Tunable abundant valley Hall effect and chiral spin-valley locking in Janus monolayer VCGeN4.

It is both conceptually and practically fascinating to explore fundamental research studies and practical applications of two-dimensional systems with the tunable abundant valley Hall effect. In this work, based on first-principles calculations, the tunable abundant valley Hall effect is proved to appear in Janus monolayer VCGeN4. When the magnetization is along the out-of-plane direction, VCGeN4 is an intrinsic ferromagnetic semiconductor with a valley feature. The intriguing spontaneous valley polarization exists in VCGeN4 due to the common influence of broken inversion and time-reversal symmetries, which makes it easier to realize the anomalous valley Hall effect. Furthermore, we observe that the valley-non-equilibrium quantum anomalous Hall effect is driven by external strain, which is located between two half-valley-metal states. When reversing the magnetization, the spin flipping makes the position of the edge state to change from one valley to another valley, demonstrating an intriguing behavior known as chiral spin-valley locking. Although the easy magnetic axis orientation is along the in-plane direction, we can utilize an external magnetic field to transform the magnetic axis orientation. Moreover, it is found that the valley state, electronic and magnetic properties can be well regulated by the electric field. Our works explore the mechanism of the tunable abundant valley Hall effect by applying an external strain and electric field, which provides a perfect platform to investigate the spin, valley, and topology.

Novel valley character and tunable quasi-half-valley metal state in Janus monolayer VSiGeP4.

The manipulation and regulation of valley characteristics have aroused widespread interest in emerging information fields and fundamental research. Realizing valley polarization is one crucial issue for spintronic and valleytronic applications, the concepts of a half-valley metal (HVM) and ferrovalley (FV) materials have been put forward. Then, to separate electron and hole carriers, a fresh concept of a quasi-HVM (QHVM) has been proposed, in which only one type of carrier is valley polarized for electron and hole carriers. Based on first-principles calculations, we demonstrate that the Janus monolayer VSiGeP4 has QHVM character. To well regulate the QHVM state, strain engineering is utilized to adjust the electronic and valley traits of monolayer VSiGeP4. In the discussed strain range, monolayer VSiGeP4 always favors the ferromagnetic ground state and out-of-plane magnetization, which ensures the appearance of spontaneous valley polarization. It is found that the QHVM state can be induced in different electronic correlations (U), and the strain can effectively tune the valley, magnetic, and electronic features to maintain the QHVM state under various U values. Our work opens up a new research idea in the design of multifunctional spintronic and valleytronic devices.

Electronic-correlation induced sign-reversible Berry phase and quantum anomalous valley Hall effects in Janus monolayer OsClBr.

Topological phase transition can be induced by electronic correlation effects combined with spin-orbit coupling (SOC). Here, based on the first-principles calculations +U approach, the influence of electronic correlation effects and SOC on topological and electronic properties of the Janus monolayer OsClBr is investigated. With intrinsic out-of-plane (OOP) magnetic anisotropy, the Janus monolayer OsClBr exhibits a sequence of states, namely, the ferrovalley (FV) to half-valley-metal (HVM) to quantum anomalous valley Hall effect (QAVHE) to HVM to FV states with increasing U values. The QAVHE is characterized by a chiral edge state linking the conduction and valence bands with a Chern number C = 1, which is closely associated with the band inversion between dx2-y2/dxy and dz2 orbitals, and sign-reversible Berry curvature. The section with larger U values (2.31-2.35 eV) is very essential for determining the new HVM and QAVHE states, and also proves that a strong electron correlation effect exists in the interior of the Janus monolayer OsClBr. When taking into consideration a representative U value (U = 2.5 eV), a valley polarization value of 157 meV can be observed, which can be switched by reversing the magnetization direction of Os atoms. It is noteworthy that the Curie temperature (TC) strongly depends on the electronic correlation effects. Our work provides a comprehensive discussion on the electronic and topological properties of the Janus monolayer OsClBr, and demonstrates that the electronic correlation effects combined with SOC can drive the emergence of QAVHE, which will open up new opportunities for valleytronic, spintronic, and topological nanoelectronic applications.

