Symmetric Weyl Research Articles

Giant photocurrent in asymmetric Weyl semimetals from the helical magnetic effect

We propose a new type of photoresponse induced in asymmetric Weyl semimetals in an external magnetic field. In usual symmetric Weyl semimetals in a magnetic field, the particles and holes produced by an incident light in different Weyl cones have opposite helicities and hence move in opposite directions, canceling each others's contributions to the photocurrent. However this cancelation does not occur if the Weyl semimetal possesses both a broken particle-hole symmetry and a broken spatial inversion symmetry. We call the resulting generation of photocurrent the helical magnetic effect because it is induced by the helicity imbalance in a magnetic field. We find that due to the large density of states in a magnetic field, the helical magnetic effect induces a remarkable large photocurrent for incident THz frequency light. This suggests a potential application of asymmetric Weyl semimetals for creating THz photosensors.

Appearance of the universal value e2/h of the zero-bias conductance in a Weyl semimetal-superconductor junction

We study the differential conductance of a time-reversal symmetric Weyl semimetal-superconductor (N-S) junction with an s-wave superconducting state. We find that there exists an extended regime where the zero-bias differential conductance acquires the universal value $e^{2}/h$ per unit channel, independent of the pairing and chemical potentials on each side of the junction, due to a perfect cancellation of Andreev and normal reflection contributions. This universal conductance can be attributed to the interplay of the unique spin/orbital-momentum locking and s-wave pairing that couples Weyl nodes of the same chirality. We expect that the universal conductance can serve as a robust and distinct signature for time-reversal symmetric Weyl fermions, and be observed in the recently discovered time-reversal symmetric Weyl semimetals.

Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points

Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum nonzero number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe4. We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe4 is a Weyl semimetal with the minimum number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.

Quantum transport in Weyl semimetal thin films in the presence of spin-orbit coupled impurities

Topological semimetals have been at the forefront of experimental and theoretical attention in condensed matter physics. Among these, recently discovered Weyl semimetals have a dispersion described by a three-dimensional Dirac cone, which is at the root of exotic physics such as the chiral anomaly in magnetotransport. In a time reversal symmetric (TRS) Weyl semimetal film, the confinement gap gives the quasiparticles a mass, while TRS is preserved by having an even number of valleys with opposite masses. The film can be tuned through a topological phase transition by a gate electric field. In this work, we present a theoretical study of the quantum corrections to the conductivity of a topological semimetal thin film, which is governed by the complex interplay of the chiral band structure, mass term, and scalar and spin-orbit scattering. We study scalar and spin-orbit scattering mechanisms on the same footing, demonstrating that they have a strong qualitative and quantitative impact on the conductivity correction. We show that, due to the spin structure of the matrix Green's functions, terms linear in the extrinsic spin-orbit scattering are present in the Bloch and momentum relaxation times, whereas previous works had identified corrections starting from the second order. In the limit of small quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to a potentially observable density dependence in the weak antilocalization correction. Moreover, when the mass term is around 30 percent of the linear Dirac terms, the system is in the unitary symmetry class with zero quantum correction and switching the extrinsic spin-orbit scattering drives the system to the weak antilocalization. We discuss the crossover between the weak localization and weak antilocalization regimes in terms of the singlet and triplet Cooperon channels, tuning the spin-orbit scattering strength.

Discovery of Lorentz-violating type II Weyl fermions in LaAlGe.

In quantum field theory, Weyl fermions are relativistic particles that travel at the speed of light and strictly obey the celebrated Lorentz symmetry. Their low-energy condensed matter analogs are Weyl semimetals, which are conductors whose electronic excitations mimic the Weyl fermion equation of motion. Although the traditional (type I) emergent Weyl fermions observed in TaAs still approximately respect Lorentz symmetry, recently, the so-called type II Weyl semimetal has been proposed, where the emergent Weyl quasiparticles break the Lorentz symmetry so strongly that they cannot be smoothly connected to Lorentz symmetric Weyl particles. Despite some evidence of nontrivial surface states, the direct observation of the type II bulk Weyl fermions remains elusive. We present the direct observation of the type II Weyl fermions in crystalline solid lanthanum aluminum germanide (LaAlGe) based on our photoemission data alone, without reliance on band structure calculations. Moreover, our systematic data agree with the theoretical calculations, providing further support on our experimental results.

General quantum-mechanical setting for field–antifield formalism as a hyper-gauge theory

A general quantum-mechanical setting is proposed for the field–antifield formalism as a unique hyper-gauge theory in the field–antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a “current time” purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger’s equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl’s symbol of the Hamiltonian. We take the path integral explicitly in the case of a hyper-gauge fermion being an arbitrary function rather than an operator.

