Nodal Loop Research Articles

Dirac fermions and spin transport in the SrVO3/SrTiO3 quantum well

The type-II Dirac fermions are characterized by a tilted Dirac cone and sustain exotic quantum transport phenomena. Here, we show the emergence of a type-II Dirac nodal loop in the SrVO3/SrTiO3 quantum well structure by density functional theory calculations and symmetry arguments. When the spin–orbit coupling (SOC) is neglected, the unavoidable crossing between two t2g bands gives rise to a nodal loop in the Brillouin zone, which is protected by the mirror symmetry. Such a nodal loop is fully gapped by including SOC, which results in a large spin Hall effect due to large spin Berry curvatures. Our findings add the unexplored functionality to oxide quantum wells and offer a practical platform to explore the interplay between topological fermions and spin transport phenomena.

Correlation driven a novel spin-polarized hourglass loop in monolayer VCl2

Hourglass loop in two-dimensional (2D) systems is typically vulnerable against spin–orbit coupling (SOC). Here, we explore 2D systems with a type of spin-polarized nodal loop that is robust under SOC and characteristic of an hourglass-type dispersion. Through first-principles calculations, we identify the monolayer VCl2 materials as a realistic material platform to realize an hourglass loop. There exist three phases, all of which are dynamically stable. For the γ-structure, as a new single spin hourglass loop material. It shows semiconducting and gapless properties in spin down and spin up channels, respectively. Moreover, it always exhibits an hourglass loop property in the absence and presence of SOC. It indicates that the hourglass has strong against SOC. Our work suggests a realistic material platform for investigating the novel physics associated with band crossings in 2D systems.

Topological charge pumping in tetramerized Kitaev chains with nodal loop in parameter space

We investigated the topological pumping charge of a tetramerized Kitaev chain with spatially modulated chemical potential, which hosts nodal loops in parameter space and violates particle number conservation. In the simplest case, with alternatively assigned hopping and pairing terms, we show that the model can be mapped into the Rice–Mele model by a partial particle-hole transformation and subsequently supports topological charge pumping as a demonstration of the Chern number for the ground state. Beyond this special case, analytic analysis shows that the nodal loops are conic curves. Numerical simulation of a finite-size chain indicates that the pumping charge is zero for a quasiadiabatic loop within the nodal loop and is ±1 for a quasiadiabatic passage enclosing the nodal loop. Our findings unveil the topology of Kitaev chains in parameter space.

Electride pure α-Zr: interstitial electrons induced type-II nodal line

Electrides have attracted significant attention in the fields of physics, materials science, and chemistry due to their distinctive electron properties characterized by weak nuclear binding. In this study, based on first-principles calculations and symmetry analysis, we report that the pure zirconium with alpha-phase (α-Zr) is expected to be the electrically neutral electride with topological nodal loop. Furthermore, the nodal loop located at the kz = 0 plane exhibits a clear drumhead-like surface state. The energy levels of the topological nodal loop can be regulated by applying uniaxial strain, resulting in the topological nodal loop being closer to the Fermi level. Remarkably, the work function of the electride Zr shows a significant anisotropy along the (001), (100), and (110) directions, particularly with a low work function of 3.14 eV along the (110) surface. Therefore, we predict that α-Zr provides a promising platform for future research on topological electrides.

Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure

Three-dimensional Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X = Si, Ge; Y = S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role in such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering reported between states of different symmetry eigenvalues at small wave vector q⃗. Here we show, using quasiparticle interference, that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g. native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state, can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin–orbit induced avoided crossing near the Fermi level by as much as 300%.

