The surface Fermi arc, as a hallmark of Weyl semimetals (WSMs), has been well known in current research, but it remains a challenge to unveil novel phenomena associated with the Fermi arc. Here, we predict a heretofore unrecognized process in WSMs, namely, the photoinduced transition between the bulk states and the Fermi arc. We find this process is significant and can lead to a large effective three-dimensional shift current on the boundaries with the Fermi arc in wide terahertz range. Moreover, due to the low symmetry of the boundaries, the surface photogalvanic effect predicted here can appear in a large class of WSMs that do not have bulk shift current. Hence, our work not only unveils a hidden photogalvanic effect in WSMs but also suggests that all the WSMs are promising material candidates for developing efficient terahertz photodetectors.
The photogalvanic effect -- a rectified current induced by light irradiation -- requires the intrinsic symmetry of the medium to be sufficiently low, which strongly limits candidate materials for this effect. In this work we explore how in Weyl semimetals the photogalvanic effect can be enabled and controlled by design of the material surface. Specifically, we provide a theory of ballistic linear and circular photogalvanic current in a Weyl semimetal spatially confined to a slab under general and variable surface boundary conditions. The results are applicable to Weyl semimetals with an arbitr…
We theoretically study the impact of impurities on the photogalvanic effect (PGE) in Weyl semimetals with weakly tilted Weyl cones. Our calculations are based on a two-nodes model with an inversion symmetry breaking offset and we employ a kinetic equation approach in which both optical transitions as well as particle-hole excitations near the Fermi energy can be taken into account. We focus on the parameter regime with a single photoactive node and control the calculation in small impurity concentration. Internode scattering is treated generically and therefore our results allow to continuousl…
In this paper we review both theoretical and experimental studies on spin-related photogalvanic effects. A short phenomenological introduction is followed by the discussion of the circular photogalvanic effect, the direct and inverse spin-galvanic effects and the trembling motion of spin-polarized electrons. Then we consider the pure spin currents and magneto-gyrotropic photocurrents. Finally, we discuss the spin-dependent photocurrents in topological insulators and Weyl semimetals.
Using first-principles calculations, we investigate the photogalvanic effect in the Weyl semimetal material TaAs. We find colossal photocurrents caused by the Weyl points in the band structuure in a wide range of laser frequency. Our calculations reveal that the photocurrent is predominantly contributed by the three-band transition from the occupied Weyl band to the empty Weyl band via an intermediate band away from the Weyl cone, for excitations both by linearly and circularly polarized lights. Therefore, it is significant to sum over all three-band transitions by considering a full set of Bl…
Weyl semimetals are gapless topological states of matter with broken inversion and/or time reversal symmetry, which can support unconventional responses to externally applied electrical, optical and magnetic fields. Here we report a new photogalvanic effect in type-II WSMs, MoTe2 and Mo0.9W0.1Te2, which are observed to support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. This effect occurs exclusively in the inversion broken phase, where crucially we find that it is associated with a spatially varying beam profile via a new dispersive contribut…
Weyl semimetal (WSM) is expected to be an ideal spintronic material owing to its spin currents carried by the bulk and surface states with spin-momentum locking. A photocurrent generation in noncentrosymmetric WSM was also predicted owing to its broken inversion symmetry and linear energy dispersion which are unique to Weyl systems. In our recent measurements, the circular photogalvanic effect (CPGE) has been demonstrated in WSM of TaAs. The CPGE voltage is proportional to the helicity of the incident light and reverses its direction on changing the radiation helicity from left handed to right…
So far, the circular photogalvanic effect (CPGE) is the only possible quantized signal in Weyl semimetals. With inversion and mirror symmetries broken, Weyl and multifold fermions in band structures with opposite chiralities can stay at different energies and generate a net topological charge. Such kind of net topological charge can present as a quantized signal in the circular polarized light induced injection current. According to current theoretical understanding, RhSi and its counterparts are believed to be the most promising candidate for the experimental observation of the quantized CPGE…
Dirac semimetals are expected to forbid the manifestation of the circular photogalvanic effect (CPGE) because of their crystal inversion symmetry. Here, we report the observation of the CPGE in Cd3As2 nanobelt field effect transistors, when the photoexcitation is focused in the vicinity of the metal contacts up to room temperature. We attribute the CPGE to the Schottky electric field induced symmetry breaking, which results in the photocurrent modulation by circularly polarized photoexcitation via spin-momentum locking. The hypothesis is supported by a suite of experiments including spatially …