Spontaneous valley polarization and valley-nonequilibrium quantum anomalous Hall effect in Janus monolayer ScBrI.

Topology and ferrovalley (FV) are two essential concepts in emerging device applications and the fundamental research field. To date, relevant reports are extremely rare about the coupling of FV and topology in a single system. By Monte Carlo (MC) simulations and first-principles calculations, a stable intrinsic FV ScBrI semiconductor with high Curie temperature (TC) is predicted. Because of the combination of spin-orbital coupling (SOC) and exchange interaction, the Janus monolayer ScBrI shows a spontaneous valley polarization of 90 meV, which is located in the top valence band. For the magnetization direction perpendicular to the plane, the changes from FV to half-valley-metal (HVM), to valley-nonequilibrium quantum anomalous Hall effect (VQAHE), to HVM, and to FV can be induced by strain engineering. It is worth noting that there are no particular valley polarization and VQAHE states for in-plane (IP) magnetic anisotropy. By obtaining the real magnetic anisotropy energy (MAE) under different strains, due to spontaneous valley polarization, intrinsic out-of-plane (OOP) magnetic anisotropy, a chiral edge state, and a unit Chern number, the VQAHE can reliably appear between two HVM states. The increasing strains can induce VQAHE, which can be clarified by a band inversion between dx2-y2/dxy and dz2 orbitals, and a sign-reversible Berry curvature. Once synthesized, the Janus monolayer ScBrI would find more significant applications in topological electronic, valleytronic, and spintronic nanodevices.

Strain-tunable skyrmions in two-dimensional monolayer Janus magnets.

The Dzyaloshinskii-Moriya interaction (DMI), which only exists in noncentrosymmetric systems, plays an important role in the formation of exotic chiral magnetic states. However, the absence of the DMI occurs in most two-dimensional (2D) magnetic materials due to their intrinsic inversion symmetry. Here, by using first-principles calculations, we demonstrate that a significant DMI can be obtained in a series of Janus monolayers of dichalcogenides XSeTe (X = Nb, Re) in which the difference between Se and Te on the opposite sides of X breaks the inversion symmetry. Remarkably, the DMI amplitudes of NbSeTe (1.78 meV) and ReSeTe (4.82 meV) are larger than the experimental value of Co/graphene (0.16 meV), and NbSeTe and ReSeTe monolayers have a high Curie temperature of 1023 K and 689 K, respectively. Through the micromagnetic simulation of XSeTe (X= Nb, Re) simulations, we also find that the ReSeTe monolayer can performance for skyrmion states by applying an external magnetic field, and importantly, the skyrmion states can be regulated and controlled under external strain. The findings pave the way for device concepts using chiral magnetic structures in specially designed 2D ferromagnetic materials.

Two -dimensional semimetal AlSb monolayer with multiple nodal-loops and extraordinary transport properties under uniaxial strain.

Two-dimensional (2D) nodal-loop semimetal (NLSM) materials have attracted much attention for their high-speed and low-consumption transporting properties as well as their fantastic symmetry protection mechanisms. In this paper, using systematic first-principles calculations, we present an excellent NLSM candidate, a 2D AlSb monolayer, in which the conduction and valence bands cross with each other forming fascinating multiple nodal-loop (NL) states. The NLSM properties of the AlSb monolayer are protected by its glide mirror symmetry, which was confirmed using a symmetry-constrained six-band tight-binding model. The transport properties of the AlSb monolayer under in-plane uniaxial strains are also studied, based on a non-equilibrium Green's function method. It is found that both compressive and tensile strains from -10% to 10% improve the transporting properties of AlSb, and it is interesting to see that flexure configurations are energetically favored when compressive uniaxial strains are applied. Our studies not only provide a novel 2D NLSM candidate with a new symmetry protection mechanism, but also raise the novel possibility for the detection of out-of-plane flexure in 2D semimetal materials.

High excellent hydrogen evolution characteristics and novel mechanism of two-dimensional tetra-phase OsN2 and ReN2.

