Nodal-line Fermions Research Articles

Growth and electronic structure of the nodal line semimetal in monolayer Cu2Si on Cu(111)

Cu2Si, a single-layer two-dimensional material with a honeycomb structure, has been proposed to have Dirac nodal line fermions. In this study, the synchrotron radiation X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, and angle-resolved photoemission spectroscopy (SR-XPS, SR-UPS, and SR-ARPES) techniques were used to investigate the dynamic process of in situ deposition of single-layer Cu2Si on a Cu(111) crystal surface via molecular beam epitaxy (MBE). Cu2Si existed as a monolayer (ML) alloy, and there were competing mechanisms of distinct chemical states of silicon in different growth periods, according to a detailed examination of the experimental SR-XPS and SR-UPS spectra. Additionally, a weak interaction between the Cu2Si ML and Cu(111) was demonstrated via SR-ARPES and first-principles computations. The unique electronic structure of the Cu2Si ML was not destroyed by either this weak interaction or the disordered silicon produced on the surface during the growth process. The study of the Cu2Si growth kinetics provides a guarantee and a basis for the future exploration of the exotic properties of Cu2Si.

Endless Dirac nodal lines and high mobility in kagome semimetal Ni3In2Se2 : a theoretical and experimental study

Kagome-lattice crystal is crucial in quantum materials research, exhibiting unique transport properties due to its rich band structure and the presence of nodal lines and rings. Here, we investigate the electronic transport properties and perform first-principles calculations for Ni3In2Se2kagome topological semimetal. First-principles calculations of the band structure without the inclusion of spin-orbit coupling (SOC) shows that three bands are crossing the Fermi level (EF), indicating the semi-metallic nature. With SOC, the band structure reveals a gap opening of the order of 10 meV.Z2index calculations suggest the topologically nontrivial natures (ν0;ν1ν2ν3) = (1;111) both without and with SOC. Our detailed calculations also indicate six endless Dirac nodal lines and two nodal rings with aπ-Berry phase in the absence of SOC. The temperature-dependent resistivity is dominated by two scattering mechanisms:s-dinterband scattering occurs below 50 K, while electron-phonon (e-p) scattering is observed above 50 K. The magnetoresistance (MR) curve aligns with the theory of extended Kohler's rule, suggesting multiple scattering origins and temperature-dependent carrier densities. A maximum MR of 120% at 2 K and 9 T, with a maximum estimated mobility of approximately 3000 cm2V-1s-1are observed. Ni3In2Se2is an electron-hole compensated topological semimetal, as we have carrier density of electron (ne) and hole (nh) arene≈nh, estimated from Hall effect data fitted to a two-band model. Consequently, there is an increase in the mobility of electrons and holes, leading to a higher carrier mobility and a comparatively higher MR. The quantum interference effect leading to the two dimensional (2D) weak antilocalization effect (-σxx∝ln(B)) manifests as the diffusion of nodal line fermions in the 2D poloidal plane and the associated encircling Berry flux of nodal-line fermions.

Flat-band and diverse quasi-fermions in Pb10(PO4)6O4

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb10(PO4)6O4, which exhibits remarkable quasi-one-dimensional topological flat-band around the Fermi level. These flat bands predominantly originate from the px/py orbitals of the oxygen molecules chain at the fully-occupied 4e Wyckoff positions and thus can be well-captured by a minimal four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent in Pb10(PO4)6O4 provides an ideal platform for the emergence of various quasi-fermions characterized by different dispersion, degeneracy, and dimensionality. These include a 0D four-fold degenerate Dirac fermion exhibiting quadratic dispersion, a 1D quadratic/linear nodal-line fermion along symmetric k-paths, a 1D hourglass nodal-line (HNL) fermion associated with the Dirac fermion, and a 2D symmetry-enforced nodal surface located on the kz = π plane. Moreover, when considering the weak ferromagnetic order, Pb10(PO4)6O4 transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100 % spin polarization. Our findings reveal the rarely coexistence of flat bands, diverse topological semimetal states and ferromagnetism in Pb10(PO4)6O4, which may provide valuable insights for further exploring the intriguing interplay between superconductivity and exotic electronic states.

