Nodal Lines Research Articles

Realizing altermagnetism in two-dimensional metal-organic framework semiconductors with electric-field-controlled anisotropic spin current.

Altermagnets exhibit momentum-dependent spin-splitting in a collinear antiferromagnetic order due to their peculiar crystallographic and magnetic symmetry, resulting in the creation of spin currents with light elements. Here, we report two two-dimensional (2D) metal-organic framework (MOF) semiconductors, M(pyz)2 (M = Ca and Sr, pyz = pyrazine), which exhibit both altermagnetism and topological nodal point and line by using first-principles calculations and group theory. The altermagnetic 2D MOFs exhibit unconventional spin-splitting and macroscopic zero magnetization caused by 4-fold rotation in crystalline real space and 2-fold rotation in spin space, leading to the generation and control of anisotropic spin currents when an in-plane electric field ( E ) is applied. In particular, pure spin current with the spin Hall effect occurs when E is applied along the angular bisector of the two spin arrangements. Our work indicates the existence of altermagnetic MOF systems and a universal approach to generate electric-field-controlled spin currents for potential applications in antiferromagnetic spintronics.

A topological nodal line semi-metal with a negative Poisson's ratio in a three-dimensional carbon network with sp2 hybridization.

In carbon allotropes, a series of topological semi-metals have been predicted, but both novel electronic properties and mechanical characteristics, e.g., a negative Poisson's ratio (NPR), are rarely discovered in the same sp2 type system. Here, a new three-dimensional carbon network, named WZGN, constructed from distorted one-dimensional zigzag graphene nanoribbons is proposed. The stability of the system is fully ensured by the phonon dispersion, AIMD simulation, and binding energy calculations. Besides, it is found that the system holds both topologically protected nodal line semi-metal properties together with an NPR property. Especially, the value of the NPR can exceed -0.36 when 21% uniaxial tensile strain along the c'-direction is applied. Our findings point out that nodal line semi-metals can be compatible with intrinsic NPR properties in a wide strain range in carbon systems with sp2 hybridization, suggesting possible applications in mechanical and electronics fields.

Nodal Lines of Eigenfunctions of Laplacian in Plane

Nodal Lines of Eigenfunctions of Laplacian in Plane

Anomalies in the Dirac bands in the proximity of correlated electrons.

Dirac fermions, particles with zero rest mass, are observed in topological materials and are believed to play a key role in the exotic phenomena in fundamental science and the advancement of quantum technology. Most of the topological systems studied so far are weakly correlated systems and the study of their properties in the presence of electron correlation is an interesting emerging area of research, where the electron correlation is expected to enhance the effective mass of the particles. Here, we studied the properties of Dirac bands in a non-symmorphic layered Kondo lattice system, CeAgSb2, employing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations. In addition to the Dirac cones due to non-symmorphic symmetry, this material hosts Dirac fermions in the squarenet layer in the proximity of a strongly correlated Ce layer exhibiting Kondo behavior. Experimental results reveal crossings of the highly dispersive linear bands at the Brillouin zone boundary due to non-symmorphic symmetry. In addition, there are anisotropic Dirac cones constituted by the squarenet Sb 5p states forming a diamond-shaped nodal line. These Dirac bands are linear in a wide energy range with an unusually high slope. Interestingly, near the local Ce 4f bands, these bands exhibit a change in the slope akin to the formation of a 'kink' observed in other materials due to electron-phonon coupling. The emergence of such exotic properties in proximity to strongly correlated electronic states has significant implications in the study of complex quantum materials including unconventional superconductors.

