Session P51: Dirac and Weyl Semimetals: Materials and Modeling--Materials Predictions and Transport Theory

Live

The field of topological semimetals continues to reveal new insights. I will discuss recent developments starting with the classification of nodal fermions in both magnetic and non-magnetic space groups. I will then introduce higher order Fermi arcs as a bulk-edge correspondence for Dirac fermions, and a refinement of the symmetry indicators that predict these hinge states. Finally, I will discuss some material predictions.   

Live

The honeycomb form of 2D group V-elements (Sb,As) was recently shown to undergo distinct topological phase transitions as function of buckling.[1] Starting out as a nodal line semimetal in the flat form, Dirac points emerge when slight buckling is introduced, which annihilate in pairs upon further buckling. Here we show that the buckled lowest energy form at the end of this series of topological transitions is a weak topological crystalline insulator (TCI) in the obstructed atomic limit (OAL).[2] Relations to the kagome, Kekul\'e and Su-Schrieffer-Heeger systems are pointed out. Further group theoretical analysis, shows that this system is a (d-2) higher order topological insulator. The resulting corner states are shown to be robust as long as the disorder remains restricted to the bulk rather than the edges. The edge states and corner states at zero energy can be gapped by breaking the inversion symmetry, which we show to lead to the possibility of a topological quantized conductance metal insulator transition by application of an electrical field perpendicular to the layers. Finally, we note that the formation of an OAL is a universal property of the annihilation of Dirac fermions of opposite winding.
[1] SKR WRL, PRB 101, 235111 (2020)
[2] SKR WRL, PRB 102, 115104 (2020)   

Live

Recently, two-dimensional layered electrides have emerged as a new class of materials which possess anionic electrons in the interstitial spaces between cationic layers. Here, based on first-principles calculations, we discover a time-reversal-symmetry-breaking Weyl semimetal phase in a unique two-dimensional layered ferromagnetic (FM) electride Gd₂C. It is revealed that the crystal field mixes the interstitial electron states and Gd-5d orbitals near the Fermi energy to form band inversions. Meanwhile, the FM order induces two spinful Weyl nodal lines (WNLs), which are converted into multiple pairs of Weyl nodes through spin-orbit coupling. Further, we not only identify Fermi-arc surface states connecting the Weyl nodes but also predict a large intrinsic anomalous Hall conductivity due to the Berry curvature produced by the gapped WNLs. Our findings demonstrate the existence of Weyl fermions in the room-temperature FM electride Gd₂C, therefore offering a new platform to investigate the intriguing interplay between electride materials and magnetic Weyl physics.   

Live

We study the effect of random potential created by different types of impurities on the transverse magnetoresistance of Weyl semimetals. It is shown that the magnetic field and temperature dependence of magnetoresistance is strongly affected by the type of impurity potential. Two limiting cases are analyzed in detail: (i) the ultra-quantum limit, when the applied magnetic field is so high that only the zeroth and first Landau levels contribute to the magnetotransport, and (ii) the semiclassical situation, for which a large number of Landau levels comes into play. A formal diagrammatic approach allowed us to obtain expressions for the components of the electrical conductivity tensor in both limits. In contrast to the oversimplified case of the δ-correlated disorder, the long-range impurity potential (including that of Coulomb impurities) introduces an additional length scale, which changes the geometry and physics of the problem. It is shown that the magnetoresistance can deviate from the linear behavior as a function of magnetic field for a certain class of impurity potentials.

[1] https://arxiv.org/abs/1506.07556
Phys. Rev. B, in press.   

Live

Objects around us constantly emit and absorb thermal radiation. For reciprocal systems, the emissivity and absorptivity are restricted to be equal by Kirchhoff's law of thermal radiation. This restriction limits the control of thermal radiation and contributes to an intrinsic loss mechanism in photonic energy harvesting systems. Existing approaches to violate Kirchhoff's law typically utilize conventional magneto-optical effects in the presence of an external magnetic field. However, these approaches require either a strong magnetic field (~3T) [1] or narrow-band resonances under a moderate magnetic field (~0.3T) [2], because the non-reciprocity in conventional magneto-optical effects is usually weak in the thermal wavelength range. Here we show that the axion electrodynamics in magnetic Weyl semimetals can be used to construct strongly nonreciprocal thermal emitters [3]. Such a thermal emitter can near completely violate Kirchhoff's law over broad angular and frequency ranges without requiring any external magnetic field.


[1] L. Zhu and S. Fan, Phys. Rev. B 90, 220301 (2014).
[2] B. Zhao, Y. Shi, J. Wang, Z. Zhao, N. Zhao, and S. Fan, Opt. Lett. 44, 17(2019).
[3] B. Zhao*, C. Guo*, C. A. C. Garcia, P. Narang, and S. Fan, Nano Lett. 20, 1923 (2020).   

