Intrinsic anomalous Hall effect in type-II Weyl semimetals

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.     

Black hole and hawking radiation by type-II Weyl fermions

The type-II Weyl and type-II Dirac fermions may emerge behind the event horizon of black holes. Correspondingly, the black hole can be simulated by creation of the region with overtilted Weyl or Dirac cones. The filling of the electronic states inside the “black hole” is accompanied by Hawking radiation. The Hawking temperature in the Weyl semimetals can reach the room temperature, if the black hole region is sufficiently small, and thus the effective gravity at the horizon is large.     

Lifshitz transitions via the type-II dirac and type-II Weyl points

The type-II Weyl and type-II Dirac points emerge in semimetals and in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. In one case, the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case, the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition, the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support, the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds.     

Anomalous Nernst effect in type-II Weyl semimetals

Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole pockets producing finite DOS at the Fermi level. The tilted conical spectrum and finite DOS at Fermi level in type-II WSMs have recently been shown to produce interesting effects such as a chiral anomaly induced longitudinal magnetoresistance that is strongly anisotropic in direction and a novel anomalous Hall effect. In this work, we consider the anomalous Nernst effect in type-II WSMs in the absence of an external magnetic field using the framework of semi-classical Boltzmann theory. Based on both a linearized model of time-reversal breaking WSM with a higher energy cut-off and a more realistic lattice model, we show that the anomalous Nernst response in these systems is strongly anisotropic in space, and can serve as a reliable signature of type-II Weyl semimetals in a host of magnetic systems with spontaneously broken time reversal symmetry.     

Topological gapless matters in three-dimensional ultracold atomic gases

Three-dimensional topological gapless matters with gapless degeneracies protected by a topological invariant defined over a closed manifold in momentum space have attracted considerable interest in various fields ranging from condensed matter materials to ultracold atomic gases. As a highly controllable and disorder free system, ultracold atomic gases provide a versatile platform to simulate topological gapless matters. Here, the current progress in studies of topological gapless phenomena in three-dimensional cold atom systems is summarized in the review. It is mainly focused on Weyl points, structured (type-II) Weyl points, Dirac points, nodal rings and Weyl exceptional rings in cold atoms. Since interactions in cold atoms can be controlled via Feshbach resonances, the progress in both superfluids for attractive interactions and non-interacting cold atom gases is reviewed.     

Chiral magnetic effect without chirality source in asymmetric Weyl semimetals

We describe a new type of the chiral magnetic effect (CME) that should occur in Weyl semimetals (WSMs) with an asymmetry in the dispersion relations of the left- and right-handed (LH and RH) chiral Weyl fermions. In such materials, time-dependent pumping of electrons from a non-chiral external source can generate a non-vanishing chiral chemical potential. This is due to the different capacities of the LH and RH chiral Weyl cones arising from the difference in the density of states in the LH and RH cones. The chiral chemical potential then generates, via the chiral anomaly, a current along the direction of an applied magnetic field even in the absence of an external electric field. The source of chirality imbalance in this new setup is thus due to the band structure of the system and the presence of (non-chiral) electron source, and not due to the parallel electric and magnetic fields. We illustrate the effect by an argument based on the effective field theory, and by the chiral kinetic theory calculation for a rotationally invariant WSM with different Fermi velocities in the left and right chiral Weyl cones; we also consider the case of a WSM with Weyl nodes at different energies. We argue that this effect is generically present in WSMs with different dispersion relations for LH and RH chiral Weyl cones, such as SrSi₂ recently predicted as a WSM with broken inversion and mirror symmetries, as long as the chiral relaxation time is much longer than the transport scattering time.     

New family of Dirac and Weyl semimetals in XAuTe (X = Na,K, Rb) ternary honeycomb compounds

We propose a new family of 3D Dirac semimetals based on XAuTe(X = K, Na, Rb) ternary honeycomb compounds, determined based on first-principles calculations, which are shown to be topological Dirac semimetals in which the Dirac points are induced by band inversion. Dirac points with four-fold degeneracy that are protected by C3 rotation symmetry and located on the Γ-A high-symmetry path are found. Through spatial-inversion symmetry breaking, a K(Au0.5 Hg0.5)(Te0.5As0.5) superlattice structure composed of KHgAs and KAuTe compounds is proven to be a Weyl semimetal with type-II Weyl points, which connect electronand hole-like bands. In this superlattice structure, the six pairs of Weyl nodes are distributed along the K-Γ high-symmetry path on the kz = 0 plane. Our research expands the family of topological Dirac and type-II Weyl semimetals.     