Comparison of pressure-based flame describing functions measured in an annular combustor under self-sustained oscillations and in an externally modulated linear combustor

One important aspect in the analysis of combustion instabilities in multiple-injector annular systems is that of representing such oscillations with a linear array of injectors. This issue is considered in the present work by comparing flame dynamics in a self-sustained oscillations situation in the annular configuration MICCA-Spray, with experiments carried out in TACC-Spray, a rectangular combustor equipped with five injectors externally modulated by driver units. In the annular system, the coupling mode is azimuthal, and in the linear array, the flames are submitted to a transverse acoustic field. An original method is used to change the limit-cycle pressure oscillations amplitude in the annular system and favor a standing mode with a well-defined nodal line position. It consists in using different arrangements of two types of injectors, leading to various azimuthal staging patterns. The range of pressure oscillation amplitudes is swept in TACC-Spray by changing the external acoustic forcing level. It is thus possible to compare the flame dynamics in forced and self-sustained situations using these two experimental facilities. This is done by examining flame describing functions (FDFs) based on downstream pressure fluctuations measured in the two configurations for different pressure oscillation amplitudes. The trends observed in the two systems are in good agreement, and there is a reasonably good match between the values of the gains and phases determined in the two configurations. The pressure-based FDFs are determined for flames located at different positions with respect to the acoustic mode. It is found that the transverse or azimuthal velocity component has only a weak influence on the pressure-based FDF, the strongest impact being observed in the neighborhood of the velocity antinode. This study demonstrates the ability of a linear-array setup modulated by a transverse mode to reproduce conditions of azimuthal coupling leading to self-sustained limit cycles in an annular combustor.

Electronic phase transition in bilayer P6mmm borophene.

In this study, using the tight-binding model and Green's function technique, we investigate potential electronic phase transitions in bilayer P6mmm borophene under the influence of external stimuli, including a perpendicular electric field, electron-hole coupling between sublayers (excitonic effects), and dopants. Our focus is on key electronic properties such as the band structure and density of states. Our findings reveal that the pristine lattice is metal with Dirac cones around the Fermi level, where their intersection forms a nodal line. The system undergoes transitions to a semiconducting state - elimination of nodal line - with a perpendicular electric field and a semimetallic state - transition from two Dirac cones to a single Dirac cone - with combined electric field and excitonic effects. Notably, with these, the system retains its massless Dirac-like bands characteristic at finite energy. However, introducing a dopant still leads to a metallic phase, but the Dirac-like bands become massive. Considering all these effects, the system ultimately reaches a semiconducting phase with massive Dirac-like bands. These results hold significance for optoelectronic applications.

Variations of topological surface states of nodal line semimetal AlB<sub>2</sub> after adsorption in aqueous environment

Topological semimetals have aroused great research interest due to their intrinsic topological physics and potential applications in devices. A key feature for all topological materials is the so-called bulk-boundary correspondence, which means that if there is non-trivial band topology in the bulk, then we can expect unique topologically protected conducting states in the surface, i.e. the topological surface state (TSS). Previously, the studies of the surface states of topological materials mainly focused on the pristine surfaces, while the topological nodal line semimetal surface states with adsorbates are rarely systematically studied. In this paper, the topological properties of the topological semimetal AlB<sub>2</sub> are studied by first-principles calculations, and the TSS position is calculated by constructing the Al- and B-terminated slab models. Observing the topological surface state, it is found that the drumhead-like TSS connects two Dirac nodes with no energy gaps on the node line, and the TSS of the Al end-terminated slab has a smaller energy dispersion than that of the B-terminated slab. The adsorption characteristics of AlB<sub>2</sub> (010) surface are studied, and it is found that the Gibbs free energy (<inline-formula><tex-math id="M2">\begin{document}$ {\Delta }{G}_{{{\mathrm{H}}}^{*}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.png"/></alternatives></inline-formula>) for hydrogen adsorption on the surface of Al is only –0.031 eV, demonstrating excellent hydrogen evolution reaction (HER) performance. The changes of TSS after H, OH and H<sub>2</sub>O are adsorbed on the surface of AlB<sub>2</sub> in aqueous solution environment are observed. The TSS change is the most significant when H is adsorbed, followed by OH adsorption. And the influence of H<sub>2</sub>O on TSS due to its electrical neutrality and weak surface adsorption is very weak. Before and after adsorption, because the topology protection TSS still exists, only the energy changes, which confirms its robustness in the environment. The results of this work provide a systematic understanding of the effects of different adsorbents on the TSS of AlB<sub>2</sub>, paving the way for future theoretical and experimental research in related fields, and alsopresent theoretical support for putting the topological materials into practical applications .

