Tight-binding Analysis Research Articles

Realization of Yin–Yang kagome bands and tunable quantum anomalous Hall effect in monolayer V3Cl6

Kagome materials serve as crucial platforms for investigating the quantum anomalous Hall effect (QAHE) due to the presence of kagome bands in their electronic structures. However, despite the theoretical predictions being proposed, kagome band material realizations have been limited. In this work, through tight-binding (TB) model analysis, by setting the nearest-neighbor hopping integrals with opposite signs, we propose a Yin–Yang kagome band structure characterized by two stable enantiomorphic kagome bands. Furthermore, we design a monolayer V3Cl6 to confirm the TB model. Three V atoms are located in different coordination environments in V3Cl6, so opposite signs of the hopping integrals between two of their orthogonal d orbitals can be achieved, which is the key to realize Yin–Yang kagome band structures. The calculated band structures obtained from first principles are consistent with those from the TB model. Additionally, we find that the two enantiomorphic flat bands in monolayer V3Cl6 possess opposite Chern number after spin–orbit coupling is considered, which can also be confirmed from symmetry index analysis. The Chern numbers as well as the topological properties can be modulated by doping hole or adjusting the magnetization directions, so the QAHE can be tuned in monolayer V3Cl6. Our results provide a practicable pathway for realizing Yin–Yang kagome band structures and achieving tunable QAHE in them.

Search for an antiferromagnetic Weyl semimetal in (MnTe) m (Sb2Te3) n and (MnTe) m (Bi2Te3) n superlattices

The interaction between topology and magnetism can lead to novel topological materials including Chern insulators, axion insulators, and Dirac and Weyl semimetals. In this work, a family of van der Waals layered materials using MnTe and Sb2Te3 or Bi2Te3 superlattices as building blocks are systematically examined in a search for antiferromagnetic Weyl semimetals, preferably with a simple node structure. The approach is based on controlling the strength of the exchange interaction as a function of layer composition to induce the phase transition between the topological and the normal insulators. Our calculations, utilizing a combination of first-principles density functional theory and tight-binding analyses based on maximally localized Wannier functions, clearly indicate a promising candidate for a type-I magnetic Weyl semimetal. This centrosymmetric material, Mn10Sb8Te22 (or (MnTe) m (Sb2Te3) n with m = 10 and n = 4), shows ferromagnetic intralayer and antiferromagnetic interlayer interactions in the antiferromagnetic ground state. The obtained electronic bandstructure also exhibits a single pair of Weyl points in the spin-split bands consistent with a Weyl semimetal. The presence of Weyl nodes is further verified with Berry curvature, Wannier charge center, and surface state (i.e. Fermi arc) calculations. Other combinations of the MnSbTe-family materials are found to be antiferromagnetic topological or normal insulators on either side of the Mn:Sb ratio, respectively, illustrating the topological phase transition as anticipated. A similar investigation in the homologous (MnTe) m (Bi2Te3) n system produces mostly nontrivial antiferromagnetic insulators due to the strong spin–orbit coupling. When realized, the antiferromagnetic Weyl semimetals in the simplest form (i.e. a single pair of Weyl nodes) are expected to provide a promising candidate for low-power spintronic applications.

Semimetallic state transition in Two-Dimensional carbon nitride covalent networks and enhanced electrocatalytic activity for nitrate to ammonia conversion

Single-atom catalysts (SACs), due to their maximum atomic utilization rate, show tremendous potential for application in the electrocatalytic synthesis of ammonia from nitrate. Yet, the development of superior supports that preserve the high selectivity, activity, and stability of SACs remains an imperative challenge. In this work, based on first-principles calculations and tight-binding (TB) model analysis, a new two-dimensional (2D) carbon nitride monolayer, C7N6, is proposed. The C7N6 structure exhibits a strong covalent network, with dynamical, thermal, and mechanical stability. Surprisingly, the structural transition from C9N4 to C7N6 corresponds to a semimetallic state transition. Further symmetry analysis unveils that the Dirac states in C7N6 are protected by space–time inversion symmetry, and the physical origin of the Dirac cone was confirmed using the TB model. Additionally, a non-zero Z2 invariant and significant topological edge states demonstrate its topologically nontrivial nature. Considering the excellent structural and topological properties of C7N6, a three-step screening strategy is designed to identify eligible SACs for electrochemical nitrate reduction reaction (NO3RR), and Ti@C7N6 is identified as possessing the best activity, with the last proton-electron coupling step *NH2→*NH3 being the potential-determining step (PDS), for which the limiting potential is 0.48 V. Moreover, a free energy diagram shows that the *NOH reaction pathway is energetically preferred on Ti@C7N6, and ab initio molecular dynamics (AIMD) calculations at 500 K confirm its good thermal stability. Our study not only provides excellent CN-based support material but also offers theoretical guidance for constructing highly active and selective SACs for nitrate reduction.

