type-I Weyl Semimetals Research Articles

Tunneling chirality Hall effect in type-I Weyl semimetals

Tunneling chirality Hall effect in type-I Weyl semimetals

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1) Dirac equation describing a Dirac material in the presence of external parallel electric and magnetic fields is solved. Considering static but non-uniform electric and magnetic profiles with translational symmetry along the y-direction, the Dirac equation is transformed into two decoupled pairs of Schrödinger equations, one for each chirality of the fermion fields. Taking trigonometric and hyperbolic profiles for the vector and scalar potentials, respectively, we arrive at SUSY partner Pöschl-Teller-like quantum potentials. Restricting to the conditions of the potentials that support an analytic zero-mode solution, we obtain a nontrivial current density perpendicular to the electric and magnetic fields, thus, defining a plane where these three vectors become coplanar, indicating the possibility of realizing the Planar Hall Effect. Furthermore, this non-vanishing current density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry. Possible application in current steering of solitonic nature through a Type-I Weyl semimetal is discussed.

Intrinsic surface superconducting instability in type-I Weyl semimetals

Intrinsic surface superconducting instability in type-I Weyl semimetals

Unexpected nontriviality of inter-band contribution and huge anisotropy of conductivity in tilted Weyl semimetals

For tilted type-I Weyl semimetals, our theoretical study indicates that the Kubo conductivity parallel to cone tilt direction increases rapidly with the Fermi energy. Hence it deviates from its Boltzmann counterpart sizably even though the electronic wavelength is so short that the quantum interference is seemingly trivial. As a result, such a system shows huge anisotropy of the conductivity. By means of the diagrammatic expansion technique, we find that the absence of backscattering and the breakdown of the time reversal symmetry in tilted Weyl semimetals are two crucial factors which bring about the nontrivial inter-band contribution to the Kubo conductivity. Our findings indicate that Boltzmann theory fails to describe reasonably the electronic transport of a tilted Weyl cone, even in the case of weak scattering and short Fermi wavelength. Though in this regime such a semiclassical transport theory is believed to be valid according to conventional arguments. This situation should be paid attention. • Via SCBA, the high order quantum corrections to conductivity are considered and it makes huge enhancement to diagonal conductivity σ z z , which is missed by the Boltzmann transport equation with the lowest order Born approximation. • The huge anisotropy of diagonal conductivity in tilted WSMs origin from the nature of the absence of backscattering and breakdown of TRS. • The interaction range of impurity potential affects the extent of anisotropy.

In-plane magnetotransport phenomena in tilted Weyl semimetals

The nontrivial Berry curvature and chiral anomaly result in plenty of interesting magnetotransport and magneto-thermoelectric transport phenomena in Weyl semimetals, two of which are the planar Hall effect and planar Nernst effect. Based on the semi-classical Boltzmann theory, we theoretically study the in-plane magnetotransport coefficients (including electric conductivity, thermoelectric conductivity and Nernst thermopower) for both type-I and type-II Weyl semimetals using a linearized low-energy Hamiltonian. We find that for tilt-coplanar setup where the electric field (or temperature gradient) is applied along the tilted direction of the Weyl nodes, the planar Hall conductivity (or planar Nernst thermopower) shows a magnetic field linear dependence. And these linear responses do no obey the reported dependence on the angle θ between the magnetic and electric field for planar Hall effect. For tilt-perpendicular setup where the applied field (E or ) and magnetic field are perpendicular to the tilted direction, the planar Hall conductivity (or planar Nernst thermopower) mainly follows a magnetic field quadratic dependence, and it satisfies the characteristic. There are also anomalous Hall effect and anomalous Nernst effect in the plane perpendicular to the tilted direction of the two oppositely tilted Weyl nodes. These findings can be verified experimentally by changing the direction and magnitude of the in-plane magnetic field.