Prediction of the two-dimensional ferromagnetic semiconductor Janus 2H-ZrTeI monolayer with large valley and piezoelectric polarizations.

Two-dimensional room-temperature Janus ferrovalley semiconductors with valley polarization and piezoelectric polarization offer new perspectives for designing multifunctional nanodevices. Herein, using first-principles calculations, we predict that the Janus 2H-ZrTeI monolayer is an intrinsic ferromagnetic semiconductor with in-plane magnetic anisotropy and a Curie temperature of 111 K. The Janus ZrTeI monolayer possesses a significant valley polarization of 141 meV due to time-reversal and inversion symmetry breaking. Based on the valley-contrasting Berry curvature, the anomalous valley Hall effect can be observed under an in-plane electric field. Meanwhile, the breaking of the inversion symmetry and mirror symmetry results in large longitudinal and transverse piezoelectric coefficients. By applying biaxial strain, the Janus 2H-ZrTeI monolayer can also be transformed into a Weyl nodal line semimetal. Furthermore, bilayers of ZrTeI with AB and BA stacking configurations allow the coexistence of valley polarization and ferroelectricity, enabling the manipulation of magnetism, ferroelectric polarization, and valley polarization through interlayer sliding. Our work provides a platform for studying valley polarization, piezoelectricity, and multiferroic coupling, which is significant for the application of multifunctional devices.

Emerging 2D Cobalt Telluride (CoxTey): from Theory to Applications

AbstractCobalt telluride, with tunable magnetism and ferromagnetism that hinged upon the stoichiometric ratio, has emerged as a new member of 2D materials in the last decade. Metallic doping by sodium (Na) and platinum (Pt) atoms below critical concentrations is found to enhance the magnetism of cobalt telluride. After thinning cobalt telluride down to few‐layer, the saturation magnetism is improved by two order of magnitudes because of the oxidation state of cobalt (Co) and reduced coordination number of the surface atoms. In 2D limit, cobalt di‐telluride possesses Dirac band structure with many nodal lines that correlate with quantum criticality and other fantastic physics. In this mini‐review, the crystal and band structures of cobalt telluride categorized by stoichiometric ratio are overviewed after briefing the introduction. Both top‐down and bottom‐up methods are then discussed to offer optimum solutions for each specified application scenario. Afterward, emerging magnetic and electronic properties and credit enhancements are launched accompanied with their key advances. Beyond these, the faced challenges and possible directions of future research are also provided, attempting to boost both fundamental physics and device applications based on 2D cobalt telluride.

Nodal line topological superconducting state in quasi-one-dimensional A2Cr3As3 (A=K,Rb,Cs) superconductors

Nodal line topological superconducting state in quasi-one-dimensional A2Cr3As3 (A=K,Rb,Cs) superconductors

V4C3 MXene: a Type-II Nodal Line Semimetal with Potential as High-Performing Anode Material for Mg-Ion Battery.

We have used density functional theory simulations to explore the topological characteristics of a new MXene-like material, V4C3, and its oxide counterpart, assessing their potential as anode materials for Mg-ion batteries. Our research reveals that V4C3 monolayer is a topological type-II nodal line semimetal, protected by time reversal and spatial inversion symmetries. This type-II nodal line is marked by unique drumhead-like edge states that appear either inside or outside the loop circle, contingent upon the edge ending. Intriguingly, even with an increase in metallicity due to oxygen functionalization, the topological features of V4C3 remain intact. Consequently, the monolayer V4C3 has a topologically enhanced electrical conductivity that amplifies further upon oxygen functionalization. During the charging phase, a remarkable storage concentration led to a peak specific capacity of 894.73 mAh g-1 for V4C3, which only decreases to 789.33 mAh g-1 for V4C3O2. When compared to V2C, V4C3 displays a significantly lower specific capacity loss due to functionalization, demonstrating its superior electrochemical properties. Additionally, V4C3 and V4C3O2 exhibit moderate average open-circuit voltages (0.54 V for V4C3 and 0.58 V for V4C3O2) and energy barriers for intercalation migration (ranging between 0.29-0.63 eV), which are desirable for anode materials. Thus, our simulation results support V4C3 potential as an efficient anode material for Mg-ion batteries.