Collective modes of type-ⅡWeyl fermions with repulsive S-wave interaction

Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.     

Vector valley Hall edge solitons in the photonic lattice with type-II Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics. They maintain their profiles during propagation, due to the joint action of lattice potential and nonlinearity, and at the same time are immune to defects or disorders, thanks to the topological protection. In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays, in which the time-reversal symmetry is effectively broken. Very recently, topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved. However, these were scalar solitary structures. Here, for the first time, we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones, which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice. This comes about because the valley Hall edge state can possess both negative and positive dispersions, which allows the mixing of two different edge states into a vector soliton. Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime, but also enlighten relevant research based on the lattices with type-II Dirac cones.     

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Tunable anisotropic anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals

Weyl semimetals and nodal line semimetals display a host of novel properties. Floquet Weyl semimetals with tunable Weyl points can be obtained from nodal line semimetals under the circularly polarized off-resonant light. Here we theoretically investigate the anomalous Nernst effect and orbital magnetization in Floquet Weyl semimetals. Due to the anisotropy of the band structure in Floquet Weyl semimetals, highly anisotropic Berry phase mediated anomalous Nernst effect and orbital magnetization in the absence of magnetic field are observed, indicating orientation-dependent applications in the design of nanodevices. The amplitude and sign of anomalous Nernst coefficient and orbital magnetization can be tuned by the light direction, amplitude and polarization. The effect of the chemical potential on anomalous Nernst coefficient and orbital magnetization is also discussed. The light-modulated anomalous Nernst effect and orbital magnetization make Floquet Weyl semimetals potential candidates for thermoelectric devices.     

Hybrid Weyl semimetal under crossed electric and magnetic fields: Field tuning of spectrum type

There are two types (WSM-I and WSM-II) of the WSMs. The WSMs of different types have various topological and transport properties. Besides pure WSM-I and WSM-II, there exists a novel type, dubbed “hybrid Weyl semimetal”, which contains the Weyl points of both types. In this Letter we consider the hybrid WSM under crossed magnetic and electric fields. The electromagnetic field induces transition between different types of spectrum in Weyl point (WP). Thus, hybrid phase of the WSM can be tunable using the electromagnetic field. Finally, we proposed a new field-induced type of hybrid WSM in which two different regimes of spectrum coexist. In this case, the spectrum near the first WP corresponds to electric regime (no Landau levels) and the spectrum in the second WP with opposite chirality corresponds to magnetic regime (there are Landau levels).     

Low-energy electronic properties of a Weyl semimetal quantum dot

We investigate the low-energy electronic structure of a Weyl semimetal quantum dot(QD) with a simple model Hamiltonian with only two Weyl points. Distinguished from the semiconductor and topological insulator QDs, there exist both surface and bulk states near the Fermi level in Weyl semimetal QDs. The surface state, distributed near the side surface of the QD, contributes a circular persistent current, an orbital magnetic moment, and a chiral spin polarization with spin-current locking. There are always surface states even for a strong magnetic field, even though a given surface state gradually evolves into a Landau level with increasing magnetic field. It indicates that these unique properties can be tuned via the QD size. In addition, we show the correspondence to the electronic structures of a three-dimensional Weyl semimetal, such as Weyl point and Fermi arc. Because a QD has the largest surface-to-volume ratio, it provides a new platform to verify Weyl semimetal by separating and detecting the signals of surface states. Besides, the study of Weyl QDs is also necessary for potential applications in nanoelectronics.     

On the calculation of group characters

It is known that characters of irreducible representations of finite Lie algebras can be obtained using the Weyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras of lower rank. By starting from the Weyl character formula, we show that these characters can be re-expressed without referring to Weyl group summations. Some useful technical points are given in detail for the instructive example of G₂ Lie algebra.     