Topological density-wave states in a particle-hole symmetric Weyl metal

We study the instabilities of a particle-hole symmetric Weyl metal with both electron and hole Fermi surfaces (FS) around the Weyl points. For a repulsive interaction, we find that the leading instability is towards a longitudinal spin-density-wave order (SDW$_z$). Besides, there exist three degenerate subleading instabilities: a charge-density-wave (CDW) instability and two transverse spin-density-wave (SDW$_{x,y}$) instabilities. For an attractive interaction the leading instabilities are towards two pair-density-wave orders (PDW) which pair the two FS's separately. Both the PDW and SDW$_z$ order parameters fully gap out FS's, while the CDW and SDW$_{x,y}$ ones leave line nodes on both FS's. For the SDW$_z$ and the PDW states, the surface Fermi arc in the metallic state evolves to a chiral Fermi line which passes the projection of the Weyl points and traverses the full momentum space. For the CDW state, the line node projects to a "drumhead" band localized on the surface, which can lead to a topological charge polarization. We verify the surface states by numerically simulating the angular-resolved photoemission spectroscopy data.

Probing unconventional superconductivity in inversion-symmetric doped Weyl semimetal

Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an s-wave superconductor in which we show that the application of a transverse uniform current in s-wave superconductor effectively cancels the momentum carried by FFLO states in doped WSM. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in s-wave superconductor that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSM. We analyze the topological phase transitions induced by nodal pair annihilation in non-equilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSM.

Chiral nodes and oscillations in the Josephson current in Weyl semimetals

The separation of the Weyl nodes in a broken time-reversal symmetric Weyl semimetal leads to helical quasi-particle excitations at the Weyl nodes, which, when coupled with overall spin conservation allows only inter-nodal transport at the junction of the Weyl semimetal with a superconductor. This leads to an unusual periodic oscillation in the Josephson current as a function of $k_0L$, where $L$ is the length of the Weyl semimetal and $2k_0$ is the inter-nodal distance. This oscillation is robust and should be experimentally measurable, providing a direct path to confirming the existence of chiral nodes in the Weyl semimetal.

Chiral tunneling in gated inversion symmetric Weyl semimetal.

Based on the chirality-resolved transfer-matrix method, we evaluate the chiral transport tunneling through Weyl semimetal multi-barrier structures created by periodic gates. It is shown that, in sharp contrast to the cases of three dimensional normal semimetals, the tunneling coefficient as a function of incident angle shows a strong anisotropic behavior. Importantly, the tunneling coefficients display an interesting periodic oscillation as a function of the crystallographic angle of the structures. With the increasement of the barriers, the tunneling current shows a Fabry-Perot type interferences. For superlattice structures, the fancy miniband effect has been revealed. Our results show that the angular dependence of the first bandgap can be reduced into a Lorentz formula. The disorder suppresses the oscillation of the tunneling conductance, but would not affect its average amplitude. This is in sharp contrast to that in multi-barrier conventional semiconductor structures. Moreover, numerical results for the dependence of the angularly averaged conductance on the incident energy and the structure parameters are presented and contrasted with those in two dimensional relativistic materials. Our work suggests that the gated Weyl semimetal opens a possible new route to access to new type nanoelectronic device.

QUASI CONFORMALLY SYMMETRIC WEYL MANIFOLDS

The present paper deals with a type of non-quasi flat Weyl manifold which is called quasi conformally symmetric. Some necessary and sufficient conditions between concircularly symmetric, conformally symmetric and quasi conformally symmetric Weyl manifolds are obtained and a special condition on the Weyl manifold admitting a semi-symmetric non-metric connection is studied.

A wavevector filter in inversion symmetric Weyl semimetal

We propose and demonstrate a wavevector filter for Weyl fermion based on evanescent wave or the interference effect in the barrier. It is shown that a perfect wavevector filter through a Weyl semimetal-based junction can be efficiently controlled by the barrier strength, the length of the barrier, and the incident energy of the Weyl fermion. Furthermore, the crystal structure oration is also vital in determining the wavevector filter effect. Those numerical results can be found in a good agreement with the theoretical analysis. It is anticipated that this property would receive wide applications in various Weyl semimetal-based electronic devices.

Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov--de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians. We show that depending on the crystal point-group symmetries and the topological properties of the bulk Bogoliubov-quasiparticle wave functions, different types of zero-energy Majorana modes can appear inside the vortex core. We find that for nodal NCSs with tetragonal point group ${C}_{4v}$ the vortex states are dispersionless along the vortex line, forming one-dimensional Majorana flat bands, while for NCSs with ${D}_{4}$ point-group symmetry the vortex modes are helical Majorana states with a linear dispersion along the vortex line. NCSs with monoclinic point group ${C}_{2}$, on the other hand, do not exhibit any zero-energy vortex-bound states. We show that in the case of the ${C}_{4v}$ $({D}_{4})$ point group the stability of these Majorana zero modes is guaranteed by a combination of reflection $(\ensuremath{\pi}$ rotation), time-reversal, and particle-hole symmetry. Considering continuous deformations of the quasiparticle spectrum in the presence of vortices, we show that the flat-band vortex-bound states of ${C}_{4v}$ point-group NCSs can be adiabatically connected to the dispersionless vortex-bound states of time-reversal symmetric Weyl superconductors. Experimental implications of our results for thermal transport and tunneling measurements are discussed.

