Surface Fermi Arcs Research Articles

Fermi Arcs and DC Transport in Nanowires of Dirac and Weyl Semimetals

AbstractThe transport properties and electron states in cylinder nanowires of Dirac and Weyl semimetals are studied paying special attention to the structure and properties of the surface Fermi arcs. The latter make the electric charge and current density distributions in nanowires strongly nonuniform as the majority of the charge density is accumulated at the surface. It is found that a Weyl semimetal wire also supports a magnetization current localized mainly at the surface because of the Fermi arcs contribution. By using the Kubo linear response approach, the direct current (DC) conductivity is calculated and it is found that its spatial profile is nontrivial. By explicitly separating the contributions of the surface and bulk states, it is shown that when the electric chemical potential and/or the radius of the wire is small, the electron transport is determined primarily by the Fermi arcs and the electrical conductivity is much higher at the surface than in the bulk. Due to the rise of the surface‐bulk transition rate, the relative contribution of the surface states to the total conductivity gradually diminishes as the chemical potential increases. In addition, the DC conductivity at the surface demonstrates noticeable peaks when the Fermi level crosses energies of the surface states.

Type-II Dirac states in full Heusler compounds XInPd2 ( X = Ti, Zr, and Hf)

We predict three full Heusler compounds XInPd2 (X = Zr, Hf and Ti) to be potential candidates for type-II Dirac semimetals. The crystal symmetry of these compounds have appropriate chemical environment with a unique interplay of inversion, time reversal and mirror symmetry. These symmetries help to give six pairs of type-II Dirac nodes on the C_4 rotation axis, closely located at/near the Fermi level. Using first principle calculations, symmetry arguments and crystal field splitting analysis, we illustrate the occurrence of such Dirac nodes in these compounds. Bulk Fermi surfaces have been studied to understand the Lorentz symmetry breaking and Lifshitz transition (LT) of Fermi surfaces. Bulk nodes are projected on the (001) and (111) surfaces which form the surface Fermi arcs, that can further be detected by probes such as angle resolved photo-emission and scanning tunneling spectroscopy. By analyzing the evolution of arcs with changing chemical potential, we prove the fragile nature and the absence of topological protection of the Dirac arcs. Our predicted compounds overcome the limitations of the previously reported PtTe2 class of compounds.

Strong bulk photovoltaic effect in chiral crystals in the visible spectrum

Structurally chiral materials hosting multifold fermions with large topological number have attracted considerable attention because of their naturally long surface Fermi arcs and bulk quantized circular photogalvanic effect (CPGE). Multifold fermions only appear in metallic states, and therefore, most studies so far have only focused on the semimetals in compounds with chiral crystal structures. In this work, we show that the structurally chiral topological trivial insulators are also exotic states, which is interesting from the application point of view, owing to their natural advantage to host a large bulk photovoltaic effect in the visible wavelength region. In the last decades, the shift current in the visible wavelength region was limited to be 10 uA/V2 . By scanning the insulators with chiral structure, we found a class of compounds with photoconductivity ranging from 20 to 80 uA/V2 , which is approximately one order of magnitude larger than that reported in other real materials. This work illustrates that the compounds with chiral structure can host both quantum CPGE and a strong shift current in the second order optical response. Moreover, this work offers a good platform for the study of the shift current and its future application by putting the focus on insulator with chiral lattices, so far overlooked in photovoltaic technologies.

Quasiparticle interference evidence of the topological Fermi arc states in chiral fermionic semimetal CoSi.

Chiral fermions in solid state feature "Fermi arc" states, connecting the surface projections of the bulk chiral nodes. The surface Fermi arc is a signature of nontrivial bulk topology. Unconventional chiral fermions with an extensive Fermi arc traversing the whole Brillouin zone have been theoretically proposed in CoSi. Here, we use scanning tunneling microscopy/spectroscopy to investigate quasiparticle interference at various terminations of a CoSi single crystal. The observed surface states exhibit chiral fermion-originated characteristics. These reside on (001) and (011) but not (111) surfaces with p-rotation symmetry, spiral with energy, and disperse in a wide energy range from ~-200 to ~+400 mV. Owing to the high-energy and high-space resolution, a spin-orbit coupling-induced splitting of up to ~80 mV is identified. Our observations are corroborated by density functional theory and provide strong evidence that CoSi hosts the unconventional chiral fermions and the extensive Fermi arc states.