We develop a theory of the direct interband and indirect intraband photogalvanic effects in Weyl semimetals belonging to the gyrotropic classes with improper symmetry operations. At zero magnetic field, an excitation of such a material with circularly polarized light leads to a photocurrent whose direction depends on the light helicity. We show that in the semimetals of the C$_{2v}$ symmetry, an allowance for the tilt term in the effective Hamiltonian is enough to prevent cancellation of the photocurrent contributions from the Weyl cones of opposite chiralities. In the case of the C$_{4v}$ sym…
Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is an integer topological invariant known as the Berry monopole charge. The discovery of new classes of Weyl materials is driving the search for novel properties that derive directly from the Berry charge. The circular photogalvanic effect (CPGE), whereby circular polarized light generates a current whose direction depends on the helicity of the absorbed photons, is a striking example of a macroscopic property that emerges from Weyl topology. Recen…
We show that, under the effect of an external magnetic field, a photogalvanic effect and the generation of second harmonic wave can be induced in inversion-symmetric and time reversal invariant Dirac semimetals. The mechanism responsible of these non linear optical responses is the magnetochiral effect. The origin of this magnetochiral effect is the band bending of the dispersion relation in real Dirac semimetals. Some observable consequences of this phenomenon are the appearance of a dc current on the surface of the system when it is irradiated with linearly polarized light or a rotation of t…
Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction \cite{chang20}, we have measured the linear and circular photogalvanic effect currents…
The acoustogalvanic effect is proposed as a nonlinear mechanism to generate a direct electric current by passing acoustic waves in Dirac and Weyl semimetals. Unlike the standard acoustoelectric effect, which relies on the sound-induced deformation potential and the corresponding electric field, the acoustogalvanic one originates from the pseudo-electromagnetic fields, which are not subject to screening. The longitudinal acoustogalvanic current scales at least quadratically with the relaxation time, which is in contrast to the photogalvanic current where the scaling is linear. Because of the in…
We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.
We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under magnetic field as a consequence of an anisotropic $B^2$ contribution, which may explain the low-field regime of recent experiments; (ii) predicts strong second harmonic generation proportional to …
The ternary van der Waals material NbIrTe$_4$ is a Type-II Weyl semimetal. We use a tunable circularly polarized mid-infrared laser to investigate the existence of band-to-band excitations using transient reflectivity in an exfoliated nanoflake and photothermoelectric and photogalvanic signals in a device. Unpolarized photothermoelectric spectroscopy shows that the absorption in the Weyl semimetal increases rapidly above 0.3 eV as expected from the increase in the density of states from DFT calculations. However, the reflectivity shows a sign change in the circular dichroism of the reflected l…
Theory of light absorption and circular photocurrent in Weyl semimetals is developed for arbitrary large light intensities with account for both elastic and inelastic relaxation processes of Weyl fermions. The direct optical transition rate is shown to saturate at large intensity, and the saturation behaviour depends on the light polarization and on the ratio of the elastic and inelastic relaxation times. The linear-circular dichroism in absorption is shown to exceed 10~\% at intermediate light wave amplitudes and fast energy relaxation. At large intensity $I$, the light absorption coefficient…
We have studied theoretically the Weyl semimetals the point symmetry group of which has reflection planes and which contain equivalent valleys with opposite chiralities. These include the most frequently studied compounds, namely the transition metals monopnictides TaAs, NbAs, TaP, NbP, and also Bi$_{1-x}$Sb$_x$ alloys. The circular photogalvanic current, which inverts its direction under reversal of the light circular polarization, has been calculated for the light absorption under direct optical transitions near the Weyl points. In the studied materials, the total contribution of all the val…
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 …
We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied …
The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied ac electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear dc current as it is second-order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of nonzero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On exam…
The second-order nonlinear optical (NLO) processes, such as the photogalvanic effect and second-order harmonic generation (SHG), play crucial roles in probing and controlling light-matter interactions for energy and device applications. To date, most studies of second-order NLO processes focus on materials with broken spatial inversion symmetry, such as proper ferroelectrics and noncentrosymmetric Weyl semimetals. Nevertheless, inversion symmetry of Shubnikov groups can be broken via spin-ordering in centrosymmetric crystals. Unfortunately, these materials are less common, and their NLO respon…
