Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session B45: Dirac and Weyl Semimetals: Theory ILive

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Sponsoring Units: DCMP Chair: Benjamin J. Wieder 
Monday, March 15, 2021 11:30AM  11:42AM Live 
B45.00001: On the topological character of threedimensional Nexus triple point degeneracies Sumiran Pujari, Ankur Das Recently a generic class of threedimensional band structures was identified that host twofold line degeneracies meeting at threefold or triple point degeneracies, which resist the usual topological characterization of isolated point degeneracies as in Dirac/Weyl semimetals. For these socalled ``Nexus" fermions which lie beyond Dirac/Weyl fermions, we lay out several concepts to characterize the wavefunction geometry and spell out its topology. Our approach is based on an understanding of the analyticity properties of Nexus wavefunctions building on a twodimensional analogue studied recently by us. We use this to write down a homological classification of various Nexus triple point degeneracies in three dimensions. 
Monday, March 15, 2021 11:42AM  11:54AM Live 
B45.00002: Geometric properties of band crossing points in two dimensions Yoonseok Hwang, JunSeo Jung, JunWon Rhim, BohmJung Yang The band crossing points (BCPs) in 2D are usually characterized by the Berry phase. In this work, we study the geometric properties of BCPs in 2D. We show that the geometric nature of BCPs are characterized by the quantum distance or quantum metric more appropriately, rather than the Berry phase. 
Monday, March 15, 2021 11:54AM  12:06PM Live 
B45.00003: Embedded Topological Semimetals Saavanth Velury, Taylor L Hughes Topological semimetals, such as Dirac or Weyl semimetals, are gapless states of matter characterized by their nodal band structures and surface states. We consider layered (topologically trivial) insulating systems in D dimensions that are composed of coupled multilayers of ddimensional topological semimetals. Despite being nominal bulk insulators we show that crystal defects having codimension Dd can robustly harbor a lower dimensional topological semimetal embedded in a trivial insulating background. As an example we show that defectbound topological semimetals can emerge in these trivial systems when stacking faults are introduced. We characterize the nature of these embedded semimetals by identifying the nodal structure of the bands and by computing the Berry phase characteristics across the Brillouin zone. Finally, we propose how an embedded topological Dirac semimetal can be identified in experiment by introducing a magnetic field and resolving the relativistic massless Dirac Landau level spectrum at low energies in an otherwise gapped system. 
Monday, March 15, 2021 12:06PM  12:18PM Live 
B45.00004: From triple points to multiband nodal links with monopole charges Patrick Lenggenhager, Xiaoxiong Liu, Stepan Tsirkin, Titus Neupert, Tomas Bzdusek We use nonAbelian topology to derive a relation between seemingly unrelated band node configurations. Namely, we show that rotationsymmetry breaking converts certain triple nodal points into multiband nodal links. To derive this relation, we first classify triple points in PTsymmetric systems with negligible spinorbit coupling, and then use quaternion invariants to identify the symmetry criteria which ensure the described conversion. 
Monday, March 15, 2021 12:18PM  12:30PM Live 
B45.00005: Edgeinduced magnetism of Dirac nodal line system in the singlecomponent molecular conductor [Pt(dmdt)_{2}] Taiki Kawamura, Biao Zhou, Akiko Kobayashi, Akito Kobayashi In the Dirac nodal line system, the Dirac points of the two dimensional Dirac cones draw lines in the three dimensional Brillouin zone. The Dirac nodal line system attracts the scientists due to the property such as the anomalous transport phenomena and topology. The firstprinciples calculation and the experiment show that the singlecomponent molecular conductor [Pt(dmdt)_{2}] is the Dirac nodal line system. 
Monday, March 15, 2021 12:30PM  12:42PM Live 
B45.00006: Diabolical touching point in the magnetic energy levels of topological nodalline metals Chong Wang, Zhongyi Zhang, Chen Fang, Aris Alexandradinata For threedimensional metals, Landau levels disperse as a function of the magnetic field and the momentum wavenumber parallel to the field. In this twodimensional parameter space, it is shown that two conicallydispersing Landau levels can touch at a diabolical point  a LandauDirac point. The conditions giving rise to LandauDirac points are shown to be magnetic breakdown (fielddriven quantum tunneling) and certain crystallographic spacetime symmetry. Both conditions are realizable in topological nodalline metals, as we exemplify with SrAs_{3}family materials. A LandauDirac point reveals itself in anomalous "batman"like peaks in the magnetoresistance, as well as in the onset of optical absorption linearly evolving to zero frequency as a function of the field magnitude/orientation. 