First‐Principles Investigation of Electronic and Thermodynamic Properties of Honeycomb CuSe

AbstractIn the realm of materials science, a fascinating class of substances known as topological nodal line semimetals have garnered significant attention. These materials possess distinctive quantum states, characterized by topologically nontrivial conduction and valence bands that intricately intersect with the Fermi level. Such unique band structures give these materials a plethora of surprising properties, including the emergence of flat Landau levels and the appearance of long‐range Coulomb interactions. Notably, certain bulk materials, namely PbTaSe2, ZrSiS, PtSn4, and Cu2Si, exhibit these intriguing topological nodal lines. However, the theoretical investigation pertaining to CuSe and its Dirac nodal line properties remains relatively limited. In this work, we have employed simulations on CuSe to elucidate its distinctive physical properties such as a Dirac matter. There exist Dirac bands and band inversion in the vicinity of Fermi levels, and Fermi surface holds a Horn‐like structure. We pointed out the occurrence of mirror reflection symmetry‐protected Dirac nodal line fermions in copper selenide (CuSe) that make CuSe a candidate for Dirac nodal line fermion started by the Se 4p and Cu 3d orbitals. The nontrivial topological edge states further verify our proposal of the mirror reflection symmetry is broken by spin‐orbit coupling. These findings provide a new perspective that advances our comprehension of the remarkable properties exhibited by these materials, thereby paving the way for the development of high‐speed and low‐dissipation devices in the future.

Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state

Role of effective mass anisotropy in realizing a hybrid nodal-line fermion state

Prediction of nodal-line fermion and phonon-mediated superconductivity in bilayer α-borophene

The electron deficiency of boron allows the formation of a variety of monolayer or few-layer two-dimensional structures (borophenes) with interesting physical properties. Recent experiments have also confirmed that interlayer covalent bonding makes the bilayer structure more stable than the monolayer. In this work based on α-borophene, we propose three free-stranding bilayer structures with dynamic stability. In these three metallic structures, the electronic band crossings around Fermi level form nodal lines. All these structures also exhibit strong electron-phonon couplings. The Bardeen–Cooper–Schrieffer superconducting critical temperature T c of the type-II structure went as high as 28.2 K, which was further improved to 32.0 K by the enhancement effect of Li adatom at the Debye frequency. However, no increase in critical temperature was observed in other Li-doping cases. Specifically, Li intercalation inside the bilayer causes a significant abrupt decrease in the critical temperature of type-I structure. Our results indicated that the bilayer borophene would be an ideal platform for the coexistence of topological electronic states and superconducting states.

Hybrid nodal-chain semimetal with emergent flat band in MgCaN2

The distinct over-tiltings of band crossings in topological semimetals generate the type-I and type-II classification of Dirac/Weyl and nodal-line fermions, accompanied by exotic electronic and magnetic transport properties. In this work, we propose a concept of hybrid nodal-chain semimetal (NCSM), which is identified by linked type-I and type-II nodal rings (NRs) and hosts inevitable flat band. Using first-principles calculations and structure search technique, a new ternary nitride MgCaN2 is proposed as the first candidate to realize a novel 3D hybrid NCSM state. Remarkably, flat band is emergent along specific direction as a characteristic signature of such a hybrid nodal-chain, thus offering a platform to explore the interplay between topological states and flat bands. By analyzing the mirror Z2 topological invariant and developing a low-energy effective model, we unveil the physical origin of the hybrid nodal-chain structure with multiple-mirror protected mechanism. Moreover, when the linked NRs are projected onto the (010) and (001) surfaces, considerable drumhead-like topological surface states can be illustrated with unique connection patterns. These results expand our understanding of NCSMs from significant band tilting effects and provide a new candidate on realizing hybrid nodal-chain fermion for further theoretical and experimental investigations.

A two-dimensional borophene monolayer with ideal Dirac nodal-line fermions.