A novel multi‐slice electromagnetic field‐circuit coupling method for transient computation of long‐distance gas‐insulated transmission lines

AbstractAccurate calculation of short‐circuit electromagnetic force is crucial for both mechanical strength check and the optimal design of gas‐insulated transmission lines (GIL). Since the full 3D numerical simulation method is highly time‐consuming, a novel lightweight 2D multi‐slice electromagnetic field‐circuit coupled method for computing transient electromagnetic force is proposed, where appropriate port voltage degrees of freedom (DoFs) are introduced for the solid GIL conductor terminals. When the transient magnetic field equations are combined with the constraint equations of circuit part, including nodal voltage and loop current DoFs, a direct field‐circuit coupling scheme is thus derived. The proposed method can simultaneously consider the effect of interphase‐shunts and ground wires, as well as the skin effect and proximity effect. It can accurately capture the transient electromagnetic characteristics of GIL spanning from several to tens of kilometers under different short‐circuit conditions. The transient electromagnetic forces, as well as the induced voltages and currents of the enclosure, are analysed by the proposed method for both single‐phase and three‐phase enclosed GIL under various short‐circuit conditions. The proposed method has the advantages of high accuracy and lightweight computational cost, and thus it is also suitable for conducting important simulation tasks such as mechanical strength checks during the design optimisation phase of long‐distance GIL.

Monolayer Cu2Se: a topological catalysis in CO2 electroreduction

This investigation provides a comprehensive exploration into the intricate interplay between topological surface states (TSS) and catalytic performance in two-dimensional (2D) materials, with specific emphasis on monolayer Cu2Se. Leveraging the unique characteristics of nodal loop semimetals (NLSMs), we delve into the precise influence of TSS on catalytic activity, particularly in the domain of CO2 electrochemical reduction. Our findings illuminate the central role played by these TSS, arising from the underlying NLSM framework, in sculpting catalytic efficiency. The length of these surface states emerges as a critical determinant of surface density of states (DOSs), a fundamental factor governing catalytic behavior. Extension of these surface states correlates with heightened surface DOSs, yielding lower Gibbs free energies and consequently enhancing catalytic performance, particularly in the electrochemical reduction of CO2. Moreover, we underscore the profound importance of preserving symmetries that protect the nodal loop. The disruption of these symmetries is found to result in a significant degradation of catalytic efficacy, underscoring the paramount significance of topological features in facilitating catalytic processes. Therefore, this study not only elucidates the fundamental role of TSS in dictating the catalytic performance of topological 2D materials but also paves the way for harnessing these unique attributes to drive sustainable and highly efficient catalysis across a diverse spectrum of chemical processes.

Two-dimensional quadratic Weyl points, nodal loops, and spin-orbit Dirac points in PtS, PtSe, and PtTe monolayers.

Topological quasiparticles have garnered significant research attention in condensed matter physics. However, they are exceedingly rare in two-dimensional systems, particularly those hosting unconventional topological quasiparticles. In this work, employing first-principles calculations and symmetry analysis, we demonstrate that PtS, PtSe, and PtTe monolayers serve as high-quality two-dimensional topological semimetal materials. These materials exhibit multiple types of topological quasiparticles around the Fermi level in the absence of spin-orbit coupling, such as conventional linear Weyl points and unconventional quadratic Weyl points in the PtS monolayer, as well as nodal loops in PtSe and PtTe monolayers. When spin-orbit coupling (SOC) is introduced, a tiny gap opens, transforming the systems into quantum spin hall insulators. Simultaneously, three spin-orbit Dirac points, robust against SOC, appear at the X, Y, and M points. We illustrate the symmetry protection, low-energy effective model, and edge states of these topological states. Our work provides an excellent material platform for studying novel two-dimensional topological quasiparticles and topological insulators.

Prediction of a two-dimensional high Curie temperature Weyl nodal line kagome semimetal.