We propose and study generic multi-Weyl semimetal (mWSM) lattice Hamiltonians that break particle-hole symmetry. These models fall into two categories: model I (model II) where the gap and tilt terms are coupled (decoupled) can host type-I and type-II Weyl nodes simultaneously (separately) in a hybrid phase (type-I and type-II phases, respectively). We concentrate on the question of how anisotropy and non-linearity in the dispersions, gaps and tilt terms influence diffusive second order transport quantities namely, the circular photogalvanic effect (CPGE) and the Berry curvature dipole (BCD) a…
As the development of topological band theory, comprehensive databases about time reversal and crystalline symmetries protected nonmagnetic topological materials were developed via first-principles calculations recently. However, owing to the low symmetry requirement of Weyl points, the symmetry-based topological indicator cannot be applied to Weyl semimetals (WSMs). Hitherto, the WSMs with Weyl points in arbitrary positions are still absent in the well-known databases. In this work, we develop an efficient algorithm to search for Weyl points automatically and establish a database of nonmagnet…
Purcell enhancement of photogalvanic currents in a van der Waals plasmonic self-cavity
Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）；Center for Free-Electron Laser Science（自由电子激光科学中心）；Department of Physics, Columbia University（哥伦比亚大学物理系）
Asymmetric Weyl semimetals, which possess an inherently chiral structure, have different energies and dispersion relations for left- and right-handed fermions. They exhibit certain effects not found in symmetric Weyl semimetals, such as the quantized circular photogalvanic effect and the helical magnetic effect. In this work, we derive the conditions required for breaking chiral symmetry by applying an external field in symmetric Weyl semimetals. We explicitly demonstrate that in certain materials with the $T_d$ point group, magnetic fields along low symmetry directions break the symmetry betw…
The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum $e^3/h^2$ for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbard interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are…
Physicists have discovered a novel topological semimetal, the Weyl semimetal, whose surface features a non-closed Fermi surface while the low energy quasiparticles in the bulk emerge as Weyl fermions. Here they share a brief review of the development and present perspectives on the next step forward.
One of the main features of Weyl semimetals is the existence of Fermi arc surface states at their surface, which cannot be realized in pure two-dimensional systems in the absence of many-body interactions. Due to the gapless bulk of the semimetal, it is, however, challenging to observe clear signatures from the Fermi arc surface states. Here, we propose to detect such novel surface states via perfect negative refraction that occurs between two adjacent open surfaces with properly orientated Fermi arcs. Specifically, this phenomenon visibly manifests in non-local transport measurement, where th…
We consider finite-sized interfaces of a Weyl semi-metal and show that the corresponding confinement potential is similar to the application of a magnetic field. Among the numerous states, which can be labeled by indices n like in Landau levels, the n = 0 surface state describes the Weyl semimetal Fermi arc at a given chemical potential. Moreover, the analogy with a magnetic field shows that an external in-plane magnetic field can be used to distort the Fermi arc and would explain some features of magneto-transport in Weyl semimetals. We derive the Fermi arc for type-I and type-II Weyl semimet…
We propose a one-parameter family of noninteracting lattice models for Weyl semimetals with 4 Weyl nodes and tunable Fermi arcs. These 2-band model Hamiltonians are time-reversal symmetric with $\mathrm{T}^2 = + 1$, and tuning the parameter changes the connectivity of the Fermi arcs continuously without affecting the location and chiralities of the Weyl nodes in the bulk Brillouin zone. The bulk polarization and magnetization are shown to vary with this parameter, a dependence inaccessible to the low energy effective field theory.
By utilizing symmetry analysis and electronic structure calculations, we investigated the low-temperature orthorhombic phase of Ag$_{2}$Se in ${\cal SG}$~17. In addition to the discovery of a nodal plane at $k_{z}=π$ protected by the joint operation of time-reversal (${\cal T}$) and the 2-fold screw rotation $S_{2z}$, we found 24 Weyl points mainly residing at the $k_{y}=0$ plane with notable Fermi arc and large quasiparticle interference pattern (QPI). Due to the absence of mirror symmetry, a pair of Weyl points with opposite chirality reside at different binding energies, which makes this sy…
Floquet engineering, the concept of tailoring a system by a periodic drive, is increasingly exploited to design and manipulate topological phases of matter. In this work, we study periodically driven higher-order topological Dirac semimetals associated with a $k$-dependent quantized quadrupole moment by applying circularly polarized light. The undriven Dirac semimetals feature gapless higher-order hinge Fermi arc states which are the consequence of the higher-order topology of the Dirac nodes. Floquet Weyl semimetal phases with hybrid-order topology, characterized by both a $k$-dependent quant…
The hallmark of Weyl semimetals is the existence of open constant-energy contours on their surface -- the so-called Fermi arcs -- connecting Weyl points. Here, we show that for time-reversal symmetric realizations of Weyl semimetals these Fermi arcs in many cases coexist with closed Fermi pockets originating from surface Dirac cones pinned to time-reversal invariant momenta. The existence of Fermi pockets is required for certain Fermi-arc connectivities due to additional restrictions imposed by the six $\mathbb{Z}_2$ topological invariants characterizing a generic time-reversal invariant Weyl …
