Fermi-arc States Research Articles

Topological Fermi-arc surface state covered by floating electrons on a two-dimensional electride

Two-dimensional electrides can acquire topologically non-trivial phases due to intriguing interplay between the cationic atomic layers and anionic electron layers. However, experimental evidence of topological surface states has yet to be verified. Here, via angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM), we probe the magnetic Weyl states of the ferromagnetic electride [Gd2C]2+·2e−. In particular, the presence of Weyl cones and Fermi-arc states is demonstrated through photon energy-dependent ARPES measurements, agreeing with theoretical band structure calculations. Notably, the STM measurements reveal that the Fermi-arc states exist underneath a floating quantum electron liquid on the top Gd layer, forming double-stacked surface states in a heterostructure. Our work thus not only unveils the non-trivial topology of the [Gd2C]2+·2e− electride but also realizes a surface heterostructure that can host phenomena distinct from the bulk.

Photoinduced Floquet higher-order Weyl semimetal in C6 symmetric Dirac semimetals

Abstract Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges. Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Circular dichroism in nonlinear topological Weyl semimetals

In recent years, the field of topological photonics has emerged as a promising area of research due to its potential for the development of new photonic devices with unique properties. Topological Weyl semimetals (TWSs), which are characterized by the presence of Weyl points in their electronic band structure, are one such example of a material with interesting topological properties. In this study, Kerr and Faraday rotations were used to determine the nonlinear characteristics of TWSs. We focused on surfaces where no Fermi arcs are involved, so that Maxwell’s equations would contain some peculiar topological terms. In Weyl semimetals with a specific topology, the distance between Weyl nodes aligned along the z-direction functions as a magnet. This results in a significant polar Kerr/Faraday rotation effect that is proportional to the separation distance, when light is directed onto the surface of the TWS that lacks Fermi arc states. Conversely, when the light is directed onto a surface with Fermi arc states, the Voigt effect is quadratically proportional to the separation distance. We considered electromagnetic wave propagation in a nonlinear Kerr-type medium. We have derived and solved the linear and nonlinear Helmholtz equations for TWSs using the tanh method. Our findings reveal that wave solutions could have some potentially significant implications for the design and optimization of photonic devices based on TWSs.

Observation of 3D acoustic quantum Hall states

Quantum Hall effect, the quantized transport phenomenon of electrons under strong magnetic fields, remains one of the hottest research topics in condensed matter physics since its discovery in 2D electronic systems. Recently, as a great advance in the research of quantum Hall effects, the quantum Hall effect in 3D systems, despite its big challenge, has been achieved in the bulk ZrTe5 and Cd3As2 materials. Interestingly, Cd3As2 is a Weyl semimetal, and quantum Hall effect is hosted by the Fermi arc states on opposite surfaces via the Weyl nodes of the bulk, and induced by the unique edge states on the boundaries of the opposite surfaces. However, such intriguing edge state distribution has not yet been experimentally observed. Here, we aim to reveal experimentally the unusual edge states of Fermi arcs in acoustic Weyl system with the aid of pseudo-magnetic field. Benefiting from the macroscopic nature of acoustic crystals, the pseudo-magnetic field is introduced by elaborately designed the gradient on-site energy, and the edge states of Fermi arcs on the boundaries of the opposite surfaces are unambiguously demonstrated in experiments. Our system serves as an ideal and highly tunable platform to explore the Hall physics in 3D system, and has the potential in the application of new acoustic devices.

Large optical conductivity of Fermi arc states in Weyl and Dirac semimetal nanowires

Large optical conductivity of Fermi arc states in Weyl and Dirac semimetal nanowires

Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence—while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system.

Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals.

Using semiclassics to surmount the hurdle of bulk-surface inseparability, we derive the superconductor vortex spectrum in nonmagnetic Weyl semimetals and show that it stems from the Berry phase of orbits made of Fermi arcs on opposite surfaces and bulk chiral modes. Tilting the vortex transmutes it between bosonic, fermionic, and supersymmetric, produces periodic peaks in the density of states that signify novel nonlocal Majorana modes, and yields a thickness-independent spectrum at magic "magic angles." We propose (Nb,Ta)P as candidate materials and tunneling spectroscopy as the ideal experiment.

Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals

Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quantized quadrupole moment and a $k$-dependent Chern number, emerge when illumining circularly polarized light. Such Floquet Weyl semimetals support both hinge Fermi arc states and topological surface Fermi arc states. In addition, Floquet Weyl semimetals with tilted Weyl cones in higher-order topological Dirac semimetals are also discussed. Considering numerous higher-order topological Dirac semimetal materials were recently proposed, our findings can be testable soon.

Exotic Weyl semimetal, emergent Fermi surface, and Lifshitz phase transition

Weyl semimetals (WSMs) with paired Weyl points in momentum space have attracted much attention in the past decade, and materials for this phase and the exotic Fermi arcs at their surface have been realized, in which the topology can be found in a finite momentum interval. Here we suggest a four-band model for WSM with two Weyl points in the ${k}_{z}$ axis, yet with totally different Fermi arcs at the surfaces. It exhibits a large anomalous Hall conductivity in the bulk, and large density of state on their surface. We analytically and numerically demonstrate the topological properties of this model from the dispersion, ${k}_{z}$-dependent Chern number, Fermi arc states, and dual topological phase. Furthermore, we investigate the effects of the magnetic field on the unusual Fermi arcs and find two emergent Fermi surfaces. Their combination can lead to diverse Lifshitz phase transitions when the thickness of the slab is decreased. The change of Fermi surfaces can be detected by the quantum oscillation, in which the contributions from a different number of closed Fermi surfaces can lead to different magnetotransport behaviors. We expect this model can stimulate the search for its realization in condensed matter physics and quantum simulating platforms.

Coexistence of Bulk-Nodal and Surface-Nodeless Cooper Pairings in a Superconducting Dirac Semimetal.

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below T_{c}∼4.5 K. Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc. These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling.

Broken symmetry and competing orders in Weyl semimetal interfaces

We consider interaction-induced broken symmetry states of two Weyl semimetal surfaces with multiple Fermi-arc (FA) states. In the presence of inter- and intra-surface Coulomb interactions, multiple broken symmetries may emerge which coexist and/or compete with one another. Interlayer exciton condensates involving different FA flavors are shown to form, with amplitudes determined by the strength of interactions and the degree of nesting among the arcs. For FA pairs which are well-separated in momentum with strong nesting, the resulting state is a particle-hole analog of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Intralayer interactions moreover induce charge density wave (CDW) ordering, so that the most general state of the system is a supersolid. These orderings in principle carry signatures in non-linear behavior and narrow band noise in Coulomb drag transport measurements.

Multifold Fermions and Fermi Arcs Boosted Catalysis in Nanoporous Electride 12CaO·7Al2 O3.

Topological materials have been recently regarded as ideal catalysts for heterogeneous reactions due to their surface metallic states and high carrier mobility. However, the underlying relationship between their catalytic performance and topological states is under debate. It has been discovered that the electride 12CaO·7Al2 O3 (C12A7:4e- ) hosts multifold fermions and Fermi arcs on the (001) surface near the Fermi level due to the interstitial electrons. Through the comparison of catalytic performance under different doping and strain conditions, based on the hydrogen evolution process, it has been demonstrated that the excellent catalytic performance indeed originates from topological properties. A linear relationship between the length of Fermi arcs, and Gibbs free energy (ΔGH* ) has been found, which not only provides the direct evidence to link the enhanced catalytic performance and surface Fermi arc states, but also fully clarifies the fundamental mechanism in topological catalysis.

Hourglass charge-three Weyl phonons

The unconventional Weyl point with nonlinear dispersion features higher topological charge $|\mathcal{C}|>1$ and multiple topologically protected Fermi arc states at its boundary. As a novel topological state, it has been attracting widespread attention. However, the unconventional Weyl point with $|\mathcal{C}|=3$ has not yet been reported in realistic materials, even though it has been theoretically proposed for more than a decade. In this work, based on first-principles calculations and theoretical analysis, we predict the existing material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$ as the first realistic example with this unconventional Weyl point. Specifically, in the phonon spectra of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$, two Weyl points with $\mathcal{C}=\ensuremath{-}3$, connected by time-reversal symmetry, appear at the neck crossing point of an hourglass-type band, leading to two hourglass charge-3 Weyl phonons. The symmetry protection and the associated novel triple- and sextuple-helicoid surface arc states of the hourglass charge-3 Weyl phonons are revealed. Our results uncover a hidden topological character of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$ and also show that the phonon spectra are a great platform for exploring unconventional topological states.

