The circular photogalvanic effect (CPGE) is the only possible quantized signal in Chiral Weyl and multi-fold semimetals with inversion and mirror symmetries broken. Here, we review CPGE in the chiral multifold semimetals in terms of classification of CPGE tensor, the quantization of CPGE from k.p effective model and topological semimetal RhSi family. Firstly, we give complete symmetric analysis of CPGE tensors for all nonmagnetic point groups, and get a table classifying matrix of response tensors. Secondly, the CPGE becomes a quantized response in the noncentrosymmetric topological semimetals, and depends on the Chern number of multifold fermions. Based on k.p effective model with linear dispersion, detailed derivations about the quantization of CPGE are given. Finally, according to ab-initio analysis for the quantized CPGE based on noninteracting electronic structures, we review previous reports and make new calculations for the chiral topological semimetals in RhSi family, which can be separated into two groups. The first group, including RhSi, PtAl and CoSi, can be the promising candidates to exhibit a quantized CPGE trace, while the second group includes PdGa, PtGa and RhSn without a quantization.
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…
We examine the magneto-optical response of chiral multifold fermions. Specifically, we show that they are ideal candidates for observing the Helical Magnetic Effect (HME) previously predicted for simple Weyl fermions. Unlike Weyl fermions, the HME is present in multifold fermions even in the simplest case where the low-energy dispersion is linear and spherically symmetric. In this ideal case, we derive an analytical expression for the HME and find it is proportional to the circular photogalvanic effect; for realistic parameters and accounting for the geometry of the setup, the HME photocurrent…
We present an optical conductivity study of the multifold semimetal PdGa, performed in a broad spectral range (100 - 20000 cm-1; 12 meV - 2.5 eV) down to T = 10 K. The conductivity at frequencies below 4000 cm-1 is dominated by free carriers while at higher frequencies interband transitions provide the major contribution. The spectra do not demonstrate a significant temperature evolution: only the intraband part changes as a function of temperature with the plasma frequency remaining constant. The interband contribution to the conductivity exhibits a broad peak at around 5500 cm-1 and increase…
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…
Recent experiments in the topological Weyl semimetal TaAs have observed record-breaking second-harmonic generation, a non-linear optical response at $2ω$ generated by an incoming light source at $ω$. However, whether second-harmonic generation is enhanced in topological semimetals in general is a challenging open question because their band structure entangles the contributions arising from trivial bands and topological band crossings. In this work, we circumvent this problem by studying RhSi, a chiral topological semimetal with a simple band structure with topological multifold fermions close…
Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals
Institute of Science Tokyo（东京科学大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Czech Academy of Sciences（捷克科学院）；the University of Tokyo（东京大学）；Hiroshima University（广岛大学）；RIKEN（理化学研究所）
Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and non-linear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of …
The experimental manifestation of topological effects in bulk materials under ambient conditions, especially those with practical applications, has attracted enormous research interest. Recent discovery of Weyl semimetal provides an ideal material platform for such endeavors. The Berry curvature in a Weyl semimetal becomes singular at the Weyl node, creating an effective magnetic monopole in the k-space. A pair of Weyl nodes carry quantized effective magnetic charges with opposite signs, and therefore, opposite chirality. Although Weyl-point-related signatures such as chiral anomaly and non-cl…
We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasi-particles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drud…
The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light's polarization, known as the circular photogalvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material par…
Nonlinear optical responses of quantum materials have recently undergone dramatic developments to unveil nontrivial geometry and topology. A remarkable example is the quantized longitudinal circular photogalvanic effect (CPGE) associated with the Chern number of Weyl fermions, while the physics of transverse CPGE in Weyl semimetals remains exclusive. Here, we show that the transverse CPGE of Lorentz invariant Weyl fermions is forced to be zero. We find that the transverse photocurrents of Weyl fermions are associated not only with the Chern numbers but also with the degree of Lorentz-symmetry …
Plasmonics in topological semimetals offers exciting opportunities for fundamental physics exploration as well as for technological applications. Here, we investigate plasmons in the exemplar chiral crystal CoSi, which hosts a variety of multifold fermionic excitations. We show that CoSi hosts two distinct plasmon modes in the infrared regime at 0.1 eV and 1.1 eV in the long-wavelength limit. The 0.1 eV plasmon is found to be highly dispersive, and originates from intraband collective oscillations associated with a double spin-1 excitation, while the 1.1 eV plasmon is dispersionless and it inv…