Nonlinear magnetoconductivity in Weyl and multi-Weyl semimetals in quantizing magnetic field

Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of the tilted type-I Weyl and multi-Weyl semimetals. In contrast to the existence of chiral charge pumping in the linear response regime, we reproduce the absence of chiral charge pumping in the nonlinear transport regime, using the Boltzmann transport framework with the Landau levels. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semimetals. The nonlinear magnetoconductivity vanishes in the ultraquantum limit, oscillates in the intermediate magnetic field regime, and saturates in the semiclassical limit. The nonlinear magnetoconductivity depends intricately on the tilt orientation, and it can be used to determine the tilt orientation in Weyl and multi-Weyl semimetals, via nonlinear magnetoresistivity or second harmonic generation experiments.

Hydrostatic pressure-induced magnetic and topological phase transitions in the MnBi2Te4 family of materials

The recent discovery of intrinsic magnetic topological insulator (TI) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ has inspired enormous research interest to explore emergent physics created by the interplay of magnetism and topology. Here we systematically investigated the influence of hydrostatic pressure on structural, magnetic, and topological electronic properties of the $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ family of materials by first-principles calculations. Our results indicate that properties of these layered materials can be effectively tuned by pressure, leading to various kinds of magnetic and topological phase transitions. These include magnetic transitions from $A$-type antiferromagnetism to novel magnetic states, such as frustrated magnetism and intralayer ferromagnetism in conditions of antiferromagnetic intralayer coupling. Moreover, rich topological phase transitions can be driven by pressure in these materials, including trivial insulator to antiferromagnetic TI, type-I or type-II Weyl semimetals, or high-order TI phases. The findings call for in-depth experimental investigations of magnetic and topological physics in these intriguing material systems under high pressure.

Goos–Hänchen and Imbert–Fedorov shifts in tiltedWeyl semimetals

We establish the beam models of Goos–Hänchen (GH) and Imbert–Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-II WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-II WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-II WSMs. By adjusting the chemical potential, the boundary between type-I and type-II WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.

Electronic structure and unconventional nonlinear response in double Weyl semimetal SrSi2

Considering a non-centrosymmetric, non-magnetic double Weyl semimetal (WSM) SrSi$_2$, we investigate the electron and hole pockets in bulk Fermi surface behavior that enables us to characterize the material as a type-I WSM. We study the structural handedness of the material and correlate it with the distinct surface Fermi surface at two opposite surfaces following an energy evolution. The Fermi arc singlet becomes doublet with the onset of spin orbit coupling that is in accordance with the topological charge of the Weyl Nodes (WNs). A finite energy separation between WNs of opposite chirality in SrSi$_2$ allows us to compute circular photogalvanic effect (CPGE). Followed by the three band formula, we show that CPGE is only quantized for Fermi level chosen in the vicinity of WN residing at higher value of energy. Surprisingly, for the other WN of opposite chirality in the lower value of energy, CPGE is not found to be quantized. Such a behavior of CPGE is in complete contrast to the time reversal breaking WSM where CPGE is quantized to two opposite plateau depending on the topological charge of the activated WN. We further analyze our finding by examining the momentum resolved CPGE. Finally we show that two band formula for CPGE is not able to capture the quantization that is apprehended by the three band formula.

Frequency manipulation of topological surface states by Weyl phase transitions.

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

General formula of chiral anomaly for type-I and type-II Weyl semimetals

Weyl semimetals (WSMs) are classified into type-I and type-II, depending on the magnitudes of the inclination of Weyl cones. It is known that these WSMs show negative longitudinal magnetoresistance originating from chiral anomaly. Moreover, we have recently revealed that type-II WSMs show positive longitudinal magnetoresistance originating from chiral anomaly. The negative longitudinal magnetoresistance in type-I WSMs can be explained utilizing the conventional formula of the chiral anomaly, which does not have the term related to the inclination of the Weyl cones. However, we cannot explain both the positive and the negative longitudinal magnetoresistance in type-II WSMs utilizing it. Therefore, in this paper, we derive the general formula including the term related to the inclination of the Weyl cones in order to explain straightforwardly the positive and the negative longitudinal magnetoresistance in type-II WSMs. Also, we consider both cases where a pair of the Weyl cones are tilted in the same direction (positive tilt chirality) and toward (or against) each other (negative tilt chirality) in order to investigate the influence of the direction to which the Weyl cones are tilted. As a result, we find that in the negative tilt chirality, the general formula is strongly affected by the inclination. These results suggest that we can estimate whether the WSMs show the positive or the negative longitudinal magnetoresistance using the general formula from the information of their tilt chirality and the magnitudes of the inclination of the Weyl cones.

Spin susceptibilities in magnetic type-I and type-II Weyl semimetals

We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation (RPA) method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $\gamma$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to type-II. The lower temperature, the sharper is the drop in $U_c$ at the critical point between them. The variation of $U_c$ with a slight doping near half-filling is also studied. It is generally found that these Weyl systems show a strongly anisotropic spin response with an enhanced doubly degenerate transverse susceptibility perpendicular to tilt direction, inherited from $\mathcal{C}_{4z}$ rational symmetry of bare Hamiltonian, but with the longitudinal response suppressed with respect to that. For small tilts $\gamma$ and strong enough interaction, we find two degenerate ordering patterns with spin order orthogonal to the tilt direction but much shorter spin correlation length parallel to the spin direction. With increasing the tilt, the system develops instabilities with respect to in-plane magnetic orders with wavevector $(0,\pi, q_z)$ and $(\pi,0, q_z)$, with $q_z$ increasing from 0 to $\pi$ before the transition to a type-II Weyl semimetal is reached. These results indicate a greater richness of magnetic phases in correlated Weyl semimetals that also pose challenges for precise theoretical descriptions.

Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator Mn(Bi1−xSbx)2Te4

The discovery of Weyl semimetals (WSMs) has fueled tremendous interest in condensed matter physics. The realization of WSMs requires the breaking of either inversion symmetry (IS) or time-reversal symmetry (TRS). WSMs can be categorized into type-I and type-II WSMs, which are characterized by untilted and strongly tilted Weyl cones, respectively. Type-I WSMs with breaking of either IS or TRS and type-II WSMs with solely broken IS have been realized experimentally, but a TRS-breaking type-II WSM still remains elusive. In this article, we report transport evidence for a TRS-breaking type-II WSM observed in the intrinsic antiferromagnetic topological insulator Mn(Bi1−xSbx)2Te4 under magnetic fields. This state is manifested by the electronic structure transition caused by the spin-flop transition. The transition results in an intrinsic anomalous Hall effect and negative c-axis longitudinal magnetoresistance attributable to the chiral anomaly in the ferromagnetic phases of lightly hole-doped samples. Our results establish a promising platform for exploring the underlying physics of the long-sought, ideal TRS-breaking type-II WSM.Received 21 June 2020Revised 25 April 2021Accepted 8 June 2021DOI:https://doi.org/10.1103/PhysRevX.11.031032Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnomalous Hall effectMagnetotransportTopological insulatorsTopological materialsTopological phase transitionPhysical SystemsAntiferromagnetsSingle crystal materialsWeyl semimetalTechniquesAngle-resolved photoemission spectroscopyCrystal growthDC susceptibility measurementsEnergy spectroscopy for chemical analysisHall barMagnetization measurementsResistivity measurementsShubnikov-de Haas effectX-ray diffractionCondensed Matter, Materials & Applied Physics

Observation of strong and anisotropic nonlinear optical effects through polarization-resolved optical spectroscopy in the type-II Weyl semimetal Td−WTe2