Interlayer RKKY interaction in ferromagnet/tilted Weyl semimetal/ferromagnet trilayer system

We have investigated the interlayer RKKY interaction in ferromagnet/Weyl semimetal/ferromagnet (FM/WSM/FM) trilayer system in the presence of the tilting effect of Weyl cones. Our investigation focuses on the influence of the unique features of WSMs: anisotropy dispersion, tilt effect, intervalley transitions, and Fermi arc states. Due to the separation of Weyl nodes, the RKKY behaviors, such as spin model, decaying rate, and oscillation period, heavily depend on the stacked direction of FMs, exhibiting strong magnetic anisotropy. Tilt of Weyl cones can increase the RKKY amplitude, change spin model, switch the antiferromagnetism and ferromagnetism, and more importantly generate the noncollinear Dzyaloshinskii-Moriya or spin-frustrated terms. Intervalley transition generates extra oscillation with period determined by separated distance between Weyl nodes, which together with Fermi-energy-induced oscillation leads to an interesting battering pattern. These signatures are significantly different from the interlayer RKKY interaction with single-node topological insulators or impurity RKKY case reported in previous literatures. More importantly, we find that the interlayer RKKY interaction decays more slowly with the spacer thickness than one reported extensively in WSMs doped with magnetic impurities, which is explained by providing a general formula. In addition, we discuss the effect from Weyl Fermi arcs. Compared to the bulk contributions, a more slowly decaying rate is found at the edges of ferromagnetic layer if the edges are parallel to the line connecting two Weyl nodes. Our research suggests that trilayer FM/WSM/FM is a more powerful platform to understand the WSM magnetic property and to extract the parameters of WSM materials by measuring the RKKY interaction.

Topological superconductivity in multifold fermion metals

Recently, multifold fermions characterized by band crossings with multifold degeneracy and Fermi surfaces with higher Chern numbers have been discovered experimentally in AlPt (Schroter et al. in Nat Phys 15:759–765, 2019) and XSi(X = Rh,Co) (Sanchez et al. in Nature 567:500–505, 2019; Rao et al. in Nature 567:496–499, 2019; Takane et al. in Phys Rev Lett 122:076402, 2019). In this work, we largely expand the family of multifold fermion materials by pointing out that several well-studied noncentrosymmetric superconductors are indeed multifold fermion metals. Importantly, their normal state topological properties, which have been ignored in previous studies, play an important role in the superconducting properties. Taking mathrm{Li} _{2}mathrm{Pd} _{3}mathrm{B} and mathrm{Li} _{2}mathrm{Pt} _{3}mathrm{B} as examples, we found a large number of unconventional degenerate points, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in mathrm{Li} _{2}mathrm{Pd} _{3}mathrm{B}, originating from the nontrivial band topology were found. Importantly, it has been shown experimentally that mathrm{Li} _{2}mathrm{Pd} _{3}mathrm{B} and mathrm{Li} _{2}mathrm{Pt} _{3}mathrm{B} are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest that mathrm{Li} _{2}mathrm{Pd} _{3}mathrm{B} is a conventional s-wave superconductor or DIII class topological superconductor with Majorana surface states. mathrm{Li} _{2}mathrm{Pt} _{3}mathrm{B}, being gapless, is likely to be a nodal topological superconductor with dispersionless surface Majorana modes. We further identified that several noncentrosymmetric superconductors, such as mathrm{Mo} _{3}mathrm{Al} _{2}mathrm{C}, PdBiSe, mathrm{Y}_{2}mathrm{C}_{3} and mathrm{La} _{2}mathrm{C}_{3}, are multifold fermion superconductors. This work calls for a revisit for the study of noncentrosymmtric superconductors which provide platforms for investigating the interplay between superconductivity and topologically nontrivial Fermi surfaces.