It is essential to find a kind of electrocatalyst for hydrogen evolution reduction (HER) comparable with a noble metal that has good conductivity and abundant active sites. Based on systematic searches by first-principles calculations, we discovered two-dimensional transition-metal nitrides, tetra-phase OsN2 and ReN2 monolayers, as potential HER electrocatalysts with superior thermodynamic and kinetic stability. They exhibited excellent catalytic activity due to the presence of multiple active sites with a density of 8 × 1015 site per cm2 and an overpotential close to 0. In addition, we also found that the synergistic effect of strain and coverage makes them have a good hydrogen evolution activity. The ΔGH of the OsN2 monolayer at 1% tensile strain under 3/4 hydrogen coverage is 0.02 eV, and that of ReN2 at 1/2 hydrogen coverage could decrease to 0.001 eV. Different from other common transition metal nitrides, we found that the active sites of OsN2 and ReN2 monolayers are both at nitrogen atoms, which could be further understood by the crystal orbital Hamiltonian population analysis between N and metal atoms. All these interesting findings not only provide new excellent candidates but also provide new insights into the mechanism of hydrogen evolution of nitrides.

Magnetic anisotropy and ferroelectric-driven magnetic phase transition in monolayer Cr2Ge2Te6.

Monolayer Cr2Ge2Te6 (ML-CGT) has attracted broad interest due to its novel electronic and magnetic properties. However, there are still controversies on the origin of its intrinsic magnetism. Here, by exploring the electronic and magnetic properties of ML-CGT, we find that the magnetic shape anisotropy (MSA) is vital for establishing the long-range ferromagnetism, except for the contribution from magnetocrystalline anisotropy energy (MCA). Electronic band analysis, combined with atomic- and orbital-resolved magnetic anisotropy from a second-order perturbation theory, further reveals that the MCA of ML-CGT is mainly originated from hybridized Te-py and -pz orbitals. The MSA from magnetic Cr atoms in ML-CGT is larger than MCA, resulting in an in-plane magnetic anisotropy. Noticeably, by constructing a heterostructure (HTS) with ferroelectric Sc2CO2, CGT undergoes an in-plane to out-of-plane spin reorientation via ferroelectric polarization switching, accompanied with an electronic property transition from semiconductor to half-metal. The Curie temperature of CGT/Sc2CO2 HTS can be enhanced to 92.4 K under the ferroelectric polarization, which is much higher than that of pristine ML-CGT (34.7 K). These results not only clarify the contradiction of magnetic mechanism of ML-CGT in previous experimental and theoretical works, but also open the door for realizing nonvolatile magnetic memory devices based on a multifunctional ferromagnetic/ferroelectric HTS.

Anisotropic nodal loop in NiB2 monolayer with nonsymmorphic configuration.

Two-dimensional (2D) materials featuring a nodal-loop (NL) state have been drawing considerable attention in condensed matter physics and materials science. Owing to their structural polymorphism, recent high-profile metal-boride films have great advantages and the potential to realize a NL. Herein, a 2D NiB2 monolayer with an anisotropic NL nature is proposed and investigated using first-principles calculations. We show that the NiB2 monolayer has excellent thermal dynamics stability, suggesting the possibility of its synthesis in experiments. Remarkably, the NL with a considerable Fermi velocity is demonstrated to be protected by nonsymmorphic glide mirror symmetry, instead of the widely known horizontal mirror symmetry. Accompanied by the proper preservation of the NL, strain engineering can not only regulate the anisotropy of the NL but also give rise to a self-doping phenomenon characterized by effective modulation of the carrier type and concentration. Moreover, this NL state is robust against the correlation effect. These findings pave the way for exploring nonsymmorphic-symmetry-enabled NL nature in 2D metal-borides.

Two-dimensional Weyl semi-half-metallic NiCS3 with a band structure controllable by the direction of magnetization.