Kagome lattices may have numerous exotic physical properties, such as stable ferromagnetism and topological states. Herein, combining the particle swarm structure search method with first-principles calculations, we identify a two-dimensional (2D) kagome Mo2Se3 crystal structure with space group P6/mmm. The results show that 2D kagome Mo2Se3 is a 100% spin-polarized topological nodal line semimetal and exhibits excellent ambient stability. The band crossing points form two nodal loops around the high-symmetry points Γ and K. On the other hand, Mo2Se3 shows intrinsic ferromagnetism with a large magnetic moment of 3.05 μB per Mo atom and magnetic anisotropy energy (MAE) of 4.78 meV. Monte Carlo simulations estimate that Mo2Se3 possesses a high Curie temperature of about 673 K. In addition, its ferromagnetic ground state can be well preserved under external strain, and the MAE can be improved by increasing the strain. More importantly, the position of each nodal line can be adjusted to the Fermi level through hole doping. This multifunctional 2D magnetic material that combines spin and topology has great potential in the field of nanoscale spintronic devices.

Quantum transport on the surfaces of topological nodal-line semimetals

Topological nodal-line semimetals are always characterized by the drumhead surface states at the open boundaries. In this paper we first derive an analytical expression for the surface Green’s function of a nodal-line semimetal. By making use of this result, we explore the charge and spin transport properties of a metallic chain on the surface of a nodal-line semimetal, as functions of the gate voltage applied on the top of the material. According to the size of the nodal loop, due to the coupling to the surface modes, the charge conductance in the chain is found to show a robust plateau at e2/h , or to exhibit multiple valleys at e2/h . Correspondingly, the spin polarization of the transmitted current is 100% at the plateau region, or exhibits multiple peaks at nearly 100% . This feature can be viewed as a transport signature of the topological nodal-line semimetals.

Weyl nodes and hybrid nodal loop with spin–orbit coupling in W2TeSe

Topological metals with unique fermionic states provide an attractive research platform for exploring various topological phenomena and have aroused great research interest. In this study, we employ first-principles calculations to predict that W2TeSe, a candidate for Weyl metal, exhibits the coexistence of type-I Weyl nodes and hybrid nodal loop. These topological features are protected by symmetries and remain robust against symmetries conserving perturbations, such as spin–orbit coupling. The number, energies, and separations of these Weyl points align with expectations for ideal topological fermions as they arise from low-energy gapless fermions near the Fermi level with significant momentum space separation.

Monolayer TiC—A high-performance Dirac anode with ultralow diffusion barriers and high energy densities for Li-ion and Na-ion batteries

Two-dimensional Dirac materials have stimulated substantial research interest as binder-free anodes in metal-ion batteries, owing to their ultrahigh electronic conductivity, large specific area, and higher energy density. Here, using first-principles density functional theory calculations, we have investigated the feasibility of monolayer TiC as a potential anode material for Li/Na-ion batteries. The results indicate that monolayer TiC exhibits excellent dynamical and thermal stability. The electronic structure of monolayer TiC shows semimetallic characteristics with a Dirac cone at the M high symmetry point and the formation of Ti or C vacancies transforms the Dirac cone into a nodal loop or a nodal surface, respectively. Thus, monolayer TiC possesses superior electrical conductivity, which can be further enhanced by the formation of Ti or C vacancies in the material. Furthermore, the calculated adsorption energy values of -0.85 and -0.46 eV for Li-ion and Na-ion, respectively, indicate that Li/Na atom adsorption over monolayer TiC is a favorable process. The density of states plots show that after the adsorption of a single Li/Na atom, monolayer TiC maintains its metallic state, which is advantageous for the diffusion of stored electrons. Most remarkably, monolayer TiC exhibits energy densities of 2684 and 2015 mWh/g for Li and Na, respectively, which are significantly higher than commercial graphite and most other 2D anode materials. The fully loaded TiC anode exhibits excellent cycle stability with volume expansions as low as 0.13 and 0.11%, for Li and Na, respectively. Furthermore, an ultrafast diffusivity with low energy barriers of 0.02 and 0.10 eV is found in monolayer TiC for Li-ion and Na-ion, respectively, which suggests that it has an excellent charge/discharge capability. These exceptional properties make monolayer TiC an excellent candidate as an anode material for Li-ion and Na-ion batteries. Finally, SiC(111) has been proposed as a candidate substrate for monolayer TiC due to its minimal lattice mismatch.