Hexagonal wurtzite MnO in ferromagnetic state: A magnetic topological spin-gapless Weyl semimetal

Magnetic topological materials have attracted increasingly attentions in recent years due to their exotic electronic behaviors emerging from the couplings of topological, magnetic, and crystalline symmetries. In this work, based on the first-principles calculations, we propose that hexagonal wurtzite MnO is a magnetic topological spin-gapless semi-half-metal with two pairs of type-I Weyl fermions near the Fermi level in ferromagnetic state, which is a promising candidate material in spintronic and piezoelectric applications. In the absence of spin-orbit coupling (SOC), it hosts one triple degeneracy point (TP) in the irreducible Brillouin zone. Owing to weak SOC, the TP splits into two type-I Weyl points that are very close to each other. The Fermi arc surface states connecting the projected Weyl points with opposite chirality are observed. Our results therefore provide a wonderful platform to study the interplay of magnetism and topology.     

Pressure-induced Lifshitz transition in the type Ⅱ Dirac semimetal PtTe_2

Numerous exotic properties have been discovered in Dirac Semimetals(DSMs) and Weyl Semimetals(WSMs). In a given DSM/WSM, the Dirac/Weyl nodes usually coexist with other bulk states, making their respective contribution elusive. In this work, we distinguish the role of bulk states from the tilted Dirac nodes on the transport properties in DSMs. Specifically, we applied pressure to a type-II DSM material, PtTe2, and studied its pressure modified electronic and lattice structure systematically by using in situ transport measurements and X-ray diffraction(XRD). A pressure-induced transition at about 20 GPa is revealed in the transport properties, while the layered lattice structure is robust against pressure as illustrated in XRD measurement results.Density functional theory(DFT) calculations suggest that this is originated from the Lifshitz transition in the bulk states. Our findings provide evidence to identify the bulk states' influence on transport from the topologically-protected DSM states in the DSM material.     

Type-I Weyl points induced by negative coupling in photonic crystal

Weyl points, which are the degenerate points in three-dimensional momentum space, have been widely studied in the photonic system, and show some intriguing phenomena such as topologically protected surface states and chiral anomalies. Type-I Weyl systems possess a complete bandgap, and topologically protected surface states can be excited without disturbing the bulk states.In this work, we investigate the influence of the sign of coupling coefficient on the topological property of the system and find that type-I Weyl points can be realized by introducing a negative coupling between the stacking layers of the designed photonic crystal. We propose a new strategy to construct a type-I Weyl system by stacking the hexagonal photonic lattice. Different from the topological nontrivial photonic system with a positive coefficient, the negative couplings in the photonic system are realized by adding another resonating site between stacking layers. We theoretically demonstrate that the effective coupling between the resonating sites in adjacent layers sign-flips through the judicious design of the nearest coupling strength and eigenfrequency of the additional sites. The surface states at opposite boundaries of the proposed system have opposite group velocities, which is the feature of type-I Weyl points. Our study provides a new method of exploring topologically protected photonic systems and developing possible topological devices.     

Magneto-transport properties of thin flakes of Weyl semiconductor tellurium

As an elemental semiconductor, tellurium has recently attracted intense interest due to its non-trivial band topology, and the resulted intriguing topological transport phenomena. In this study we report systematic electronic transport studies on tellurium flakes grown via a simple vapor deposition process. The sample is self-hole-doped, and exhibits typical weak localization behavior at low temperatures. Substantial negative longitudinal magnetoresistance under parallel magnetic field is observed over a wide temperature region, which is considered to share the same origin with that in tellurium bulk crystals, i.e., the Weyl points near the top of valence band. However, with lowering temperature the longitudinal magnetoconductivity experiences a transition from parabolic to linear field dependency, differing distinctly from the bulk counterparts. Further analysis reveals that such a modulation of Weyl behaviors in this low-dimensional tellurium structure can be attributed to the enhanced inter-valley scattering at low temperatures. Our results further extend Weyl physics into a low-dimensional semiconductor system, which may find its potential application in designing topological semiconductor devices.     

Entanglement Rule of Wigner Operators at a Beamsplitter

It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter.