Weyl Fermions Research Articles

Weyl Fermions and broken symmetry phases of laterally confined 3He films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D) 3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum, , for Cooper pairs. The power law suppression of the angular momentum, for , in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid 3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at . The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length . The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at , in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Gravitational waves from SU(N)/SP(N) composite Higgs models

We study possible strong first-order electroweak phase transitions in Composite Higgs models and we quantify the part of parameter space that can be probed with future gravitational wave experiments. We focus on models where the Composite Higgs sector arises from underlying four-dimensional strongly interacting gauge theories with fermions, and where the Standard Model fermion masses are induced via linear mixing terms with composite fermions — the so-called fermion partial compositeness framework. We perform our analysis for the general class of Composite Higgs models arising from N Weyl fermions in a pseudo-real representation of the new strongly interacting gauge group that dynamically triggers the global chiral symmetry breaking pattern SU(N) → Sp(N). The minimal model has N = 4 and for N > 4 the models feature complex scalar dark matter candidates arising as pseudo-Nambu-Goldstone bosons. We find a large number of points in the models parameter space which yield strong first-order electroweak phase transitions and identify the most important operators characterizing the strength of the phase transition. Almost all of these points are testable with future GW detectors such as LISA, Taiji, Tianqin, BBO, DECIGO and Ultimate-DECIGO.

When ℤ2 one-form symmetry leads to non-invertible axial symmetries

We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is ℤ2. This includes SU(N) gauge theories with matter in the (anti)symmetric and N even, and USp(2N) with a Weyl fermion in the adjoint, i.e. mathcal{N} = 1 SYM. We study the mixed ’t Hooft anomaly between the discrete axial symmetry and the 1-form symmetry and show that when it is non-trivial, it leads to non-invertible symmetries upon gauging the ℤ2. The TQFT dressing the non-invertible symmetry defects is universal to all the cases we study, namely it is always a U(1)2 CS theory coupled to the ℤ2 2-form gauge field. We uncover a pattern where the presence or not of non-invertible defects depends on the rank of the gauge group.

Topology stabilized fluctuations in a magnetic nodal semimetal

The interplay between magnetism and electronic band topology enriches topological phases and has promising applications. However, the role of topology in magnetic fluctuations has been elusive. Here, we report evidence for topology stabilized magnetism above the magnetic transition temperature in magnetic Weyl semimetal candidate CeAlGe. Electrical transport, thermal transport, resonant elastic X-ray scattering, and dilatometry consistently indicate the presence of locally correlated magnetism within a narrow temperature window well above the thermodynamic magnetic transition temperature. The wavevector of this short-range order is consistent with the nesting condition of topological Weyl nodes, suggesting that it arises from the interaction between magnetic fluctuations and the emergent Weyl fermions. Effective field theory shows that this topology stabilized order is wavevector dependent and can be stabilized when the interband Weyl fermion scattering is dominant. Our work highlights the role of electronic band topology in stabilizing magnetic order even in the classically disordered regime.

Zeeman Field-Induced Two-Dimensional Weyl Semimetal Phase in Cadmium Arsenide.

We report a topological phase transition in quantum-confined cadmium arsenide (Cd_{3}As_{2}) thin films under an in-plane Zeeman field when the Fermi level is tuned into the topological gap via an electric field. Symmetry considerations in this case predict the appearance of a two-dimensional Weyl semimetal (2D WSM), with a pair of Weyl nodes of opposite chirality at charge neutrality that are protected by space-time inversion (C_{2}T) symmetry. We show that the 2D WSM phase displays unique transport signatures, including saturated resistivities on the order of h/e^{2} that persist over a range of in-plane magnetic fields. Moreover, applying a small out-of-plane magnetic field, while keeping the in-plane field within the stability range of the 2D WSM phase, gives rise to a well-developed odd integer quantum Hall effect, characteristic of degenerate, massive Weyl fermions. A minimal four-band k·p model of Cd_{3}As_{2}, which incorporates first-principles effective g factors, qualitatively explains our findings.