Hourglass nodal loop phonons in two dimensions jointly supported by fourfold rotation and glide mirror symmetries

Hourglass nodal loop phonons in two dimensions jointly supported by fourfold rotation and glide mirror symmetries

Giant Bulk Electrophotovoltaic Effect in Heteronodal-Line Systems.

The realization of a giant and continuously tunable second-order photocurrent is desired for many nonlinear optical (NLO) and optoelectronic applications, which remains a great challenge. Here, based on a two-band model, we propose a concept of the bulk electrophotovoltaic effect, that is, an out-of-plane external electric field (E_{ext}) that can continuously tune in-plane shift current along with its sign flip in a heteronodal-line (HNL) system. While strong linear optical transition around the nodal loop may potentially generate giant shift current, an E_{ext} can effectively control the radius of the nodal loop, which can continuously modulate the shift-vector components inside and outside the nodal loop holding opposite signs. This concept has been demonstrated in the HNL HSnN/MoS_{2} system using first-principles calculations. The HSnN/MoS_{2} heterobilayer can not only produce a shift-current conductivity with magnitude that is one to two orders larger than other reported systems, but it can also realize a giant bulk electrophotovoltaic effect. Our finding opens new routes to create and manipulate NLO responses in 2D materials.

Electronic structure and topological phase transition in multi-orbital triangular lattice with rotation and mirror symmetry breaking

Triangular lattice is one of the most generic structures in the two-dimensional (2D) limit with numerous exotic properties, such as magnetic frustration and quantum spin liquid. Here, we investigate the electronic properties of a multi-orbital (p x , p y , p z ) triangular lattice while focusing on the role of rotation and mirror symmetry breaking in regulating the topological phase diagram. The tight-binding modeling reveals that rotation symmetry () breaking splits the Dirac point and preserves the nodal loop. A further inclusion of broken horizontal mirror symmetry () destroys the nodal loop. Consequently, with spin–orbit coupling (SOC), the (p x , p y , p z )-orbital triangular lattice is topologically non-trivial with only or symmetry breaking. With both symmetries breaking, it becomes trivial, except when the SOC is large enough to initiate band inversion. For real materials, we propose that the recently grown AgSe/AgTe monolayer in a binary honeycomb structure is an ideal system to realize the multi-orbital triangular lattice. The first-principles calculations demonstrate that free-standing AgSe and AgTe are Z 2 non-trivial. On the Ag(111) substrate, AgSe becomes trivial because of the breaking of both and symmetries, whereas AgTe remains non-trivial because of the strong SOC of Te. Our work not only provides physical insights into the experimentally synthesized 2D binary honeycomb structures but also highlights the manipulation of electronic and topological properties through symmetry/orbital physics, which are valuable for designing new quantum materials and devices.

Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet

Antiferromagnets (AFMs) with anomalous quantum responses have lead to new progress for the understanding of their magnetic and electronic structures from symmetry and topology points of view. Two typical topological states are the collinear antiferromagnetic Weyl semimetal (WSM) and Weyl nodal loop semimetal (WNLSM). In comparison with the counterparts in ferromagnets and non-collinear AFMs, the WSMs and WNLSMs in collinear AFMs are still waiting for experimental verification. In this work, we theoretically predicted the coexistence of Weyl points (WPs) and Weyl nodal loops (WNLs) in transition metal oxide RuO2. Owing to the small magnetocrystalline anisotropy energy, the WPs and WNLs can transform to each other via tuning the Neel vector. Moreover, since the WPs are very close to Fermi level and the WNLs are even crossing Fermi level, the topological states in RuO2 can be easily probed by photoemission and STM methods. Our result provides a promising material platform for the study of WSM and WNLSM states in collinear AFMs.