Structurally chiral materials hosting multifold fermions with large topological number have attracted considerable attention because of their naturally long surface Fermi arcs and bulk quantized circular photogalvanic effect (CPGE). Multifold fermions only appear in metallic states, and therefore, most studies so far have only focused on the semimetals in compounds with chiral crystal structures. In this work, we show that the structurally chiral topological trivial insulators are also exotic states, which is interesting from the application point of view, owing to their natural advantage to h…
Non-symmorphic chiral topological crystals host exotic multifold fermions, and their associated Fermi arcs helically wrap around and expand throughout the Brillouin zone between the high-symmetry center and surface-corner momenta. However, Fermi-arc splitting and realization of the theoretically proposed maximal Chern number rely heavily on the spin-orbit coupling (SOC) strength. In the present work, we investigate the topological states of a new chiral crystal, PtGa, which has the strongest SOC among all chiral crystals reported to date. With a comprehensive investigation using high-resolutio…
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…
Higher-fold chiral fermions that go beyond two-fold Weyl fermions have recently been reported in crystalline systems. Here, we focus on such excitations in several binary, ternary and quaternary alloys/compounds with CoGe, BiSbPt and KMgBO3 as the representative examples that belong to the crystal space group (SG) 198. We found distinct three-fold, four-fold and six-fold chiral fermions in the bulk via Density Functional computations. We provide general symmetry arguments for the protection of these degeneracies with special emphasis on the four-fold fermions. Our surface spectra simulations s…
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…
The theoretical proposal of chiral fermions in topological semimetals has led to a significant effort towards their experimental realization. In particular, the Fermi surfaces of chiral semimetals carry quantized Chern numbers, making them an attractive platform for the observation of exotic transport and optical phenomena. While the simplest example of a chiral fermion in condensed matter is a conventional $|C|=1$ Weyl fermion, recent theoretical works have proposed a number of unconventional chiral fermions beyond the Standard Model which are protected by unique combinations of topology and …
We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished based on the degeneracy of the band crossings, their codimension (e.g., point or line nodes), as well as the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give ris…
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…
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…
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…
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 curva…
As a fascinating topological phase of matter, Weyl semimetals host chiral fermions with distinct chiralities and spin textures. Optical excitations involving those chiral fermions can induce exotic carrier responses, and in turn lead to novel optical phenomena. Here, we discover strong coherent chiral terahertz emission from the Weyl semimetal TaAs and demonstrate unprecedented manipulation over its polarization on a femtosecond timescale. Such polarization control is achieved via the colossal ultrafast photocurrents in TaAs arising from the circular or linear photogalvanic effect. We unravel …
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…
The observation of chirality is ubiquitous in nature. Contrary to intuition, the population of opposite chiralities is surprisingly asymmetric at fundamental levels. Examples range from parity violation in the subatomic weak force to the homochirality in essential biomolecules. The ability to achieve chirality-selective synthesis (chiral induction) is of great importance in stereochemistry, molecular biology and pharmacology. In condensed matter physics, a crystalline electronic system is geometrically chiral when it lacks any mirror plane, space inversion center or roto-inversion axis. Typica…
Topological Weyl semimetals have been attracting broad interest. Recently, a new type of Weyl point with topological charge of $4$, termed as charge-4 Weyl point (C-4 WP), was proposed in spinless systems. Here, we show the minimum symmetry requirement for C-4 WP is point group $T$ together with ${\cal T}$ symmetry or point group $O$. We establish a minimum tight-binding model for C-4 WP on a cubic lattice with time-reversal symmetry and without spin-orbit coupling effect. This lattice model is a two-band one, ontaining only one pair of C-4 WPs with opposite chirality around Fermi level. Based…
Quantized Photocurrents in Gapless Topological Matter
Princeton University（普林斯顿大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Nanyang Technological University（南洋理工大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Indian Institute of Technology Delhi（德里印度理工学院）；Stanford University（斯坦福大学）；Paul Scherrer Institute（保罗谢尔研究所）；Bruker Scientific, LLC（布鲁克科学有限责任公司）；University of California, Los Angeles（加州大学洛杉矶分校）