How massless are Weyl fermions in Weyl semimetals

How massless are Weyl fermions in Weyl semimetals

Possible evidence of Weyl fermion enhanced thermal conductivity under magnetic fields in the antiferromagnetic topological insulator Mn(Bi1−xSbx)2Te4

We report thermal conductivity and Seebeck effect measurements on $\text{Mn}{({\text{Bi}}_{1\ensuremath{-}x}{\text{Sb}}_{x})}_{2}{\text{Te}}_{4}$ (MBST) with $x=0.26$ under applied magnetic fields below $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Our data shows clear indications of the electronic structure transition induced by the antiferromagnetic (AFM) to ferromagnetic (FM) transition driven by applied magnetic field as well as significant positive magnetothermal conductivity in the Weyl semimetal state of MBST. Further, by examining the dependence of magnetothermal conductivity on field orientation for MBST and comparison with the magnetothermal conductivity of ${\text{MnBi}}_{2}{\text{Te}}_{4}$, we see possible evidence of a contribution to thermal conductivity due to Weyl fermions in the FM phase of MBST. From the temperature dependence of the Seebeck coefficient under magnetic fields for MBST, we also observed features consistent with the Fermi surface evolution from a hole pocket in the paramagnetic state to a Fermi surface with coexistence of electron and hole pockets in the FM state. These findings provide further evidence for the field-driven topological phase transition from an AFM topological insulator to a FM Weyl semimetal.

Kramers nodal lines and Weyl fermions in SmAlSi

Kramers nodal lines (KNLs) have recently been proposed theoretically as a special type of Weyl line degeneracy connecting time-reversal invariant momenta. KNLs are robust to spin orbit coupling and are inherent to all non-centrosymmetric achiral crystal structures, leading to unusual spin, magneto-electric, and optical properties. However, their existence in in real quantum materials has not been experimentally established. Here we gather the experimental evidence pointing at the presence of KNLs in SmAlSi, a non-centrosymmetric metal that develops incommensurate spin density wave order at low temperature. Using angle-resolved photoemission spectroscopy, density functional theory calculations, and magneto-transport methods, we provide evidence suggesting the presence of KNLs, together with observing Weyl fermions under the broken inversion symmetry in the paramagnetic phase of SmAlSi. We discuss the nesting possibilities regarding the emergent magnetic orders in SmAlSi. Our results provide a solid basis of experimental observations for exploring correlated topology in SmAlSi

Impurity and dispersion effects on the linear magnetoresistance in the quantum limit

Magnetoresistance, that is, the change of the resistance with the magnetic field, is usually a quadratic function of the field strength. A linear magnetoresistance usually reveals extraordinary properties of a system. In the quantum limit where only the lowest Landau band is occupied, a quantum linear magnetoresistance was believed to be the signature of the Weyl fermions with 3D linear dispersion. Here, we comparatively investigate the quantum-limit magnetoresistance of systems with different band dispersions as well as different types of impurities. We find that the magnetoresistance can also be linear for the quadratic energy dispersion. We show that both longitudinal and transverse magnetoresistance can be linear if long-range-Gaussian-type impurities dominate, but Coulomb-type impurities can only induce linear transverse magnetoresistance. Moreover, we find a negative longitudinal magnetoresistance in massless Dirac fermions, regardless of the impurity type, as a result of the combined effect of the linear dispersion and the scattering mechanism. Our findings well explain some of the linear magnetoresistance observed in the experiments and provide insights to the understanding of quantum-limit magnetoresistance.

Trace anomalies for Weyl fermions: too odd to be true?

We review recent discussions regarding the parity-odd contribution to the trace anomaly of a chiral fermion. We pay special attention to the perturbative approach in terms of Feynman diagrams, comparing in detail the results obtained using dimensional regularization and the Breitenlohner–Maison prescription with other approaches.

Scattering-dependent transport of SrRuO3 films: From Weyl fermion transport to hump-like Hall effect anomaly

Recent observation of quantum transport phenomena of Weyl fermions has brought much attention to $4d$ ferromagnetic perovskite ${\mathrm{SrRuO}}_{3}$ as a magnetic Weyl semimetal. Additionally, the hump-like Hall effect anomaly, which might have a topological origin, has been reported for this material. Here, we show that the emergence of such phenomena is governed by the degree of scattering determined by the defect density (Ru-deficiency- and/or interface-driven-defect scattering) and measurement temperature (phonon scattering), where the former is controlled by varying the growth conditions of the ${\mathrm{SrRuO}}_{3}$ films in molecular beam epitaxy as well as the film thickness. The resulting electronic transport properties can be classified into three categories: clean, intermediate, and dirty regimes. The transport of Weyl fermions emerges in the clean regime, whereas that of topologically trivial conduction electrons in the ferromagnetic metal state prevails in the intermediate and dirty regimes. In the clean and intermediate regimes, anomalous Hall resistivity obeys a scaling law incorporating the intrinsic Karplus-Luttinger and extrinsic side-jump mechanisms. The hump-like Hall effect anomaly is observed only in the dirty regime, which is contrary to the scaling law between anomalous Hall resistivity and longitudinal resistivity. Hence, we conclude that this anomaly is not inherent to the material and does not have a topological origin. We also provide defect- and temperature-dependent transport phase diagrams of stoichiometric ${\mathrm{SrRuO}}_{3}$ and Ru-deficient ${\mathrm{SrRu}}_{0.7}{\mathrm{O}}_{3}$ where the appearance of Weyl fermions and hump-like Hall effect anomaly is mapped. These diagrams may serve as a guideline for designing $\mathrm{Sr}\phantom{\rule{0.16em}{0ex}}{\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{O}}_{3}$-based spintronic and topological electronic devices.