As a relatively new member of two-dimensional materials, borophene has gained huge interest over the past years, especially in the field of discovering new topological materials, such as Dirac nodal line semimetals. Here, based on first-principles calculations, for the first time, we find a completely flat borophene monolayer (named χ2/9) with ideal Dirac nodal line states around the Fermi level. A tight-binding model using the Slater-Koster approach is proposed to demonstrate that the unique electronic feature of χ2/9 that mainly originated from the first-nearest neighbor interactions of the pz orbitals of boron. According to our symmetry analysis, the Dirac nodal line in χ2/9 is guaranteed by the out-of-plane mirror or C2 rotational symmetry and the negligible pz orbital coupling. The chemical bonding analysis reveals the rare electronic properties of this material, which can be attributed to the multicentered π bonds.

Quantum transport evidence of isolated topological nodal-line fermions

Anomalous transport responses, dictated by the nontrivial band topology, are the key for application of topological materials to advanced electronics and spintronics. One promising platform is topological nodal-line semimetals due to their rich topology and exotic physical properties. However, their transport signatures have often been masked by the complexity in band crossings or the coexisting topologically trivial states. Here we show that, in slightly hole-doped SrAs3, the single-loop nodal-line states are well-isolated from the trivial states and entirely determine the transport responses. The characteristic torus-shaped Fermi surface and the associated encircling Berry flux of nodal-line fermions are clearly manifested by quantum oscillations of the magnetotransport properties and the quantum interference effect resulting in the two-dimensional behaviors of weak antilocalization. These unique quantum transport signatures make the isolated nodal-line fermions in SrAs3 desirable for novel devices based on their topological charge and spin transport.

Fabrication of honeycomb AuTe monolayer with Dirac nodal line fermions

Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions (DNLFs). Here, we successfully synthesized a gold telluride (AuTe) monolayer by direct tellurizing an Au(111) substrate. Low energy electron diffraction measurements reveal that it is (2×2) AuTe layer stacked onto (3×3) Au(111) substrate. Moreover, scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure. Scanning transmission electron microscopy reveals that it is a single-atom layer. In addition, first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry, which is validated by angle-resolved photoemission spectra. Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.

Two-dimensional tetragonal ZnB: A nodalline semimetal with good transport properties

Nodal-line semimetals have become a research hot-spot due to their novel properties and great potential application in spin electronics. It is more challenging to find 2D nodal-line semimetals that can resist the spin–orbit coupling (SOC) effect. Here, we predict that 2D tetragonal ZnB is a nodal-line semimetal with great transport properties. There are two crossing bands centered on the S point at the Fermi surface without SOC, which are mainly composed of the p xy orbitals of Zn and B atoms and the p z orbitals of the B atom. Therefore, the system presents a nodal line centered on the S point in its Brillouin zone (BZ). And the nodal line is protected by the horizontal mirror symmetry Mz . We further examine the robustness of a nodal line under biaxial strain by applying up to −4% in-plane compressive strain and 5% tensile strain on the ZnB monolayer, respectively. The transmission along the a direction is significantly stronger than that along the b direction in the conductive channel. The current in the a direction is as high as 26.63 μA at 0.8 V, and that in the b direction reaches 8.68 μA at 0.8 V. It is interesting that the transport characteristics of ZnB show the negative differential resistance (NDR) effect after 0.8 V along the a (b) direction. The results provide an ideal platform for research of fundamental physics of 2D nodal-line fermions and nanoscale spintronics, as well as the design of new quantum devices.

Spin-triplet superconductivity in Weyl nodal-line semimetals

Topological semimetals are three dimensional materials with symmetry-protected massless bulk excitations. As a special case, Weyl nodal-line semimetals are realized in materials having either no inversion or broken time-reversal symmetry and feature bulk nodal lines. The 111-family, including LaNiSi, LaPtSi and LaPtGe materials (all lacking inversion symmetry), belongs to this class. Here, by combining muon-spin rotation and relaxation with thermodynamic measurements, we find that these materials exhibit a fully-gapped superconducting ground state, while spontaneously breaking time-reversal symmetry at the superconducting transition. Since time-reversal symmetry is essential for protecting the normal-state topology, its breaking upon entering the superconducting state should remarkably result in a topological phase transition. By developing a minimal model for the normal-state band structure and assuming a purely spin-triplet pairing, we show that the superconducting properties across this family can be described accurately. Our results demonstrate that the 111 materials reported here provide an ideal test-bed for investigating the rich interplay between the exotic properties of Weyl nodal-line fermions and unconventional superconductivity.

Threefold Fermions, Weyl Points, and Superconductivity in the Mirror Symmetry Lacking Semiconductor TlCd2Te4.

The topological phase transition and exotic quasiparticles in materials have attracted much attention because of their potential in spintronics and mimic of elementary particles. Especially, great research interest has been paid to search for the Weyl fermions in solid-state physics. By using first-principles calculations, we predict that the multinary semiconductor alloy exhibits threefold fermions and nodal-line fermions, which are protected by the improper rotational symmetry. Moreover, owing to the lack of inversion and mirror symmetries, the threefold fermions split into Weyl fermions when the spin-orbit coupling is included. The chiral charge of Weyl points and the time-reversal topological invariant are investigated. The topological surface states, spin texture, and electron-phonon coupling analysis are presented. Our study demonstrates as a good platform to understand topological phase transitions as well as possible coexistance of topological Weyl semimetal and superconductivity in one single material.

Theoretical realization of two-dimensional half-metallicity and fully spin-polarized multiple nodal-line fermions in monolayer PrOBr

Two-dimensional (2D) half metallicity and topological aspects of matter are the focus of current research because of the promising applications in nanoscale spintronics and quantum electronics. In this work, we report the perfect combination of half-metallic properties and electronic topological properties in single 2D phase, namely, the PrOBr monolayer. The material only possesses conducting electrons in the spin-up channel, while it shows a large insulating gap of 3.5 eV in the spin-down channel with the Curie temperature as high as 423 K. In the conducting spin channel, it exhibits multiple band crossings, which can surprisingly realize the coexistence of fully spin-polarized open/closed, and type-I/type-II/hybrid-type nodal lines. The coexistence of so many nodal line states has been neither identified in 2D materials nor identified in half metals before. The protection mechanism, the spin-orbit coupling impact, and the effective models for the nodal lines have been clarified. Our results suggest that the PrOBr monolayer is a good electronic material with (i) 2D half metallicity; (ii) multiple nodal lines of 100% spin polarization.

Type-II nodal line fermions in the Z2 topological semimetals AV6Sb6 ( A =K, Rb, and Cs) with a kagome bilayer

The recently discovered layered kagome metals AV3Sb5 (A=K, Rb, and Cs) attract intensive interest due to their intertwining with superconductivity, charge-density-wave state, and nontrivial band topology. In this work, we show by first-principles calculations and symmetry arguments that unconventional type-II Dirac nodal line fermions close to the fermi level are present in another latest class of experimentally synthesized kagome compounds AV6Sb6 (A=K, Rb, and Cs). These compounds possess a unique kagome (V3Sb)2 bilayer that dominates their electronic and topological properties, instead of the kagome V3Sb monolayer in AV3Sb5. Crystal symmetry guarantees that the type-II Dirac nodal lines with quantized Berry phase lie in reflection-invariant planes of the Brillouin zone. We further reveal that the type-II Dirac nodal lines remain nearly intact in the presence of spin-orbital coupling and can be categorized as a Z2 classification. The findings establish AV6Sb6 as a class of new fascinating prototypes, which will extend the knowledge of interplay between unconventionally topological fermions and exotic quantum ordered states in kagome systems.

Weyl Monoloop Semi-Half-Metal and Tunable Anomalous Hall Effect.

Nodal monoloop, enjoying the cleanest scenario with a single loop, is recognized as the basic building block of intricate linked loops including chains, nets, and knots. Here, we explore the interplay of magnetic ordering and band topology in one system by introducing a brand-new quantum state, referred to as Weyl monoloop semi-half-metal, which is characterized by a single loop at the Fermi level stemming from the same spin channel. Such a nodal line Fermion, yielding 100% spin polarization, is protected by mirror () symmetry. As a prominent example, a realistic rutile-type metal fluorides LiV2F6 achieves the hitherto unmaterialized state, featuring fully spin-polarized ultraflat surface states. More interestingly, LiV2F6 has a "soft" ferromagnetic property, which is one of the desired systems to control the anomalous Hall effect by rotating the magnetization direction. Our findings offer a promising candidate for exploring the topology and magnetism with intriguing effects.

Honeycomb AgSe Monolayer Nanosheets for Studying Two-dimensional Dirac Nodal Line Fermions

Honeycomb AgSe Monolayer Nanosheets for Studying Two-dimensional Dirac Nodal Line Fermions

Band engineering of honeycomb monolayer CuSe via atomic modification* *Project supported by the National Key Research & Development Projects of China (Grant No. 2016YFA0202300), the National Natural Science Foundation of China (Grant No. 61888102), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB30000000).

Two-dimensional monolayer copper selenide (CuSe) has been epitaxially grown and predicted to host the Dirac nodal line fermion (DNLF). However, the metallic state of monolayer CuSe inhibits the potential application of nanoelectronic devices in which a band gap is needed to realize on/off properties. Here, we engineer the band structure of monolayer CuSe which is an analogue of a p-doped system via external atomic modification in an effort to realize the semiconducting state. We find that the H and Li modified monolayer CuSe shifts the energy band and opens an energy gap around the Fermi level. Interestingly, both the atomic and electronic structures of monolayer CuHSe and CuLiSe are very different. The H atoms bind on top of Se atoms of monolayer CuSe with Se–H polar covalent bonds, annihilating the DNLF band of monolayer CuSe dominated by Se orbitals. In contrast, Li atoms prefer to adsorb at the hexagonal center of CuSe, preserving the DNLF band of monolayer CuSe dominated by Se orbitals, but opening band gaps due to a slight buckling of the CuSe layer. The realization of metal-to-semiconductor transition from monolayer CuSe to CuXSe (X = H, Li) as revealed by first-principles calculations makes it possible to use CuSe in future electronic devices.

Evidence of topological nodal lines and surface states in the centrosymmetric superconductor SnTaS2

The discovery of signatures of topological superconductivity in superconducting bulk materials with topological surface states has attracted intensive research interest recently. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we demonstrate the existence of topological nodal-line states and drumheadlike surface states in centrosymmetric superconductor $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_{2}$, which is a type-II superconductor with a critical transition temperature of about 3 K. The valence bands from Ta $5d$ orbitals and the conduction bands from Sn $5p$ orbitals cross each other, forming two nodal lines in the vicinity of the Fermi energy without the inclusion of spin-orbit coupling (SOC), protected by the spatial-inversion symmetry and time-reversal symmetry. The nodal lines are gapped out by SOC. The drumheadlike surface states, the typical characteristics in nodal-line semimetals, are quite visible near the Fermi level. Our findings indicate that $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_{2}$ offers a promising platform for exploring the exotic properties of the topological nodal-line fermions and helps in the study of topological superconductivity.

The low-energy electron band structure of a two-dimensional Dirac nodal-line semimetal grown on a silicon surface

The low-energy electron band structure of Cu $$_2$$ Si on Si(111) has been investigated using angle-resolved photoemission spectroscopy. Cu $$_2$$ Si exhibits two Dirac nodal-lines, stemming from the crossing of one electron-pocket with two hole-pockets, that are protected by mirror reflection symmetry. When Cu $$_2$$ Si is placed on Si(111), the hole-pockets and their satellite bands due to the quasi- $$5\times 5$$ periodicity are clearly observed whereas the electron-pocket is observed with very weak spectral intensity. Interestingly, close to the Fermi energy, the hole-pockets exhibit almost linear energy-momentum dispersion when their spectral width is also linearly proportional to energy. These findings indicate that Cu $$_2$$ Si on Si(111) can host Dirac nodal-line fermions, of which low-energy excitations might depart from those of the conventional Fermi liquid.