Tunable topological magnon phases in layered ferrimagnets

The introduction of effective spin-orbit couplings into magnon systems provides the opportunities to discover exotic and fascinating topological phases. In this work, we theoretically study the magnon spin-orbit coupling due to the natural dipole-dipole interaction in a layered collinear easy-axis ferrimagnet with two types of ferromagnetic sublayers coupled via antiferromagnetic interlayer exchange interaction, where we predict a nodal-loop semimetal phase and a Weyl semimetal phase in perpendicularly and laterally magnetized geometries, respectively. By driving the spin texture into a spin-canting phase with a magnetic field perpendicular to the easy axis, the nodal loop with a normal easy axis reduces to two Weyl points in the noncollinear spin configuration. Magnon arcs in the Weyl semimetal phases in both geometries are predicted in ferrimagnetic film with finite layers. Our results reveal the role of noncollinear spin texture on magnon topology, which may enrich the investigations in topological ferrimagnonics.

Stability Compensation Design and Analysis of a Piezoelectric Ceramic Driver with an Emitter Follower Stage.

Piezoelectric ceramic has been widely applied in many fields because of its characteristics, and the performance of piezoelectric ceramic is determined strongly by its driver. In this study, an approach to analyzing the stability of a piezoelectric ceramic driver with an emitter follower stage was presented, and a compensation was proposed. First of all, using the method of modified nodal analysis and loop gain analysis, the transfer function for the feedback network was analytically deduced, and the cause of the instability of the driver was found to be the pole composed of the effective capacitance from the piezoelectric ceramic and the transconductance from the emitter follower. Then, a compensation involving a novel delta topology composed of an isolation resistor and a second feedback path was proposed, and its function principle was discussed. Simulations showed a correspondence between the analysis and the effectiveness of the compensation. Finally, an experiment was set up with two prototypes, one with compensation, and the other without compensation. Measurements showed the elimination of oscillation in the compensated driver.

Tetragonal Mexican-hat dispersion and switchable half-metal state with multiple anisotropic Weyl fermions in penta-graphene

Due to the paired valence electrons configuration, all known two-dimensional (2D) carbon allotropes are intrinsically nonmagnetic. Based on the reported 2D carbon structure database and first-principles calculations, herein we demonstrate that inherent ferromagnetism can be obtained in the prominent allotrope, penta-graphene, which has a unique Mexican-hat valence band edge, giving rise to van Hove singularities and electronic instability. Induced by modest hole-doping that is achievable in electrolyte gate, the semiconducting penta-graphene can be transformed into different ferromagnetic half-metals with room-temperature stability and switchable spin directions. In particular, multiple anisotropic Weyl states, including type-I and type-II Weyl cones and hybrid quasi Weyl nodal loop, can be found in a sizable energy window of spin-down half-metal under proper strains. These findings not only identify a promising carbon allotrope to obtain the inherent magnetism for carbon-based spintronic devices, but highlight the possibility to realize different Weyl states by combining the electronic and mechanical means as well.

Magneto-optical conductivity of nodal loop semimetals

In this paper, we calculate the Landau levels (LLs) and magneto-optical conductivity of nodal loop semimetals. We find the LLs have two inflection points at kz=0 and kz=2 with curved structure and linear structure, respectively. With the increase of magnetic field B, there are three different LLs structures. The longitudinal and Hall conductance are calculated in the three region of B with different chemical potential. Compared with other system, there are two different transition peaks from kz=0 and kz=2. We obtained that the positions of interband and intraband transitions of the conductivity occur at En+1±En/2 and En+1±En/2 with the chemical potential moving into the positive branch LLs. We find the interband peaks are redistributed for the Hall conductivity. Finally the magnetoresistivity and circular polarization are also distinguished as a measure for probing the properties of nodal loop semimetals in experimentally.