Tunable Colossal Anomalous Hall Conductivity in Half-Metallic Material Induced by d-Wave-Like Spin-Orbit Gap.

The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function in spin-torque devices and advanced magnetic sensors. Among systems with near-half-metallicity and broken time-reversal symmetry, cobalt disulfide (CoS2) has proven to be a material capable of significantly enhancing its AHC. In this study, the AHC of CoS2 is empirically assessed by manipulating the chemical potential through Fe- (hole) and Ni- (electron) doping. The primary mechanism underlying the colossal AHC is identified through the application of density functional theory and tight-binding analyses. The main source of this substantial AHC is traced to four spin-polarized massive Dirac dispersions in the kz = 0 plane of the Brillouin zone, located slightly below the Fermi level. In Co0.95Fe0.05S2, the AHC, which is directly proportional to the momentum-space integral of the Berry curvature (BC), reached a record-breaking value of 2507 Ω-1cm-1. This is because the BCs of the four Dirac dispersions all exhibit the same sign, a consequence of the d-wave-like spin-orbit coupling among spin-polarized egorbitals.

Engineering Layertronics in Two-Dimensional Ferromagnetic Multiferroic Lattice.

Layertronics, rooted in the layer Hall effect (LHE), is an emerging fundamental phenomenon in condensed matter physics and spintronics. So far, several theoretical and experimental proposals have been made to realize LHE, but all are based on antiferromagnetic systems. Here, using symmetry and tight-binding model analysis, we propose a general mechanism for engineering layertronics in a two-dimensional ferromagnetic multiferroic lattice. The physics is related to the band geometric properties and multiferroicity, which results in the coupling between Berry curvature and layer degree of freedom, thereby generating the LHE. Using first-principles calculations, we further demonstrate this mechanism in bilayer (BL) TcIrGe2S6. Due to the intrinsic inversion and time-reversal symmetry breakings, BL TcIrGe2S6 exhibits multiferroicity with large Berry curvatures at both the center and corners of the Brillouin zone. These Berry curvatures couple with the layer physics, forming the LHE in BL TcIrGe2S6. Our work opens a new direction for research on layertronics.

Layer-Polarized Anomalous Hall Effects from Inversion-Symmetric Single-Layer Lattices.

In the field of physics and materials science, the discovery of the layer-polarized anomalous Hall effect (LP-AHE) stands as a crucial development. The current research paradigm is rooted in topological or inversion-asymmetric valleytronic systems, making such a phenomenon rather rare. In this work, a universal design principle for achieving the LP-AHE from inversion-symmetric single-layer lattices is proposed. Through tight-binding model analysis, we demonstrate that by stacking into antiferromagnetic van der Waals bilayer lattices, the coupling physics between PT symmetry and vertical external bias can be realized. This coupling reveals the previously neutralized layer-locked Berry curvature, compelling the carriers to move in a specific direction within a given layer, thereby realizing the LP-AHE. Intriguingly, the chirality of the LP-AHE can be effectively switched by modulating the direction of vertical external bias. First-principles calculations validate this mechanism in bilayer T-FeCl2 and MnPSe3. Our results pave the way for new explorations of the LP-AHE.

Topology and giant circular dichroism of enantiomorphic Kagome bands in a designed covalent organic framework.

Covalent organic frameworks (COFs) are an emerging class of crystalline organic materials that have shown potential to be a new physical platform. In this work, a designed COF named AB-COF, which has novel enantiomorphic Kagome bands, is proposed and a feasible route to synthesize it is given. Via a combination of first-principles calculations and tight-binding analysis, we investigate the electronic structures and the phase interference of the COF. It becomes topologically nontrivial when doping one iodine atom in a unit cell. The Berry curvatures of the valence band (VB) and conduction band (CB) of the iodine-doped AB-COF show opposite values and different distributions. This provides an opportunity to study the new mechanism of circular dichroism from the different Berry curvatures of the VB and CB. Surprisingly, the circular-dichroism dissymmetry factor of AB-COF reaches a theoretical maximum value, and the oscillator strength data are in agreement with this result. When two iodine atoms are doped in a unit cell, the Berry curvatures of the VB and CB also have different values, but with more symmetry and similar distributions. This behavior enhances the circular dichroism with a wider range of dissymmetric absorption, and the circular dichroism dissymmetry factor also reaches its theoretical maximum value.

