Hear the Sound of Weyl Fermions

Quasiparticles and collective modes are two fundamental aspects that characterize a quantum matter in addition to its ground state features. For example, the low energy physics for Fermi liquid phase in He-III was featured not only by Fermionic quasiparticles near the chemical potential but also by fruitful collective modes in the long-wave limit, including several different sound waves that can propagate through it under different circumstances. On the other hand, it is very difficult for sound waves to be carried by the electron liquid in the ordinary metals, due to the fact that long-range Coulomb interaction among electrons will generate plasmon gap for ordinary electron density fluctuation and thus prohibits the propagation of sound waves through it. In the present paper, we propose a unique type of acoustic collective modes in Weyl semimetals under the magnetic field called chiral zero sound. The chiral zero sound can be stabilized under so-called "chiral limit", where the intra-valley scattering time is much shorter than the inter-valley one, and only propagates along an external magnetic field for Weyl semimetals with multiple-pairs of Weyl points. The sound velocity of the chiral zero sound is proportional to the field strength in the weak field limit, whereas it oscillates dramatically in the strong field limit, generating an entirely new mechanism for quantum oscillations through the dynamics of neutral bosonic excitation, which may manifest itself in the thermal conductivity measurements under magnetic field.Comment: 9+16 pages, 2+0 figures, a new appendix added, accepted in PR

Real-space recipes for general topological crystalline states

Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively studied in band theory and have been experimentally discovered, the classification and diagnosis of their strongly interacting counterparts are relatively less well understood. Here we present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space "building blocks" and "connectors". Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are "glue" that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the "no-open-edge condition" and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology.Comment: 17+44 pages, 7+1 figures, 0+2 tables. The content is the same as the published version, but arranged differentl

Diagnosis for topological semimetals in the absence of spin-orbital coupling

Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one of several candidate materials, starting from first principles. In these calculations, it is crucial that all topological band crossings, including their types and positions in the Brillouin zone, are found. While band crossings along high-symmetry lines, which are routinely scanned in numerics, are simple to locate, the ones at generic momenta are notoriously time-consuming to find, and may be easily missed. In this paper, we establish a theoretical scheme of diagnosis for topological semimetals where all band crossings are at generic momenta in systems with time-reversal symmetry and negligible spin-orbital coupling. The scheme only uses the symmetry (inversion and rotation) eigenvalues of the valence bands at high-symmetry points in the BZ as input, and provides the types, numbers and configurations of all topological band crossings, if any, at generic momenta. The nature of new diagnosis scheme allows for full automation and parallelizations, and paves way to high throughput numerical predictions of topological materials.Comment: 21 pages, 5 figures, 1 table; v4: accepted in PRX, a "PRELIMINARIES" section adde

Higher-order Topology of Axion Insulator EuIn2_2As2_2

Based on first-principles calculations and symmetry analysis, we propose that EuIn$_2$As$_2$ is a long awaited axion insulator with antiferromagnetic (AFM) long range order. Characterized by the parity-based invariant $\mathbb Z_4=2$, the topological magneto-electric effect is quantized with $\theta=\pi$ in the bulk, with a band gap as large as 0.1 eV. When the staggered magnetic moment of the AFM phase is along $a/b$ axis, it's also a TCI phase. Gapless surface states emerge on (100), (010) and (001) surfaces, protected by mirror symmetries (nonzero mirror Chern numbers). When the magnetic moment is along $c$ axis, the (100) and (001) surfaces are gapped. As a consequence of a high-order topological insulator with $\mathbb Z_4=2$, the one-dimensional (1D) chiral state can exist on the hinge between those gapped surfaces. We have calculated both the topological surface states and hinge state in different phases of the system, respectively, which can be detected by ARPES or STM experiments

Calibration of a Parametric-Stochastic Model

Conceptually, stochastic parametric modeling offers a powerful tool to select a scale for expressing catchment variability for hydrologic simulation and relating model parameters to catchment characteristics. Practically, success depends on having an efficient method for model calibration. The calibration of a stochastic model is much more difficult than a deterministic one because simulation shifts from using fixed parameters to simulate of flows as deterministic values to taking multiple combinations of paramter values randomly from distributions to simulate flows as stochastic variables. The proposed method calibrates the first two moments of each parameter distribution to represent the average and the variability of catchment characteristics by using two objective functions. One minimizes relative errors between recorded and simulated flows, and the other bounds the range of simulated flows to cover the recorded flows. The method was successfully calibrated for four watersheds, and the results promise new understanding that will contribute to more reliable models