Study of the mercury chalcogenide single crystals by means of a combination of laser pump-probe thermoreflectance technique with Fabry–Perot interferometer

Near-surface layers of the mercury chalcogenide (HgSe and n-HgTe) single crystals with the electron concentration in the range of 7 × 1014–4.2 × 1018 сm−3 were studied using the laser pump-probe thermoreflectance (TR) technique combined with the Fabry–Perot (FP) interferometer in the wide temperature interval of 10–300= K. The TR–FP measurements were carried out toward samples with a freshly etched reflective surface. As a result, a minimum in the time dependence of the TR–FP signal and sign inversion of the TR–FP signal were revealed both for HgSe and n-HgTe within the specified temperature range. Noticeably, both anomalies were observed for n-HgTe at substantially lower temperatures than that for HgSe. The proposed qualitative interpretation of the observed anomalies is based on the hypothesis of two types of Weyl nodes located in the Brillouin zone of mercury chalcogenides involving specific for the Weyl semimetals energy barriers, separating the bulk Weyl fermion helical states from the topologically protected Fermi-arc surface states.

Topological enhancement of nonlinear transport in unconventional point-node semimetals

The topological singularity of the Bloch states close to the Fermi level significantly enhances nonlinear electric responses in topological semimetals. Here, we systematically characterize this enhancement for a large class of topological nodal-point fermions, including those with linear, linear-quadratic, and quadratic dispersions. Specifically, we determine the leading power-law dependence of the nonlinear response functions on the chemical potential $\ensuremath{\mu}$ defined relative to the nodal point. We identify two characteristics that qualitatively improve nonlinear transports compared to those of conventional Dirac and Weyl fermions. First, the type-II (overtilted) spectrum leads to the $log\ensuremath{\mu}$ enhancement of nonlinear response functions having zero scaling dimension with respect to $\ensuremath{\mu}$, which is not seen in a type-I (moderately or not tilted) spectrum. Second, the anisotropic linear-quadratic dispersion increases the power of small-$\ensuremath{\mu}$ divergence for the nonlinear response tensors along the linearly dispersing direction. Our work reveals new experimental signatures of unconventional nodal points in topological semimetals as well as provides a guiding principle for giant nonlinear electric responses.

Observation of Fermi arcs and Weyl nodes in a noncentrosymmetric magnetic Weyl semimetal

Weyl semimetal (WSM), a novel state of quantum matter, hosts Weyl fermions as emergent quasiparticles resulting from the breaking of either inversion or time-reversal symmetry. Magnetic WSMs that arise from broken time-reversal symmetry provide an exceptional platform to understand the interplay between magnetic order and Weyl physics, but only a few WSMs have been realized. Here, we identify CeAlSi as a new noncentrosymmetric magnetic WSM via angle-resolved photoemission spectroscopy (ARPES) and first-principles, density-functional theory based calculations. Our surface-sensitive vacuum ultraviolet ARPES data confirm the presence of surface Fermi arcs as the conclusive evidence for the existence of the Weyl semimetallic state in CeAlSi. We also observe bulk Weyl cones at the Fermi arc terminations in CeAlSi using bulk-sensitive soft-x-ray ARPES measurements. These results implicate CeAlSi as a unique platform for investigating exotic quantum phenomena resulting from the interaction of topology and magnetism.

Finite-momentum instability of a dynamical axion insulator

Due to the chiral anomaly, Weyl semimetals can exhibit a signature topological magnetoelectric response known as an axion term which is determined by the microscopic band structure. In the presence of strong interactions Weyl fermions may form a chiral condensate, with the intrinsic dynamics and fluctuations of the associated condensate phase producing a dynamical contribution to the axion response. Here we show that an imbalance in the density of right- and left-handed electrons drives an instability of the chiral condensate towards finite momentum and leads to strong fluctuations in the axion response. We derive a long-wavelength theory of Lifschitz type governing the dynamics of the Goldstone mode and use this to characterize its associated spatial fluctuations, which manifest as an inhomogeneous anomalous Hall effect. We show that these fluctuations produce signatures in inelastic light-scattering experiments across a broad spectrum of frequencies, and can be used to determine the structure factor for the axionic collective mode.