Two-dimensional (2D) Weyl semi-half-metals (WSHMs) have attracted tremendous interest for their fascinating properties combining half-metallic ferromagnetism and Weyl fermions. In this work, we present a NiCS3 monolayer as a new 2D WSHM material using systematic first-principles calculations. It has 12 fully spin-polarized Weyl nodal points in one spin channel with a Fermi velocity of 3.18 × 105 m s-1 and a fully gapped band structure in the other spin channel. It exhibits good mechanical and thermodynamic stabilities and the Curie temperature is estimated to be 403 K. The Weyl points are protected by vertical mirror plane symmetry along Γ-K, and each of them remains gapless even under spin-orbit coupling when the direction of spin is perpendicular to the Γ-K line including the Weyl point, which makes it possible to control the opening and closing of Weyl points by applying and rotating external magnetic fields. Our work not only provides a promising 2D WSHM material to explore the fundamental physics of symmetry protected ferromagnetic Weyl fermions, but also reveals a potential mechanism of band engineering of 2D WSHM materials in spintronics.

A novel spin-valley-coupled nodal-ring semimetal in single-layer Ta2C3.

Nodal-ring semimetals with band crossing are the new type of quantum materials that have attracted considerable interest from scholars for research. In general, the spin-orbit coupling (SOC) effect opens a band gap at the Dirac point. Therefore, finding 2D nodal-ring semimetals with resistance to SOC has more challenges. Based on first-principles calculations, we propose here that the two-dimensional (2D) Ta2C3 monolayer is a novel nodal-ring semimetal. In particular, Ta2C3 forms six closed rings in the Brillouin zone (BZ) with SOC, which originates from the dxy,x2-y2 orbitals of Ta and the pz orbitals of C. The nodal-ring bands at the K point in Ta2C3 exhibits characteristics of valley splitting and spin polarization due to the breaking of inversion symmetry and SOC. The masximal spin-splitting at the K point is as large as 268.87 meV and 61.90 meV for the conduction band minimum (CBM) and valence band maximum (VBM), respectively. The massless Dirac fermions in the non-equivalent valley have the opposite Berry curvature and spin moment. Therefore, 2D Ta2C3 is novel spin-valley-coupled nodal-ring semimetal. In addition, we found interesting negative differential resistance effects when calculating its transport properties. Our results not only provide an ideal platform for studying the combination of new physical properties, spintronics and valleytronics, but also open the way for designing low-power and fast-transport electronic devices.

Half-Dirac semimetals and the quantum anomalous Hall effect in Kagome Cd2N3 lattices.

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter as low-dimensionality opens unprecedented opportunities for manipulating the quantum state of low-cost electronic nanodevices. The search for high-temperature HDSs is still a current hotspot and yet challenging experimentally. Herein based on first-principles calculations, we propose the realization of Half Dirac semimetals (HDS) in two-dimensional (2D) Kagome transition-metal nitride Cd2N3, which is robust against strain engineering. Monte Carlo simulations reveal that Cd2N3 possesses a Curie temperature reaching up to T C = 225 K, which is much higher than that of the reported monolayers CrI3 (T C = 45 K) and Cr2Ge2Te6 (T C = 20 K). The band crossings in Cd2N3 are gapped out by the spin-orbit coupling, which brings about the quantum anomalous Hall (QAH) effect with a sizeable band gap of E g = 4.9 meV, characterized by the nonzero Chern number (C = 1) and chiral edge states. A tight-binding model is further used to clarify the origin of HDSs and nontrivial electronic properties. The results suggest monolayer transition-metal nitrides as a promising platform to explore fascinating physical phenomena associated with novel 2D emergent HDSs and QAH insulators toward realistic spintronics devices, thus stimulating experimental interest.

Glide Mirror Plane Protected Nodal-Loop in an Anisotropic Half-Metallic MnNF Monolayer.

