dimensional honeycomb magnet ErBr3. We show that the magnetic properties of this compound are entirely governed by the dipolar interactions which generate a continuously degenerate non-collinear ground-state on the honeycomb lattice with spins confined in the plane. We find that the magnon dispersion exhibits Dirac-like cones when the ma…
We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states wi…
The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) ν=0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated wit…