On Demand

In the present talk, I will propose a new way to classify centrosymmetric metals by studying the
Zeeman effect caused by an external magnetic field described by the momentum dependent g-factor
tensor on the Fermi surfaces. Nontrivial U(1) Berry's phase and curvature can be generated once the
otherwise degenerate Fermi surfaces are split by the Zeeman effect, which will be determined by
both the intrinsic band structure and the structure of g-factor tensor on the manifold of the Fermi
surfaces. Such Zeeman effect generated Berry's phase and curvature can lead to three important
experimental effects, modification of spin-zero effect, Zeeman effect induced Fermi surface Chern
number, and the in-plane anomalous Hall effect. By first-principle calculations, we study all these
effects on two typical material, ZrTe5 and TaAs2, and the results are in good agreement with the
existing experiments.   

Live

As a novel class of crystals where the excess electrons residing within the cationic framework serve as anions, electrides manifest intriguing magnetic features and topological nature [1], which has aroused great interests among the community of materials science. Here, we propose a design scheme of seeking potential electrides derived from conventional materials. Starting from rare-earth element based halides, we exclude the halogen and perform the global structure optimization, so as to obtain excess electrons confined inside interstitial cavities. Spin polarized interstitial states are realized by chemical substitution with magnetic lanthanides. In addition, band topology is particularly explored for the predicted electrides. In this presentation, we primarily report two families of newly designed electrides, A₂C₂ and A₂Ge (A= Y, Gd, etc.), both of which turn out to be topological nodal line semimetals in the absence of spin-orbit coupling. Our work opens a new avenue to predict electrides, and reveals the close relationship between electrides, magnetism and topological phases.

[1] M. Hirayama, et al. Physical Review X 8.3: 031067 (2018).   

Live

The combination of type-II Weyl semimetal and the coexistence of broken time-reversal symmetry and inversion symmetry is highly unusual. RAlX materials (R = rare earth, X = Si, Ge) have recently attracted much attention as rare examples of such materials. We focus on NdAlSi due to its interesting magnetic and electronic properties. It shows multiple magnetic phase transitions mediated by RKKY-type interactions with ferromagnetism at 7.2 K and ferrimagnetism (up-up-down Nd spin ordering) at 3.3 K. Using first-principles density-functional theory, we find 20 pairs of Weyl nodes in the paramagnetic phase, 28 pairs of Weyl nodes in the ferromagnetic phase, and 26 pairs of Weyl nodes in the antiferromagnetic phase. We also focus on the Fermi surfaces associated with the Weyl nodes hosting a nesting vector consistent with the experimentally observed magnetic ordering at q ~ [2/3,2/3,0]. Our work exposing the connections between the Weyl node structure and the magnetic ordering should be applicable to this class of materials more broadly, stimulating further interest in their remarkable properties.   

Live

Unlike conventional Weyl nodes, unconventional ones carry a quantized monopole charge C>1, and their existence needs the protection of crystalline symmetries in addition to translation symmetry. There have been many studies on unconventional Weyl nodes, yet we have so far missed one, which is the twofold Weyl node with C=4^[1]. In this talk, I will first explain why researchers missed the twofold degenerate quadruple Weyl node (TQW) by introducing the research history of unconventional Weyl nodes. Then, I will explain how to obtain the TQW in crystals. Afterward, a series of LaIrSi-type materials that have the TQW in both their spinless electronic band structure and the phonon spectra will be discussed. In the electronic band structure, the TQW will evolve into a fourfold quadruple Weyl node and change both the chirality and the monopole charge after considering spin-orbit coupling, which is uncommon in the known Weyl semimetals. At last, I will discuss the relationship between the winding number and pseudospin and offer an intuitive way to understand the complex pseudospin texture of the TQW. If there is enough time, I also would like to make a brief introduction to experimentally detecting the TQW in BaPtGe^[2].

[1] PHYSICAL REVIEW B 102, 125148 (2020)
[2] arXiv:2010.00764 (2020).   

Live

Based on irreducible representations (or symmetry eigenvalues) and compatibility relations, a material can be predicted to be a topological/trivial insulator [satisfying compatibility relations] or a topological semimetal [violating compatibility relations]. However, Weyl semimetals usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy compatibility relations, or if the symmetry indicators are zero. In this work, we propose a new topological invariant χ for the systems with S4 symmetry [i.e., the improper rotation S4 (≡ IC4z) is a proper four-fold rotation (C4z) followed by inversion (I)], which can be used to diagnose the Weyl semimetal phase. Moreover, χ can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to the high-throughput screening in first-principles calculations, we predict a lot of Weylsemimetals in both nonmagnetic and magnetic compounds. Various interesting properties (e.g. magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted Weyl semimetals, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.   

On Demand

Linear magnetoresistance has been observed in a range of low-density, two-dimensional electron systems. For three-dimensional systems, linear magnetoresistance can be explained in terms of semiclassical drift of electrons in a smooth disorder potential. But as of yet there is no analogous theory for two-dimensional electron systems. Here we address this issue by studying the magnetoresistance of 2D electrons in a smooth random potential, as created, for example, by charged impurities in the substrate. In the presence of a sufficiently large magnetic field, electron trajectories experience a drift of their guiding centers along equipotential contours, in addition to the rapid cyclotron motion. Scattering from impurities or phonons allows electrons to hop from one equipotential contour to another, and at large enough magnetic field this process dominates their diffusion. We study the resulting electron diffusion constant, which determines the electrical resistance. Using scaling arguments and numerical simulations, we find regimes in which the magnetoresistance scales as B⁰, B^10/13, and B^10/7.