Vortical effects in chiral band structures

The chiral vortical effect is a chiral anomaly-induced transport phenomenon characterized by an axial current in a uniformly rotating chiral fluid. It is well understood for Weyl fermions in high energy physics, but its realization in condensed matter band structures, including those of Weyl semimetals, has been controversial. In this work, we develop the Kubo response theory for electrons in a general band structure subject to space- and time-dependent rotation or vorticity relative to the background lattice. For continuum Hamiltonians, we recover the chiral vortical effect in the static limit and the transport or uniform limit when the fluid, strictly, is not a Fermi liquid. In the transport limit of a Fermi liquid, we describe an effect that we dub the gyrotropic vortical effect. The latter is governed by Berry curvature of the occupied bands while the former contains an additional contribution from the magnetic moment of electrons on the Fermi surface. The two vortical effects can be understood as kinematic analogs of the well-known chiral and gyrotropic magnetic effects in chiral band structures. We address recent controversies in the field and conclude by describing device geometries that exploit Ohmic or Seebeck transport to drive the vortical effects.

Field-induced chiral transitions in the Weyl semimetal TaP

The chiral anomaly effect has been regarded as a hallmark of Weyl semimetals. While most research focuses on the change of electrical conductivity due to the chiral charge-pumping effect, these transport measurements are accompanied by other effects such as weak antilocalization which are difficult to exclude. Also, the magnetic field intensity at which the energy dispersion of the Landau level starts to display the chiral anomaly effect is hard to identify. Here, we report the evolutionary process of the energy dispersion of the zeroth Landau level under increasing magnetic fields, and we elucidate the relationship between the chiral Landau level and the Fermi level via magneto-optical measurements in Weyl semimetal TaP. Two series of Landau-level transitions have been extracted and fitted well to a massless Weyl fermion model and a classical semiconductor model, respectively. The field-induced chiral Landau-level transition is obtained from a comparison between the spectra under Voigt geometry and Faraday geometry in an increasing magnetic field. The chiral nature of the zeroth Landau level is found to enhance with the increase of magnetic field and clearly manifests in the magneto-optical spectrum above 13 T. The state transition of the zeroth Landau level can be explained by the strength of the field-induced chiral anomaly effect and the position of the Fermi level. These magneto-optical results unveil the chiral Landau-level transitions in TaP, which serves as an ideal material platform to analyze the chiral anomaly effect.

Nonlinear photoconductivities and quantum geometry of chiral multifold fermions

Chiral multifold fermions are quasiparticles that appear only in chiral crystals such as transition metal silicides in the cubic B20 structure (i.e., the CoSi family), and they may show exotic physical properties. Here we study the injection and shift photoconductivities and also the related geometrical quantities for several types of chiral multifold fermions, including spin-1/2 as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple-point, and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal symmorphic model to describe the triple-point fermions (TPF). We also consider the more realistic model Hamiltonian for the CoSi family including both linear and quadratic terms. We find that injection currents due to circularly polarized light are quantized as a result of the Chern numbers carried by the multifold fermions within the linear models. Surprisingly, we discover that in the TPF model, the linear shift conductivities, responsible for the shift current generation by linearly polarized light, are proportional to the pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

Pressure-induced transition from a Mott insulator to a ferromagnetic Weyl metal in La2O3Fe2Se2

The insulator-metal transition in Mott insulators, known as the Mott transition, is usually accompanied with various novel quantum phenomena, such as unconventional superconductivity, non-Fermi liquid behavior and colossal magnetoresistance. Here, based on high-pressure electrical transport and XRD measurements, and first-principles calculations, we find that a unique pressure-induced Mott transition from an antiferromagnetic Mott insulator to a ferromagnetic Weyl metal in the iron oxychalcogenide La2O3Fe2Se2 occurs around 37 GPa without structural phase transition. Our theoretical calculations reveal that such an insulator-metal transition is mainly due to the enlarged bandwidth and diminishing of electron correlation at high pressure, fitting well with the experimental data. Moreover, the high-pressure ferromagnetic Weyl metallic phase possesses attractive electronic band structures with six pairs of Weyl points close to the Fermi level, and its topological property can be easily manipulated by the magnetic field. The emergence of Weyl fermions in La2O3Fe2Se2 at high pressure may bridge the gap between nontrivial band topology and Mott insulating states. Our findings not only realize ferromagnetic Weyl fermions associated with the Mott transition, but also suggest pressure as an effective controlling parameter to tune the emergent phenomena in correlated electron systems.

Causal structure of interacting Weyl fermions in condensed matter systems

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other’s energy-momentum dispersion cones–analogous to two events that can only have a causal connection if they lie in each other’s light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated ‘thick horizon’ in the emergent causal structure.