Realizing high-Tc ambient-pressure superconductivity in hole-doped hydride Mg(BH4)2

Hydrogen-based superconductors provide a promising route to the long-sought goal of room-temperature superconductivity (SC), however, ultrahigh pressure required to maintain their structural stability hinders the experimental investigation and potential applications. Here, we propose a novel route to design high-Tc hydride superconductors at ambient pressure by hole doping into previously reported hydrogen storage material Mg(BH4)2. Based on the first-principles calculations, we found that with a moderate hole doping of 0.1 holes per formula unit, the insulator Mg(BH4)2 transforms into the metal accompanied by the emergency of large B–H σ electronic states at the Fermi level (EF), and thus strong electron-phonon coupling SC is obtained with Tc up to ∼ 100 K, and with further increase of hole-doped concentration, the Tc can be promoted to 140 K. Additionally, the topological analysis demonstrates that the hole-doped Mg(BH4)2 has symmetry-protected Dirac nodal lines around the EF, giving rise to the delicate surface states. These findings indicate that Mg(BH4)2 not only provides an ideal candidate to attain high-Tc SC by hole doping at ambient pressure, but also to explore more exotic physics for the coexistence of high-Tc SC and topology.

Validation of a model on the coupling between circular membrane and Helmholtz resonator

Recently, a model was proposed to describe the resonance characteristics of a modified Helmholtz resonator with a circular membrane fitted to one of the cavity walls. The model is based on two equations of motion: 1) One equation for the transverse wave formed on the membrane and 2) the second for the displacement of the air volume in the port of the Helmholtz resonator. When two equations were solved for the displacement of the membrane as a function of the radius, it was shown that, due to the coupling, the resonance frequencies would vary depending on the parameters of the Helmholtz resonator, which may be observed only for the modes with circular nodal lines. In the current study, the proposed model was further validated in a series of measurements under various conditions, and the results were discussed and compared to the predictions of previous models.

High-frequency measurement method of normal-incidence sound absorption coefficient with a square cross-section impedance tube using eight microphones

The authors have proposed a high-frequency measurement method of normal-incidence absorption coefficient with a circular cross-section impedance tube using eight microphones. This method enables measurement at frequencies about three times higher than the conventional two-microphone method. This study investigates the case of using an impedance tube with a square cross-section. Four microphones are placed at intersections of the (2, 2) acoustic mode nodal lines in one cross-section. When the signals of these microphones are summed, the effects of higher-order acoustic modes whose cut-on frequencies are lower than that of the (4, 0) acoustic mode are canceled. In this case, normal-incidence sound absorption coefficients can be measured at four times higher frequency than the conventional one. Numerical and experimental results are presented to demonstrate the validity and feasibility of the method.