Enantiomorphic kagome bands in a two-dimensional covalent organic framework with non-trivial magnetic and topological properties.

The kagome lattice is one of the most intriguing topics to study. It has a frustrated flat band touching a set of Dirac bands and can possess various promising properties, such as ferromagnetism, superconductivity, and a non-trivial topology. Covalent organic frameworks (COFs) are a rare type of inorganic material, however, they can provide a platform for generating certain required lattices. Based on first-principles density functional theory calculations, we show that a newly synthesized two-dimensional COF named COF-SH has novel enantiomorphic kagome bands, which include two sets of flat bands touching the Dirac bands around the Fermi level. The Bloch wave of the flat-valence band at the K-point shows the kagome nature of the phase interference. Under charge doping, the COF-SH exhibits a ferromagnetic ground state. Moreover, when COF-SH is doped with iodine atoms, a sizable gap in the system is opened between the flat bands and the Dirac bands due to the spin-orbit coupling (SOC) effect. Meanwhile, the spin degeneracy is lifted since the organic layer loses electrons due to the oxidizing property of iodine. In addition, our tight-binding analysis with the SOC effect shows that the flat valence band separates from the Dirac bands and holds a nonzero Chern number. Consequently, this I-doped COF can give rise to a quantum anomalous Hall effect.

Atypical breathing driven two-dimensional valley multiferroicity.

Valley multiferroicity, coupled with ferro-valleytricity and primary ferroicities in a single phase, is of fundamental significance in condensed-matter physics and materials science, as it provides a convenient route to reverse the anomalous valley Hall (AVH) effect. Current research in this field focuses mainly on ferromagnetic ferro-valleytricity, whereas ferroelectric ferro-valleytricity is seldom explored. Here, using symmetry arguments and tight-binding model analysis, we report a novel mechanism of coupling ferro-valleytricity with ferroelectricity, i.e., single-phase valley multiferroicity, in a two-dimensional magnetic lattice. This mechanism correlates to the atypical breathing nature of the magnetic lattice. Importantly, the valley physics, associated with Berry curvature, can be reversed under a ferroelectric transition, thereby guaranteeing the ferroelectrically reversible AVH effect. The underlying physics are discussed in detail. Based on first-principles calculations, we further confirm valley multiferroicity in a real 2D magnetic material of single-layer Gd2CO2. The explored phenomena and mechanism are not only useful for fundamental research in valley multiferroics but also enable a wide range of applications in nanodevices.

Computational Modeling, Simulation and Tight–Binding Analysis of Electronic Characteristics of Defective Germanene Nanoribbons for Future Applications of High Sensitivity Ge-Based Nanosensors

In this research, the electronic characteristics of germanene sheet and nanoribbons using the computational modeling, simulation and tight binding approximation are investigated. Our analysis is focused on the pristine sheet of germanene as well as defective monolayer. The obtained results show that applying the Stone–Wales defect into the germanene monolayer changes the energy band structure. The E-k curves around the Dirac point are no longer linear, in which a band gap is opened, and the Fermi velocity is reduced. Furthermore, the main parameters such as density of states, carrier concentration in degenerate and non-degenerate limits, carrier effective mass, conductance and AC conductivity of germanene are analytically modeled with the inclusion of the spin–orbit coupling effect, temperature and ribbon width. Obtained results demonstrate that the inclusion of the spin–orbit coupling makes a small splitting of the energy levels and creating a small band gap. Finally, the Tight binding and computational values are compared with our simulation results and available data, and a rational agreement is reported in terms of trend and value. The findings of this study provide theoretical reference for the design of germanene-based nanosensors and optoelectronic devices.