Two-dimensional (2D) nodal-loop (NL) semimetals have attracted tremendous attention for their abundant physics and potential device applications, whereas the realization of gapless NL semimetals robust against spin-orbit coupling (SOC) remains a big challenge. Recently, breakthroughs have been made with the realization of gapless NL semimetals in 2D half-metallic materials, where NLs were protected by a horizontal mirror plane symmetry. Here we first propose an alternative nonsymmorphic horizontal glide mirror plane symmetry which could protect the NLs in 2D materials. On the basis of comprehensive first-principles calculations and symmetry analysis, we found that the glide mirror symmetry together with intrinsic out-of-plane spin polarization can protect the NL against SOC in a half-metallic semimetal, namely, the MnNF monolayer. Moreover, we predict that the MnNF monolayer has strong anisotropic characteristics, tunable band structure by changing the magnetization direction, and 100% spin-polarized transport properties. Our work not only provides a novel 2D half-metallic semimetal with strong anisotropy but also broadens the scope of 2D nodal-loop materials.

Two-dimensional honeycomb-kagome Ta2S3: a promising single-spin Dirac fermion and quantum anomalous hall insulator with half-metallic edge states.

Recent experimental success in the realization of two-dimensional (2D) magnetism has invigorated the search for new 2D magnetic materials with a large magnetocrystalline anisotropy, high Curie temperature, and high carrier mobility. Using first-principles calculations, here we predict a novel class of single-spin Dirac fermion states in a 2D Ta2S3 monolayer, characterized by a band structure with a large gap in one spin channel and a Dirac cone in the other with carrier mobility comparable to that of graphene. Ta2S3 is dynamically and thermodynamically stable under ambient conditions, and possesses a large out-of-plane magnetic anisotropy energy and a high Curie temperature (TC = 445 K) predicted from the spin-wave theory. When the spin and orbital degrees of freedom are allowed to couple, the Ta2S3 monolayer becomes a Chern insulator with a fully spin-polarized half-metallic edge state. An effective four-band tight-binding model is constructed to clarify the origin of a semi-Dirac cone in a spin-up channel and nontrivial band topology, which can be well maintained on a semiconducting substrate. The combination of these unique single-spin Dirac fermion and quantum anomalous Hall states renders the 2D Ta2S3 lattice a promising platform for applications in topologically high fidelity data storage and energy-efficient spintronic devices.

Discovery of a ferroelastic topological insulator in a two-dimensional tetragonal lattice.

Ferroelasticity and band topology are two intriguing yet distinct quantum states of condensed matter materials. Their coexistence in a single two-dimensional (2D) lattice, however, has never been observed. Here, we found that the 2D tetragonal HfC monolayer allowed simultaneous presence of ferroelastic and topological orders. By using first-principles calculations, we found that it could allow a low switching barrier with reversible strain of 17.4%, indicating that the anisotropic properties are achievable experimentally for a 2D tetragonal lattice. More interestingly, the tuning of topological behaviors with strain led to spin-separated and gapless edge states, that is, the quantum spin Hall effect. These findings from the coupling of two quantum orders offer insights into ferroelastic control over topological edge states for achieving multifunctional properties in next-generation 2D nanodevices.

Discovery of a novel spin-polarized nodal ring in a two-dimensional HK lattice.

Nodal-ring materials with a spin-polarized feature have attracted intensive interest recently due to their exotic properties and potential applications in spintronics. However, such a type of two-dimensional (2D) lattice is rather rare and difficult to realize experimentally. Here, we identify the first 2D Honeycomb-Kagome (HK) lattice, Mn-Cyanogen, as a new single-spin nodal-ring material by using first-principles calculations. Mn-Cyanogen shows gapless and semiconducting properties in spin-up and spin-down orientations, respectively, indicating a spin-gapless semiconductor nature. Remarkably, a spin-polarized nodal ring induced by px,y/pz band inversion is captured from the 3D band structure, which is irrelevant to spin-orbit coupling. The origin of the single-spin nodal-ring can be further clarified by the effective tight-binding (TB) model. These results open a new avenue to achieving spin-polarized nodal-ring materials with promising applications in spintronic devices.

Strain-Tuned Topological Insulator and Rashba-Induced Anisotropic Momentum-Locked Dirac Cones in Two-Dimensional SeTe Monolayers.