Unpaired topological triply degenerate point for spin-tensor-momentum-coupled ultracold atoms

The realization of triply degenerate points (TDPs) with exotic fermionic excitations has opened a new perspective for the understanding of our nature. Here we explore the coexistence of single unpaired TDP and multiple twofold Weyl points (WPs) and propose an experimental scheme with ultracold pseudospin-1 atomic gases trapped in optical lattices. We show that the predicted single unpaired TDP emerged by the interplay of quadratic spin-vector- and spin-tensor-momentum-coupling could possess a topological nontrivial middle band. This exotic TDP with mirror symmetry breaking is essential different from the recently observed TDPs that must appear in pairs due to the Nielsen-Ninomiya theorem and host the topological trivial middle band. Strikingly, the topologically protected Fermi-arc states directly connect the unpaired TDP with additional WPs, in contrast to the conventional Fermi-arc states that connect the same degeneracies of band degenerate points with opposite chirality. Furthermore, the different types of TDPs with unique linking structure of Fermi arcs can be readily distinguished by measuring spin texture along high-symmetry lines of the system. Our scheme provides a platform for emerging new fermions with exotic physical phenomena and versatile device applications.

Finite size effect on the Fermi arc surface states in Weyl semimetal

A hallmark of the Weyl semimetal is the presence of two gapless Fermi arc surface states between two Weyl nodes. The Fermi arc surface states give rise to quantum anomalous Hall effect. Through analytically solving a finite size Weyl semimetal slab, we find that the two surface states can couple together producing a gap in the spectrum of Fermi arc surface states. Due to the finite size effect, the quantum anomalous Hall effect of Fermi arc states will be modified. This effect is anticipated to be measurable in experiment.

Non-Hermitian Weyl semimetal and its Floquet engineering

It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topological insulator with the coexisting Fermi arc and chiral boundary states, a widely tunable Hall conductivity with multiple quantized plateaus, and a Weyl semimetal with anomalous Fermi arcs formed by the crossing of gapped bound state, can be generated by the Floquet engineering. Revealing the leading role of the skin effect in determining the feature of a semimental, our result supplies a useful way to artificially synthesize exotic non-Hermitian Weyl semimetals by periodic driving.

Phonon-limited transport and Fermi arc lifetime in Weyl semimetals

Weyl semimetals harbor topological Fermi-arc surface states which determine the nontrivial charge current response to external fields. We here study the quasiparticle decay rate of Fermi arc states arising from their coupling to acoustic phonons, as well as the phonon-limited conductivity tensor for a clean Weyl semimetal slab. Using the phonon modes for an isotropic elastic continuum with a deformation potential coupling to electrons, we determine the temperature dependence of the quasiparticle decay rate, both near and far away from the arc termination points. By solving the coupled Boltzmann equations for the bulk and arc state distribution functions in the slab geometry, we show how the linear response conductivity depends on key parameters such as the temperature, the chemical potential, the geometric shape of the Fermi arcs, or the slab width. The chiral nature of Fermi arc states causes an enhancement of the longitudinal conductivity along the chiral direction at low temperatures, together with a 1/T^2 scaling regime at intermediate temperatures without counterpart for the conductivity along the perpendicular direction.

Weyl nodes with higher-order topology in an optically driven nodal-line semimetal

Creating and manipulating topological states is a key goal of condensed matter physics. Periodic driving offers a powerful method to manipulate electronic states, and even to create topological states in solids. Here, we investigate the tunable Floquet states in a periodically driven higher-order nodal line semimetal with both spatial inversion and time-reversal symmetries. We found that the Floquet Weyl semimetal states, which support both one-dimensional hinge Fermi arc and two-dimensional surface Fermi arc states, can be induced in the higher-order nodal-line semimetal by shining circularly polarized light. Moreover, we show that the location of Weyl nodes and the curvature of surface Fermi arcs can be tuned by adjusting the propagation direction and incident angle of light.