Nodal Line Topological Superconducting State in Quasi-One-Dimensional A2Cr3As3 (A = K, Rb, Cs) Superconductors

Nodal Line Topological Superconducting State in Quasi-One-Dimensional A2Cr3As3 (A = K, Rb, Cs) Superconductors

Coexistence of multiple dirac nodal points and nodal lines in two-dimensional carbon nanotube arrays

Seeking for novel fermions in two-dimensional (2D) materials is of practical significance for devices with extraordinary transport properties. In this work, 2D carbon nanotube arrays (CNTAs) formed by ‘fusible’ connection of uniform CNTs are studied based on first-principles calculations. We find the coexistence of multiple Dirac points and diverse nodal lines (including type I, type II, and type III in band crossing modes, and both open and closed in forms) formed by four entangled bands near the Fermi levels. Such kind of coexistence, which can be regarded as the splitting of eight-fold degeneracy or double Dirac nodal lines, is the results of the interaction between the upper and lower surfaces of CNTAs, and leads to the nontrivial arc-like, drumhead-like, and torus edge states in their nanoribbons concurrently. Our study suggests that CNTAs can be excellent platforms to study the entanglements between different states, and excellent candidates for quantum devices.

Angle-resolved photoemission study of NbGeSb with non-symmorphic symmetry

We investigate the electronic structure of NbGeSb with non-symmorphic symmetry. We employ angle-resolved photoemission spectroscopy (ARPES) to observe and identify the bulk and surface states over the Brillouin zone. By utilizing high-energy photons, we identify the bulk Fermi surface and bulk nodal line along the direction X–R, while the Fermi surface of the surface state is observed by using low-energy photons. We observe the splitting of surface bands away from the high-symmetry point X¯ . The density functional theory calculations on bulk and 1 to 5-layer slab models, as well as spin textures of NbGeSb, verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface. These splitted surface bands cross with each other, forming two-dimensional Weyl-like crossings that are protected by mirror symmetry. Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

Topological properties and anomalous transport in van der Waals ferromagnets Fe n GeTe2: a comparative study

Recently synthesized topological van der Waals (vdW) Fe n GeTe2 (n=3,4, and 5) series of compounds have drawn a lot of research interest due to their interesting magnetic properties and anomalous transport behavior. However, understanding the topological aspect of these materials’ electronic band structure is either scant or absent in the literature. In this work, we perform a comparative study of the electronic structure of all three materials to understand their topological properties and their effect on transport properties using the first-principles calculations and to derive the effective tight-binding model for these systems. All three systems exhibit ferromagnetic behavior, and the contribution of various Fe d-orbitals are also studied. Spin-orbit coupling (SOC) causes the degeneracy to be lifted and results in a finite Berry curvature (BC). Finite BC contributes to the intrinsic anomalous Hall conductivity (AHC) and Nernst conductivity (ANC) of these systems. We show that Fe3GeTe2 and Fe5GeTe2 have similar nodal line formations, while Fe4GeTe2 exhibits nodal points close to Fermi energy E F . We calculate AHC (σ xy ) at zero temperature and ANC (α xy ) at room temperature for n = 3, 4 and 5 and find that our values are consistent with transport and magnetic measurement.

High-Performance Hydrogen Evolution Reaction Catalysts in Two-Dimensional Nodal Line Semimetals.

The discipline of topological quantum catalysts (TQCs) is developing due to the emergence of exotic quantum materials and their corresponding catalysts. Although a series of 3D TQCs with different topological signatures are proposed, the emergence of 2D TQCs in 2D topological semimetals is still rarely touched by others. As a typical example, we proposed that the 2D nodal line semimetal Cu2Si monolayer is a superior TQC for hydrogen evolution reaction (HER). Using first-principles calculations, we find that the Cu2Si monolayer exhibits two Γ-centered nodal lines (L1 and L2) in the kz = 0 plane. The Gibbs free energy (ΔGH*) of Cu2Si is as low as 0.195 eV, comparable to that of Pt, and better than other conventional catalysts. Moreover, it is found that changing the position of nodal lines (relative to the Fermi level) under different electron/hole conditions can effectively affect the catalytic activity of HER. Besides Cu2Si, the emergence of high HER performance in other 2D nodal line semimetals, Ti3C2, Cr2S3, ScCl, and CuSe, is also theoretically determined. These results highlight the critical role of nodal lines in studying electrocatalytic mechanisms for TQCs and benefit the seeking of high-performance HER catalysts without noble metals on a 2D scale.