The unique bulk crossing points in the band structure of topological Weyl semimetals have been shown to enhance nonlinear optical and optoelectronic properties, even for light at optical wavelengths. Such pronounced nonlinear optical effects have been studied in type-I Weyl semimetals, yet few studies have quantified these effects in type-II Weyl semimetals. We here present an optical experimental study with polarization resolution of two nonlinear optical effects in the type-II Weyl semimetal ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$. We begin by investigating the bulk optical second-harmonic response of this material using the rotational anisotropy of the second-harmonic generation. This technique allows us to simultaneously investigate the dependence of the second-harmonic response on the symmetry of the crystal and to quantify the size of that response, which we compare to other nonlinear crystals. We then use polarized time-resolved optical reflectivity spectroscopy to identify the nonlinear optical effect of impulsive stimulated Raman scattering as the origin of the coherent oscillations of the 0.25-THz shear mode. We find that the strength of this response in ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$ is enhanced compared with the observation of other modes excited through the displacive excitation of coherent phonons. Notably, both the second-harmonic response and the coherent excitations of the phonons demonstrate strong anisotropy, displaying a clear dependence on the polarization of the light used in the experiments. We use point-symmetry analyses of the material to guide our understanding of these observations and perform fluence-dependent measurements to investigate the electron-phonon coupling.

Role of Weyl cone tilting in the spin Hall effect of light

We systematically study the role of Weyl cone tilting in the spin Hall effect of light (SHEL) in doped Weyl semimetals (WSMs), and propose a new scheme to determine the type of a WSM and to sense the tilt degree of Weyl cones precisely. It is found that in the case of a small amount of doping, the SHEL in type-I WSMs shows almost no dependence on the tilt degree of Weyl cones, while the SHEL in type-II WSMs is extremely sensitive to variations in the degree of tilt. However, in the case of a large amount of doping, not only the SHEL in type-II WSMs but also the SHEL in type-I WSMs show strong dependences on the tilt degree. These trends are mainly attributed to the variation of the real part of the Hall conductivity with the tilt degree. Remarkably, by using a quantum weak measurement, the tiny SHEL shifts can be amplified and detected to a desirable accuracy. Based on the obviously different tilt-dependent characteristics of amplified SHEL shifts in WSMs, we propose a new scheme to determine the type of a WSM and to sense the tilt degree precisely. By adjusting the doping level, the sensing sensitivity can reach up to 1461.55 µm per degree of tilt. This study may provide an application reference for the fabrication of WSM parameter sensors and other topological photoelectric devices.

Acoustic plasmons in type-I Weyl semimetals

Massless chiral fermions emergent in inversion symmetry-breaking Weyl semimetals (WSMs) reside in the vicinity of multiple low symmetry nodes and thus acquire strongly anisotropic dispersion. We investigate the longitudinal electromagnetic modes of two-component degenerate Weyl plasma relevant to the realistic band structure of type-I WSM. We show that the actual spectrum of three dimensional collective density excitations in TaAs family of WSM is gaples due to emergence of acoustic plasmons corresponding to out-of-phase oscillations of the plasma components. These modes exist around the [001] crystallographic direction and are weakly damped, thanks to large difference in the Weyl velocities of the $W_1$ and $W_2$ quasiparticles when propagating along [001]. We show that acoustic plasmons can manifest themselves as slow beatings of electric potential superimposed on fast plasmonic oscillations upon charge relaxation. The revealed acoustic modes can stimulate purely electronic superconductivity, collisionless plasmon instabilities, and formation of Weyl soundarons.

Role of time reversal symmetry and tilting in circular photogalvanic responses

We study the role of time reversal symmetry (TRS) in the circular photogalvanic (CPG) responses considering chiral Weyl semimetal (WSM) while a quantized CPG response is guaranteed by broken of both inversion symmetry (IS) and mirror symmetries. The TRS broken WSM yields one left and one right chiral Weyl nodes (WNs) while there are two left and right chiral WNs for TRS invariant WSM. We show that these features can potentially cause the quantization of CPG response at higher values compared to the topological charge of the underlying WSM. This is further supported by the fact that Berry curvature and velocity behave differently whether the system preserves or breaks the TRS. We find the CPG responses for TRS invariant type-II WSM to be quantized at two and four times the topological charge of the activated WNs while the chemical potential are respectively chosen in the vicinity of energies associated with left and right chiral WNs. By contrast, irrespective of the above choice of the chemical potential, the quantization in CPG response is directly given by the topological charge of the activated WNs for TRS broken case. Interestingly, we notice non-quantized peak in CPG response when energies of WNs associated with opposite chiralities are close to each other as it is the case for TRS invariant type-I WSM considered here. Moreover, we show that the tilt can significantly modify the CPG response as velocity in the tilt direction changes which enters into the CPG tensor through the Fermi distribution function. Given these exciting outcomes, the second order CPG response emerges as a useful indicator to characterize the system under consideration. Furthermore, we investigate the momentum resolved structure of CPG response to relate with the final results and strengthen our analysis from the perspective of the lattice models.