Penta-MN8 family: First realization of type-5 pentagonal tessellation in 2D hexagonal crystals with intriguing properties

Tessellation of the Euclidean plane by congruent pentagons has long been of great interest. However, periodic pentagonal patterns realized in crystallography reported so far are limited to type-2 or type-4 tiling in typical square lattices. Based on the recently synthesized N18 macrocycles together with Hückel aromaticity and 18-electron rules, we design a family of pentagonal metal polynitrides, penta-MN8 (M = Mg, Ca, Sr, Ba; Sn, Pb; Cd; Mo, W), the first materials realization of type-5 mathematical pattern with novel pentagonal tiles in 2D hexagonal lattices. The penta-MN8 family exhibits rich stable phases (γ, α/α′, and β) and diverse Poisson's ratios ranging from 0.299 to -0.488. Among these nitrogen-richest monolayer nitrides hitherto, penta-MgN8 possesses firm stability up to 700 K and under low pressure originating from unique aromaticity over the polymeric nitrogen network, which could be synthesized under ∼50 GPa as confirmed by global structure search. Moreover, penta-MgN8 exhibits a fully flat band near Fermi level over the whole 2D Brillouin zone, deriving from the combination of pentagonal pattern and hexagonal lattice as verified with tight-binding model analysis. Such electronic structures fill in the blank of clear kagome flat bands in known kagome nitrides and pentagon-based materials, resulting in very heavy fermions with huge effective mass (55.7 m0) that are favorable to achieve quantum zero-field Wigner crystals. Our work presents a new pentagonal-materials class with unprecedented coordination, lattice symmetry, and physical properties compared to existing pentagon-based systems, which makes a breakthrough in exploring the materials realization of the mathematical models for pentagonal tessellation.

Realization of a Two-Dimensional Checkerboard Lattice in Monolayer Cu2N

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of the checkerboard lattice in monolayer Cu2N. Experimentally, monolayer Cu2N can be realized in the well-known N/Cu(100) and N/Cu(111) systems that were previously mistakenly believed to be insulators. Combined angle-resolved photoemission spectroscopy measurements, first-principles calculations, and tight-binding analysis show that both systems host checkerboard-derived hole pockets near the Fermi level. In addition, monolayer Cu2N has outstanding stability in air and organic solvents, which is crucial for further device applications.

Realization of flat bands by lattice intercalation in kagome metals

Recently there has been intense interest in kagome metals, which are expected to host flat bands (FBs). However, the observed ``FBs'' are not flat over the whole two-dimensional Brillouin zone and overlap strongly with other bands. In fact, the FB does not truly exist in a default $d$-orbital kagome lattice, and the conditions for its existence in kagome metals are unknown. Here, based on tight-binding model analyses of the interplay between orbital and lattice symmetry, we establish such conditions. We show that for a single $d$-orbital kagome lattice assuming large crystal field splitting (CFS), only the ${d}_{{z}^{2}}$ orbital gives rise to a FB, while ${d}_{xy}, {d}_{{x}^{2}\ensuremath{-}{y}^{2}}, {d}_{xz}$, and ${d}_{yz}$ orbitals can only produce a FB with a rotated $d$-orbital basis so that they conform with the underlying kagome lattice symmetry. Most importantly, we demonstrate that both conditions of $d$-orbital rotation and large CFS can be ideally satisfied by intercalating the kagome lattice with a hexagonal sublattice without disrupting the destructive interference of FB wave function. Furthermore, we propose layered metalorganic frameworks as promising candidate kagome metals to realize FBs.

Field-controlled quantum anomalous Hall effect in electron-doped CrSiTe3 monolayer

We report Chern insulating phases emerging from a single layer of layered chalcogenide CrSiTe3, a transition metal trichacogenides (TMTC) material, in the presence of charge doping. Due to strong hybridization with Te p orbitals, the spin-orbit coupling effect opens a finite band gap, leading to a nontrivial topology of the Cr eg conduction band manifold with higher Chern numbers. Our calculations show that quantum anomalous Hall effects can be realized by adding one electron in a formula unit cell of Cr2Si2Te6, equivalent to electron doping by 2.36 × 1014 cm−2 carrier density. Furthermore, the doping-induced anomalous Hall conductivity can be controlled by an external magnetic field via spin-orientation-dependent tuning of the spin-orbit coupling. In addition, we find distinct quantum anomalous Hall phases employing tight-binding model analysis, suggesting that CrSiTe3 can be a fascinating platform to realize Chern insulating systems with higher Chern numbers.

Tight-binding analysis of the effect of strain on the band structure of GaN

The effects of strain on the band structure of GaN are investigated by using an empirical tight-binding method. The impacts on its bandgap, carrier effective mass, and group velocity are discussed. By analyzing the orbital components at the top of the valence band, the cause of the variation of the band structure including effective-mass exchange is discussed. Analysis of the average group velocity indicates that tensile uniaxial or compressive biaxial strain may be beneficial for achieving higher breakdown voltage in vertical GaN devices due to the smaller group velocity of the valence band. For the same reason, we also predict higher breakdown voltages due to tensile biaxial strain for horizontal devices.

Topological properties of MoP[formula omitted]N[formula omitted] (x = 0, 0.25, 0.5, 0.75, 1) compounds: A density functional approach

Triply Degenerate Point (TDP) fermions in tungsten–carbide-type materials such as MoP which represent new topological states of quantum matter, have generated great interest recently. However, the TDPs in these materials are found to be far below the Fermi level (∼ −1.5eV) leading to the TDP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically investigate the existence of TP fermions with TDPs close to the Fermi level in MoN, which has the same structure as MoP, and the ternary MoP1−xNx ordered alloys which their crystal structure is defined by replacing P atoms by N atoms in MoP compound. The topological properties of MoP1−xNx (x = 0, 0.25, 0.5, 0.75, 1) ordered alloys are systematically investigated by combining first-principles calculations and Wannier tight-binding analysis. The obtained Wannier Charge Centers (WCCs) are applied to calculate the topological invariant Z2 number. Our calculations show that hexagonal MoP, MoP0.75N0.25, MoP0.25N0.75, and MoN compounds are topological semimetals hosting triply degenerate nodal points resulting from band crossing between degenerate and nondegenerate bands along the high-symmetry directions of the Brillouin Zone, being protected by crystalline symmetries. Among these compounds, the triple degenerate points in MoP0.75N0.25 are much closer to the Fermi level. MoP0.75N0.25 hosts some points slightly above (42 meV, 73 meV and 87 meV) the Fermi energy. On the other hand, our ab initio calculations suggest that the MoP0.5N0.5 compound with orthorhombic structure does not host any triple degenerate point. It hosts a multitude of topological features including Weyl Points and nodal lines. The calculations indicate that these nodal lines are located in the vicinity of Fermi level.

Flat optical conductivity in the topological kagome magnet TbMn6Sn6

Kagome magnet TbMn$_6$Sn$_6$ is a new type of topological material that is known to support exotic quantum magnetic states. Experimental work has identified that TbMn$_6$Sn$_6$ hosts Dirac electronic states that could lead to topological and Chern quantum phases, but the optical response of the Dirac fermions of TbMn$_6$Sn$_6$ and its properties remain to be explored. Here, we perform optical spectroscopy measurement combined with first-principles calculations on single-crystal sample of TbMn$_6$Sn$_6$ to investigate the associated exotic phenomena. TbMn$_6$Sn$_6$ exhibits frequency-independent optical conductivity spectra in a broad range from 1800 to 3000 cm$^{-1}$ (220-370 meV) in experiments. The theoretical band structures and optical conductivity spectra are calculated with several shifted Fermi energy to compare with the experiment. The theoretical spectra with 0.56 eV shift for Fermi energy are well consistent with our experimental results. Besides, the massive quasi-two-dimensional (quasi-2D) Dirac bands, which have linear band dispersion in $k_x$-$k_y$ plane and no band dispersion along the $k_z$ direction, exist close to the shifted Fermi energy. According to tight-binding model analysis, the quasi-2D Dirac bands give rise to a flat optical conductivity, while its value is smaller than, about one tenth of, that from the calculations and experiments. It indicates that the other trivial bands also contribute to the flat optical conductivity.

Engineering topological states in a two-dimensional honeycomb lattice.

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr3, CrCl3, and VBr3 monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr3), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.

Understanding the complex electronic structure of Mg3Sb2 and the effect of alloying through first-principles tight-binding models

The complex chemical bonding in Mg3Sb2 includes interactions beyond the Mg s–Sb p ones, as revealed by first-principles tight-binding analysis.

Spontaneous Valley Polarization in a Ferromagnetic Fe(OH)2 Monolayer

At present, creating sizable spontaneous valley polarization is at the center of the study of valleytronics, which, however, is still a huge challenge. In this work, we determined that the ferromagnetic Fe(OH)2 monolayer of the hexagonal lattice is a highly appealing candidate for valleytronics by using first-principles calculations in conjunction with tight-binding model analysis. In light of the simultaneous inversion symmetry breaking and time-reversal symmetry breaking, we illustrated that the strong spin-orbit coupling and robust ferromagnetic exchange interaction cause a spontaneous valley polarization as large as 67 meV for Fe(OH)2, indicative of room-temperature application. In addition, the physics of valley-selective circular dichroism, spin/valley Hall effects, and topological phase transition were also discussed.