The discovery of Weyl and Dirac semimetals has produced a number of dramatic physical effects, including the chiral anomaly and topological Fermi arc surface states. We point out that a very different but no less dramatic physical effect is also to be found in these materials: discrete scale invariance. This invariance leads to bound state spectra for Coulomb impurities that repeat when the binding energy is changed by a fixed factor, reminiscent of fractal behavior. We show that this effect follows from the peculiar dispersion relation in Weyl and Dirac semimetals. It is observed when such a material is placed in very strong magnetic field B: there are oscillations in the magnetoresistivity somewhat similar to Shubnikov-de Haas oscillations but with a periodicity in ln B rather than 1/B. These oscillations should be present in other thermodynamic and transport properties. The oscillations have now been seen in three topological semimetals: ZrTe$_{5}$, TaAs, and Bi.
We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e. a three-dimensional metal with linear band touchings acting as point-like sources of Berry curvature in momentum space, termed "Weyl-Berry monopoles". We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a universal dissipationless second-order anom…
Type-II Weyl semimetals are characterized by the tilted linear dispersion in the low-energy excitations, mimicking Weyl fermions but with manifest violation of the Lorentz invariance, which has intriguing quantum transport properties. The magnetoconductivity of type-II Weyl semimetals is investigated numerically based on lattice models in parallel electric and magnetic field. We show that in the high-field regime, the sign of the magnetoconductivity of an inversion-symmetry-breaking type-II Weyl semimetals depends on the direction of the magnetic field, whereas in the weak field regime, positi…
While several magnetic topological semimetals have been discovered in recent years, their band structures are far from ideal, often obscured by trivial bands at the Fermi energy. Square-net materials with clean, linearly dispersing bands show potential to circumvent this issue. CeSbTe, a square-net material, features multiple magnetic field-controllable topological phases. Here, it is shown that in this material, even higher degrees of tunability can be achieved by changing the electron count at the square-net motif. Increased electron filling results in structural distortion and formation of …
We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This correspondence has potential implications in both directions. We illustrate the proposal by investigating its consequences for the spectral and transport properties of Dirac and Weyl semimetals. Particular realizations of this framework give rise to Dirac nodal spectra with nodal lines and rings. We demonstrate a bulk-boundary correspondence between bulk topolog…
Contemporary Insights into Electronic Structure and Microscopic Transport in Nodal-Line Semimetals
International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所马格托国际研究中心）；Division of Synchrotron Radiation Research, Lund University（隆德大学同步辐射研究系）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）；Department of Materials Science, University of Milan-Bicocca（米兰比可卡大学材料科学系）；Consiglio Nazionale delle Ricerche CNR-SPIN, c/o Universitá degli Studi ”G. D’Annunzio”（加富尔国家研究委员会CNR-SPIN（安努齐奥大学））；SPIN-CNR, UOS Salerno（萨莱诺SPIN-CNR联合办公室）
Evolution from Landau Quantization to Discrete Scale Invariance Revealed by Quantum Oscillations in Topological Materials
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Center for Neutron Science and Technology, School of Physics, Sun Yet-sen University（中山大学物理学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Wuhan National High Magnetic Field Center, Huazhong University of Science & Technology（华中科技大学武汉国家强磁场中心）；Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院前沿量子研究中心）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
We show that the quantum geometry of the Fermi surface can be numerically described by a 3-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. The approach is demonstrated by calculating the anomalous Hall and spin Hall cond…
Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W,Mo)Te2 and (W,Mo)P2 families of materials, a large numbers of experiments have been dedicated to unveil the possible manifestation of type-II WSM, e.g. the surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved phot…
Discrete scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity which can be rarely observed in quantum systems. Here we report the log-periodic quantum oscillations in the magnetoresistance (MR) and the Hall traces of HfTe5 crystals, which reveals the appearance of DSI. The oscillations show the same logB-periodicity in the behavior of MR and Hall, indicating an overall effect of the DSI on the transport properties. Moreover, the DSI feature in the Hall resistance signals its close relation to the carriers. Combined with theoretical simulations, we further clarify the ori…
The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is broken, has only been experimentally studied in very few materials. In contrast to discrete nodes, nodal lines with rich topological configurations can lead to more unusual transport phenomena. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we provide compelling evidence of nodal-line fermions in centrosymmetric semime…
Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned…
Recently, log-periodic quantum oscillations have been detected in topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with D…
Topological nodal-line semimetals (TNLSMs) are materials whose conduction and valence bands cross each other, meeting a topologically-protected closed loop rather than discrete points in the Brillouin zone (BZ). The anticipated properties for TNLSMs include drumhead-like nearly flat surface states, unique Landau energy levels, special collective modes, long-range Coulomb interactions, or the possibility of realizing high-temperature superconductivity. Recently, SrAs3 has been theoretically proposed and then experimentally confirmed to be a TNLSM. Here, we report high-pressure experiments on Sr…