Weyl semimetals constitute a newly discovered class of three-dimensional topological materials with linear touchings of valence and conduction bands in the bulk. The most striking property of topological origin in these materials, so far unequivocally observed only in photoemission experiments, is the presence of open constant-energy contours at the boundary --- the so-called Fermi arcs. In this work, we establish the universal characteristics of Fermi-arc contributions to surface quasiparticle interference. Using a general phenomenological model, we determine the defining interference pattern…
We propose an analytical model describing Fermi arc surface states observed in the recent investigations of Weyl semimetals. The effective two-valley Hamiltonian is supplemented by the boundary conditions taking into account both the intravalley and intervalley interfacial interaction. We demonstrate that the latter is crucial for the formation of the surface states having the form consistent with the experimental data. Depending on the magnitude and interplay between the intravalley and intervalley interactions, the Fermi arc connects two nearby or distant valleys. Moreover, the emergence of …
The disjointed Fermi-arcs in Weyl semimetals can intertwine with chiral bulk modes and participate in unusual closed magnetic orbits in the presence of a vertical magnetic field. Here we carry out the quantum oscillation study of such unusual Weyl magnetic orbits in Dirac semimetal Cd3As2, a close cousin of Weyl semimetals. We find that extra two-dimensional (2D) quantum oscillations emerge at high field, which superimpose on 3D bulk background and can be attributed to the Weyl magnetic orbits, when the thickness of nanoplates is smaller than the mean free path of the electrons. Further eviden…
We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools - semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals - we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically c…
The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e. disjoint segments of a two-dimensional Fermi contour. We present a quantum-mechanical non-local theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry. These are collective excitations constructed from topological Fermi arc and bulk electron states and arising from electron-electron interactions, which are treated in the realm of the random phase approximation. Our theory includes quantum effects associated with the penetration of the Fermi arc surface states into the bulk and dissipation, which is intrinsi…
Weyl semimetals are gapless three-dimensional topological materials where two bands touch at even number of points in the Brillouin zone. In this work we study a zincblende lattice model realizing a time-reversal invariant Weyl semimetal. The bulk dynamics is decribed by twelve helical Weyl nodes. Surface states form a peculiar quasi two-dimensional helical metal fundamentally different from the Dirac form typical for topological insulators. Allowed direction of velocity and spin of low-energy surface excitations are locked to the cubic symmetry axes. The studied system illustrates general pro…
In the recently discovered Weyl semimetals, the Fermi surface may feature disjoint, open segments -- the so-called Fermi arcs -- associated with topological states bound to exposed crystal surfaces. Here we show that the collective dynamics of electrons near such surfaces sharply departs from that of a conventional three-dimensional metal. In magnetic systems with broken time reversal symmetry, the resulting Fermi arc plasmons (FAPs) are chiral, with dispersion relations featuring open, hyperbolic constant frequency contours. As a result, a large range of surface plasmon wave vectors can be su…
Fermi arc surface states, the manifestation of the bulk-edge correspondence in Weyl semimetals, have attracted much research interest. In contrast to the conventional Fermi loop, the disconnected Fermi arcs provide an exotic 2D system for exploration of novel physical effects on the surface of Weyl semimetals. Here, we propose that visible conductance oscillation can be achieved in the planar junctions fabricated on the surface of Weyl semimetal with a pair of Fermi arcs. It is shown that Fabry-Pérot-type interference inside the 2D junction can generate conductance oscillation with its visibil…
The recent experimental discovery of a Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state band structure, consisting of Fermi arcs. So far, work has focused on Weyl semimetals with strong spin-orbit coupling (SOC). However, Weyl semimetals with weak SOC may allow tunable spin-splitting for device applications and may exhibit a crossover to a spinless topological phase, such as a Dirac line semimetal in the case of spinless TaAs. NbP, isostructural to TaAs, may realize the first Weyl semimetal in the limit o…
Weyl semimetals are known to host massless surface states called Fermi arcs. These Fermi arcs are the manifestation of the bulk-edge correspondence in topological matter and thus are analogous to the topological chiral surface states of topological insulators. It has been shown that the latter, depending on the smoothness of the surface, host massive Volkov-Pankratov(VP) states that coexist with the chiral ones. Here, we investigate these VP states in the framework of Weyl semimetals, namely their density of states and magneto-optical response. We find the selection rules corresponding to opti…