Longitudinal magnetoconductivity of tilted type-I Weyl semimetals from semiclassical to ultra-quantum regime

Weyl semimetals (WSMs) display many unusual magnetotransport phenomena. Here, based on the Landau quantization and Boltzmann equation, we theoretically study the longitudinal magnetoconductivity for tilted type-I WSMs from weak to strong magnetic field within a unified framework. It is found that, in semiclassical (weak magnetic field) regime, the conductivity has an angular dependent B-linear term besides the B-quadratic term common to isotropic nodes. In ultra-quantum (strong magnetic field) regime, the magnetoconductivity shows a linear dependence on B, and this dependence is affected by the tilt. In the intermediate regime, magnetoconductivity shows a tilt-modified quantum oscillation behavior due to the oscillation in the density of state. These findings recover the results for isotropic nodes without tilt, and suggest a possible way to identify the tilt axis of tilted WSMs through magnetotransport experiment.

A comparison of magnetoconductivities between type-I and type-II Weyl semimetals

It is well known that Weyl semimetals (WSMs) are classified into two types of type-I and type-II depending on whether or not they have electron and hole pockets. Also, these WSMs have peculiar transport properties such as negative longitudinal magnetoresistance and planar Hall effect because of a chiral anomaly. In this paper, however, we show that the chiral anomaly can cause positive longitudinal magnetoresistance in type-II WSMs. Here, we investigate longitudinal and transverse magnetoconductivities of time reversal symmetry broken type-I and type-II WSMs using a tight-binding model. The model allows us to describe both types of type-I and type-II WSMs by tuning parameters, and it has two Weyl points that are separated along the kx-direction. The numerical calculations of these conductivities are performed using the Boltzmann equation including the Berry curvature. It is found that longitudinal magnetoconductivities in the x-direction can have both positive and negative values depending on the magnitude of the inclination of a Weyl cone. This is because the zeroth Landau energy-level becomes either a hole-like one or an electron-like one depending on the magnitude of the inclination of the Weyl cone in type-II WSMs. These results imply that we can make a high MR-ratio device using type-II WSMs by tuning the inclination of their cones if it is possible to change their energy bands by the application of electric field and so on.

Transverse chiral magnetic photocurrent induced by linearly polarized light in mirror-symmetric Weyl semimetals

A new class of photocurrents is predicted to occur in both type-I and type-II Weyl semimetals. Unlike the previously studied photocurrents in chiral materials, the proposed current requires neither circularly polarized light, nor an absence of symmetry with respect to a plane of reflection. We show that if a Weyl semimetal has a broken inversion symmetry then linearly polarized light can induce a photocurrent transverse to the direction of an applied magnetic field, in spite of the symmetry with respect to a reflection plane and the time reversal symmetry. The class of materials in which we expect this to occur is sufficiently broad and includes the transition metal monopnictides such as TaAs. The effect stems from the dynamics of Weyl chiral quasi-particles in a magnetic field, restricted by the symmetries described above; because the resulting current is transverse to the direction of magnetic field, we call it the transverse chiral magnetic photocurrent. The magnitude of the resulting photocurrent is predicted to be significant in the THz frequency range, about $0.75\; \mathrm{\mu A}$ for type-I and $2.5\; \mathrm{\mu A}$ for type-II Weyl semimetals. This opens the possibility to utilize the predicted transverse chiral magnetic photocurrent for sensing unpolarized THz radiation.