Quantum oscillations of thermopower in WTe2 thin films

Few-layer ${\mathrm{WTe}}_{2}$ displays fascinating phenomena, which are believed to be closely related to the topological character of its band structure. In this work we investigate quantum oscillations of thermopower in thin ${\mathrm{WTe}}_{2}$ films. Besides four oscillation frequencies commonly observed in bulk materials, we observe an additional oscillation frequency, which has previously been attributed to topological surface states [Nat. Commun. 8, 2150 (2017)]. Through analysis of the temperature, angular, and film thickness dependence of the frequency, we conclude that it is not due to the cyclotron resonance of the surface Fermi arcs in Weyl semimetals, but rather from the bulk bands. Emergence of these bulk bands at the Fermi level is due to a band reconstruction in thin layers. They contribute to transport and may be responsible for some properties of few-layer ${\mathrm{WTe}}_{2}$.

Chiral fermion reversal in chiral crystals

In materials chiral fermions such as Weyl fermions are characterized by nonzero chiral charges, which are singular points of Berry curvature in momentum space. Recently, new types of chiral fermions beyond Weyl fermions have been discovered in structurally chiral crystals CoSi, RhSi and PtAl. Here, we have synthesized RhSn single crystals, which have opposite structural chirality to the CoSi crystals we previously studied. Using angle-resolved photoemission spectroscopy, we show that the bulk electronic structures of RhSn are consistent with the band calculations and observe evident surface Fermi arcs and helical surface bands, confirming the existence of chiral fermions in RhSn. It is noteworthy that the helical surface bands of the RhSn and CoSi crystals have opposite handedness, meaning that the chiral fermions are reversed in the crystals of opposite structural chirality. Our discovery establishes a direct connection between chiral fermions in momentum space and chiral lattices in real space.

Weyl semimetal phase in the noncentrosymmetric superlattice W2XY(X,Y=S,Se,Te,X≠Y)

We investigated the topological properties and strain modulation of transition-metal monochalcogenides ${\mathrm{W}}_{2}XY(X,Y=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\mathrm{Se},\phantom{\rule{0.16em}{0ex}}\mathrm{Te},X\ensuremath{\ne}Y)$ by combining the first-principles method and the Wannier-based tight-binding method. The number and chirality of Weyl node, surface spectra, and surface Fermi arcs are calculated to identify their topological properties. The ${\mathrm{W}}_{2}XY$ compounds are nodal line semimetals in the absence of spin-orbit coupling (SOC). When SOC turns on, the nodal lines split into 24 Weyl nodes on the ${k}_{z}\ensuremath{\ne}0$ planes, which are related by time-reversal, ${C}_{3\mathrm{z}}$ rotational, and mirror symmetries. Weyl points' energies are close to the Fermi level and the maximal separation between two Weyl points with opposite handedness in reciprocal space is on the order of magnitude of $0.1\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$, which can be accessed by angle-resolved photoemission spectroscopy. Interestingly, the Weyl semimetal phase exhibits great robustness and asymmetric response under uniaxial/biaxial compression and tensile strain. The positions of Weyl points change significantly and lead to a striking modulation of topological properties under in-plane biaxial strain. These findings are important for studying the behavior of Weyl fermions in layered materials and useful for realizing their applications in topological electronic devices.

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe_{2} (X=Mo,W).

In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials. In particular, monolayers of centrosymmetric β-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric γ-phase MoTe_{2} and WTe_{2} have been identified as type-II Weyl semimetals. However, angle-resolved photoemission spectroscopy and STM probes of these semimetals have revealed huge, arclike surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this Letter, we calculate the bulk and surface electronic structure of both β- and γ-MoTe_{2}. We find that β-MoTe_{2} is, in fact, a Z_{4}-nontrivial higher-order TI (HOTI) driven by double band inversion and exhibits the same surface features as γ-MoTe_{2} and γ-WTe_{2}. We discover that these surface states are not topologically trivial, as previously characterized by the research that differentiated them from the Weyl Fermi arcs but, rather, are the characteristic split and gapped fourfold Dirac surface states of a HOTI. In β-MoTe_{2}, this indicates that it would exhibit helical pairs of hinge states if it were bulk insulating, and in γ-MoTe_{2} and γ-WTe_{2}, these surface states represent vestiges of HOTI phases without inversion symmetry that are nearby in parameter space. Using nested Wilson loops and first-principles calculations, we explicitly demonstrate that, when the Weyl points in γ-MoTe_{2} are annihilated, which may be accomplished by symmetry-preserving strain or lattice distortion, γ-MoTe_{2} becomes a nonsymmetry-indicated, noncentrosymmetric HOTI. We also show that, when the effects of spin-orbit coupling are neglected, β-MoTe_{2} is a nodal-line semimetal with Z_{2}-nontrivial monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by double band inversion are the weak-spin-orbit coupling limit of HOTIs, implying that MNLSMs are higher-order topological semimetals with flat-band-like hinge states, which we find to originate from the corner modes of 2D "fragile" TIs.

Field theory approach to the quantum transport in Weyl semimetals

We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the Landauer-B\"uttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the Wiedemann-Franz law.

Electric field manipulation of surface states in topological semimetals

We investigate the consequences of applying electric fields perpendicularly to thin films of topological semimetals. In particular, we consider Weyl and Dirac semimetals in a configuration such that their surface Fermi arcs lie on opposite edges of the films. We develop an analytical approach based on perturbation theory and a single-surface approximation and we compare our analytical results with numerical calculations. The effect of the electric field on the dispersion is twofold: it shifts the dispersion relation and renormalizes the Fermi velocity, which would, in turn, have direct effects on quantum transport measurements. Additionally, it modifies the spatial decay properties of surface states which will impact the connection of the Fermi arcs in opposite sides of a narrow thin film.

Coexistence of Weyl and Type‐II Triply Degenerate Fermions in a Ternary Topological Semimetal YPtP

Based on first‐principles calculations and effective model analysis, the long‐ago synthesized material YPtP is identified as a topological semimetal (TSM) material for studying the interaction between Weyl and triply degenerate fermions. When the spin–orbit coupling (SOC) is ignored, a triply degenerate point (TDP) and two types of ring‐shaped gapless nodal lines coexist in YPtP. When SOC is considered, the TDP turns to two type‐II TDPs, and the nodal lines open the bandgap and one of them transforms into 12 pairs of Weyl points. Thus, YPtP is a ternary TSM with the coexistence of type‐II TDPs and Weyl points. The surface states and Fermi arcs in YPtP further verify the topological characteristics of YPtP. The results herein provide a new platform for exploring ternary topological materials and the interaction between the two different fermions.

Topological d+s wave superconductors in a multiorbital quadratic band touching system

Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work, we theoretically propose a novel way to attain topological superconductors with non-trivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with $j\!=\!3/2$ electrons, we investigate the dominant superconducting channels for a multi-orbital quadratic band-touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors d-wave pairing, the absence of the particle-hole symmetry necessarily induces parasitic s-wave pairing. Based on the Landau theory with $SO(3)$ symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2)}\!+\!s$) and time-reversal-symmetry broken phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2,xy)}\!+\!id_{x^2-y^2}\!+\!s$). These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological winding numbers $\pm2$, leading to non-trivial surface states such as drumhead-like surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-heusler compound YPtBi, and suggest possible future experiments.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Interplay between magnetic, metal/insulator and topological phases in Hg1−xMnxTe alloys: prediction of a ferromagnetic Weyl semimetal at x = 0.25

We report a theoretical investigation of magnetic, electronic, and topological properties of Hg1−xMnxTe alloys. We consider periodic structures with Mn concentrations as x = 0, 0.25, 0.5, 0.75, and 1. Our hybrid DFT/Hartree–Fock calculations for the bandgaps of antiferromagnetic (ground-state) phases are in good agreement with experiments. The calculations also show that the modification of the magnetic ordering from anti- to ferromagnetic leads to a significant bandgap reduction, resulting in a metal/insulator transition at higher Mn concentrations. We show that a ferromagnetic Weyl semimetal phase is achieved for x = 0.25, where a single pair of Weyl nodes mirrored by the point in the momentum space is observed. The non-trivial topological property of the ferromagnetic Hg0.75Mn0.25Te is confirmed by the calculation of the chirality of each Weyl node, which are connected by a surface Fermi arc of a semi infinite Hg0.75Mn0.25Te.

Quantized surface transport in topological Dirac semimetal films

Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin film samples, where bulk dimensionality, Fermi energy, and band topology are systematically controlled. We reveal essential involvement of bulk states in the quantized surface transport and the resultant quantum Hall degeneracy depending on the bulk occupation. Our demonstration of surface transport controlled in film samples also paves a way for engineering Fermi-arc-mediated transport in topological semimetals.

Broken symmetry driven phase transitions from a topological semimetal to a gapped topological phase in SrAgAs

We show the occurence of Dirac, Triple point, Weyl semimetal and topological insulating phase in a single ternary compound using specific symmetry preserving perturbations. Based on {\it first principle} calculations, \textbf{\textit{k.p}} model and symmetry analysis, we show that alloying induced precise symmetry breaking in SrAgAs (space group P6$_3/mmc$) leads to tune various low energy excitonic phases transforming from Dirac to topological insulating via intermediate triple point and Weyl semimetal phase. We also consider the effect of external magnetic field, causing time reversal symmetry (TRS) breaking, and analyze the effect of TRS towards the realization of Weyl state. Importantly, in this material, the Fermi level lies extremely close to the nodal point with no extra Fermi pockets which further, make this compound as an ideal platform for topological study. The multi fold band degeneracies in these topological phases are analyzed based on point group representation theory. Topological insulating phase is further confirmed by calculating Z2 index. Furthermore, the topologically protected surface states and Fermi arcs are investigated in some detail.

The coupling effects of surface plasmons and Fermi arc plasmons in Weyl semimetals

We study the effects of coupling between surface plasmon and Fermi arc plasmon modes on a planar surface of the Weyl semimetal. A model Hamiltonian is proposed in the second quantization representation for the system of coupled surface plasmon and Fermi arc plasmon modes. We obtain the dispersion relations of coupled modes using the Bogoliubov transformation technique. We identify the upper coupled mode as the renormalized surface plasmon and the lower coupled mode as the renormalized Fermi arc plasmon. It is shown how the magnitude of the coupling depends on both the bare mode dispersions and their dampings. We also demonstrate that coupling increases the surface plasmon mode lifetime. Obtained results for the surface plasmon mode are qualitatively consistent with the recent experimental data of Weyl semimetals.

Observation of unconventional chiral fermions with long Fermi arcs in CoSi.

Chirality-the geometric property of objects that do not coincide with their mirror image-is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions-Weyl fermions-were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1-4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5-8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion-spin-1 and charge-2 fermions-at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.

Robust Twin Pairs of Weyl Fermions in Ferromagnetic Oxides.

The ferromagnetic Weyl semimetals with inversion symmetry usually possess odd pairs of Weyl fermions. Here, we present an inversion eigenvalue argument to dictate the existence of even pairs of ferromagnetic Weyl fermions. We show, by a combination of first-principles calculations and symmetry analyses, that this exotic topological feature can be verified in ferromagnetic oxides in different space groups. In particular, a realistic candidate, i.e., hollandite RbCr_{4}O_{8} with a high Curie temperature (∼295 K), hosts intriguing twin pairs of Weyl fermions, which are robustly stable against perturbations. Moreover, our effective model and symmetry analysis show that the twin pairs of Weyl fermions originate from a mirrored nodal ring pair. The nontrivial surface states and Fermi arcs of RbCr_{4}O_{8} are clearly visible, further revealing the topological features. This work strengthens the understanding of the parity analysis in exploring ferromagnetic topological materials with unconventional fermionic excitations.

Weyl points of mechanical diamond

A spring-mass model arranged in a diamond structure --- mechanical diamond --- is analyzed in terms of topology in detail. We find that, additional springs connecting the next-nearest-neighbor pairs of mass points and the modulation of the mass parameters to the pristine mechanical diamond generates multiple pairs of Weyl points in the frequency dispersion. Evolution of the Weyl point positions in the Brillouin zone against the uniform outward tension is tracked and explained by the point group symmetry, especially tetrahedral symmetry of the NNN springs. Interestingly, there happens a rapid transmutation of the monopole charges of the Weyl points as the tension varies. We also show surface Fermi arcs in the case with anisotropy in the NNN springs.