Rashba spin-orbit coupling (SOC) in topological insulators (TIs) is a very interesting phenomenon and has received extensive attention in two-dimensional (2D) materials. However, the coexistence of Rashba SOC and band topology, especially for materials with a square lattice, is still lacking. Here, by using first-principles calculations, we propose for the first time a SeTe monolayer as a 2D candidate with these novel properties. We find that the square lattice exhibits anisotropic band dispersions near the Fermi level and a Rashba effect related to large SOC and inversion asymmetry, which leads to a Dirac semimetal state. Another prominent feature is that SeTe can achieve a topological state under a tensile strain of only 1%, characterized by the Z2 invariant and helical edge states. Our findings demonstrate that SeTe is a promising material for novel electronic and spintronics applications.

Nontrivial topology and topological phase transition in two-dimensional monolayer Tl.

Topological insulating material with dissipationless edge states is a rising star in spintronics. While most two-dimensional (2D) topological insulators belong to group-IV or -V elements in a honeycomb lattice, herein, we propose a new topological phase in the 2D hexagonal group-III crystal, h-Tl, based on a tight-binding model and density-functional theory calculation. Analysis of band dispersion reveals a Dirac nodal-ring near the Fermi level, which is attributed to px,y/pz band crossing. Upon inclusion of spin-orbit coupling (SOC), h-Tl turns into a quantum spin Hall insulator under 21% biaxial strain, confirmed by integrating spin Berry curvature in the Brillouin zone and spin-polarized edge states. A prominent feature of its electronic properties is that the effect of SOC plays two essential roles of both topological gap opening and band inversion between px,y/pz orbitals, which is the first observed phenomenon in 2D materials. This study extends the scope of 2D elemental topological insulators and presents a platform to design new 2D topotronics materials.

Strain-Induced Quantum Spin Hall Effect in Two-Dimensional Methyl-Functionalized Silicene SiCH3.

Quantum Spin Hall (QSH) has potential applications in low energy consuming spintronic devices and has become a researching hotspot recently. It benefits from insulators feature edge states, topologically protected from backscattering by time-reversal symmetry. The properties of methyl functionalized silicene (SiCH3) have been investigated using first-principles calculations, which show QSH effect under reasonable strain. The origin of the topological characteristic of SiCH3, is mainly associated with the s-pxy orbitals band inversion at Γ point, whilst the band gap appears under the effect of spin-orbital coupling (SOC). The QSH phase of SiCH3 is confirmed by the topological invariant Z2 = 1, as well as helical edge states. The SiCH3 supported by hexagonal boron nitride (BN) film makes it possible to observe its non-trivial topological phase experimentally, due to the weak interlayer interaction. The results of this work provide a new potential candidate for two-dimensional honeycomb lattice spintronic devices in spintronics.

Na2C monolayer: a novel 2p Dirac half-metal with multiple symmetry-protected Dirac cones.

A Dirac half-metal material, which has a gapped band structure in one spin channel but Dirac cones in the other, combines two intriguing properties of 100% spin polarization and massless Dirac fermions and has recently started to attract increasing attention. In this work, using first-principles calculations we predict that the disodium carbide (Na2C) monolayer is an intrinsic 2p Dirac half-metal material with 12 fully spin-polarized and symmetry-protected Dirac cones, and a slightly gapped (53 meV) spin-polarized nodal line coexisting in one spin channel, leaving the other spin channel insulated with a gap of 1.9 eV. There are two kinds of Dirac cones in Na2C, protected by different crystalline symmetries, both of which are robust against biaxial strains (±5%) and spin-orbit coupling effects, with Fermi velocities of up to 5.2 × 105 m s-1. Ferromagnetism is mainly contributed to by the unpaired 2p electrons in the carbon, with a Curie temperature estimated to be 382 K, and the origin of the 2p magnetism could be explained by the superexchange mechanism between C2- anions with the Na+ cation as a bridge. Our results not only indicate a promising candidate for high-speed spintronic devices, but also reveal the hidden mechanism of the origin of symmetric protection and ferromagnetic exchange interactions in a Dirac semi-metal, which would provide a feasible strategy for the design of Dirac materials.