Causal signal transmission by quantum fields. V: Generalised Keldysh rotations and electromagnetic response of the Dirac sea

The connection between real-time quantum field theory (RTQFT) [see, e.g., A. Kamenev and A. Levchenko, Adv. Phys. 58 (2009) 197] and phase-space techniques [E. Wolf and L. Mandel, Optical Coherence and Quantum Optics (Cambridge, 1995)] is investigated. The Keldysh rotation that forms the basis of RTQFT is shown to be a phase-space mapping of the quantum system based on the symmetric (Weyl) ordering. Following this observation, we define generalised Keldysh rotations based on the class of operator orderings introduced by Cahill and Glauber [K.E. Cahill, R.J. Glauber, Phys. Rev. 177 (1969) 1882]. Each rotation is a phase-space mapping, generalising the corresponding ordering from free to interacting fields. In particular, response transformation [L.I. Plimak, S. Stenholm, Ann. Phys. (N.Y.) 323 (2008) 1989] extends the normal ordering of free-field operators to the time-normal ordering of Heisenberg operators. Structural properties of the response transformation, such as its association with the nonlinear quantum response problem and the related causality properties, hold for all generalised Keldysh rotations.Furthermore, we argue that response transformation is especially suited for RTQFT formulation of spatial, in particular, relativistic, problems, because it extends cancellation of zero-point fluctuations, characteristic of the normal ordering, to interacting fields. As an example, we consider quantised electromagnetic field in the Dirac sea. In the time-normally-ordered representation, dynamics of the field looks essentially classical (fields radiated by currents), without any contribution from zero-point fluctuations. For comparison, we calculate zero-point fluctuations of the interacting electromagnetic field under orderings other than time-normal. The resulting expression is physically inconsistent: it does not obey the Lorentz condition, nor Maxwell’s equations.

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (−W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. First, what class of multitime averages the −W approximates and, second, how to proceed if the average in question does not belong to this class. To answer the first question, we develop a (in principle, exact) path-integral approach in phase space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The −W equations emerge as an approximation within these path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages, Kubo’s renowned formula relating the linear-response function to two-time commutators suffices. The −W is directly generalized to the response properties of the system allowing one to calculate approximate time normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

Static charged fluid around a massive magnetic dipole

An analytical solution of Einstein-Maxwell equations with a static fluid as a source is presented. The spacetime is represented by the axially symmetric Weyl metric and the energy-momentum tensor describes a coupling of a fluid with an electromagnetic field. When appropriate limits are performed we recover the well-known solutions of Gutsunaev-Manko and Schwarzschild. Also, using Eckart's thermodynamics, we calculated the temperature, the mechanical pressure, the charge density, and the energy density of the system. The analysis of thermodynamic quantities suggests that the solution can be used to represent a magnetized compact stellar object surrounded by a charged fluid.

Letter: Cerenkov Radiation from a Charged Particle in a Weyl–Dirac Theory

A thin shell can separate an interior region of Riemannian geometry from an exterior spherically symmetric Weyl space. We explore the possibility that a charged particle propagating in the gravitational field outside this thin shell could emit Cerenkov radiation. Some astrophysical scenarios in which such effect could arise are discussed.

Spherically symmetric static solutions in Weyl integrable spacetime

Solutions of spherically symmetric and static Weyl integrable spacetime are presented for three different cases: vacuum, electromagnetic and scalar external fields.

Multiexponent Weyl Metrics

Three subclasses of stationary axially symmetric diagonal Weyl metrics satisfying the empty-space Einstein equations are presented in an explicit form. These solutions generalize the $C$ metric (mass with constant acceleration) and contain six free parameters. Four of these parameters appear as exponents playing a role similar to $\ensuremath{\delta}$ in the Tomimatsu-Sato solution (mass with quadrupole moment). For integer values of the exponents these metrics are constructed from rational functions only. Special cases include various metrics of physical interest.

Directional singularities in Weyl gravitational fields

The Kretschmann scalar R μνϱσ R μνϱσ is evaluated for an arbitrary, axially symmetric Weyl gravitational field. From the analysis of this scalar it is found that certain Weyl solutions exhibit directional type singularities, i.e., the singular behaviour of the scalar depends upon the direction by which the singular point is approached.