Monday, March 15, 2021 12:42PM  12:54PM Live 
B45.00007: Triply degenerate point in threedimensional spinless systems Xiaolong Feng, Weikang Wu, Zhiming Yu, Shengyuan Yang As the rise of quantum topological materials, a number of fermionic qusaiparticle are identified in solids, associated with exotic properties. Beyond the conventional Dirac and Weyl fermions, multifold fermions attract lots of attention without analog in quantum field theory. Here, we perform an exhaustive search of triply degenerate points (TDPs) in 230 nonmagnetic space groups in the absence of SOC. Different from Dirac points with up to cubic dispersions, TDPs are found to hold only up to quadratic dispersions either at highsymmetry points (HSPs) or on highsymmetry lines (HSLs). While QTDPs at HSPs possess quadratic dispersions in all directions, the ones on HSLs only disperse quadratically in k_{x}k_{y} plane. When located at highsymmetry points in chiral SGs, TDPs are found to host a topological charge of ±2 with linear dispersions, which are also known as spin1 Weyl points. We also break certain symmetry to investigate their phase transitions. Though the results support their existences in a range of space groups, their stable material realization is still limited. 
Monday, March 15, 2021 12:54PM  1:06PM Live 
B45.00008: Quantum anomalies in interacting topological semimetals Lei Yang, Chong Wang, Anton Burkov In this talk we explore the following question: can strong electronelectron interactions open a gap in topological semimetals while mantaining their topological response without breaking the protecting symmetries, or introducing topological order? We demonstrate that the answer is no, and show that what prevents it is the topological response, arising from quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses may be related to magnetoelastic properties of topological semimetals, and are detectable in the presence of appropriate symmetry defect loop linkings. We provide a comprehensive summary of symmorphic symmetryprotected semimetal topological responses which fully determine the topological order of realisable stronglycorrelated gapped states. 
Monday, March 15, 2021 1:06PM  1:18PM Live 
B45.00009: Tunable chiral symmetry breaking in symmetric Weyl materials Sahal Kaushik, Evan Philip, Jennifer Cano Asymmetric Weyl semimetals, which possess an inherently chiral structure, have different energies and dispersion relations for left and righthanded 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 between left and righthanded fermions; the symmetry breaking can be tuned by changing the direction and magnitude of the magnetic field. In some cases, we find an imbalance between the number of type I left and righthanded Weyl cones (which is compensated by the number of type II cones of each chirality.) 
Monday, March 15, 2021 1:18PM  1:30PM Live 
B45.00010: Antiferromagnetism and spin density waves in threedimensional Dirac metals Grigory Bednik We study possible magnetic instabilities in Dirac semimetals. We find that Dirac electrons naturally host antiferromagnetic or spindensity wave ground states, though their specific configurations may vary depending on a specific model, as well as chemical potential and temperature. We also discuss paramagnetic susceptibility of Dirac semimetals. In the cases when Dirac electrons do not have orbital momentum, the magnetic properties may be μ and T independent. 
Monday, March 15, 2021 1:30PM  1:42PM Live 
B45.00011: Bulk topology of stable threedimensional Dirac semimetals Alexander Tyner, Shouvik Sur, Danilo Puggioni, James M Rondinelli, Pallab Goswami The bandtouching points of stable, threedimensional, Kramersdegenerate, Dirac semimetals act as the singularities of nonAbelian, SO(5)Berry’s connections, and their homotopy classification is still an important, open problem. In this work, we solve this problem by performing second homotopy classification of Berry’s connections, and determine the topological universality classes of stable Dirac semimetals. The generic twodimensional planes, orthogonal to the direction of nodal separation, and lying between two Dirac points are shown to be exotic topological insulators, supporting quantized, chromomagnetic flux or a relative Chern number, and gapped edge states. The Dirac points are identified as a pair of unitstrength, SO(5) monopole and antimonopole, where the relative Chern number can jump by ±1. With analytical solutions of surface states, we show the nonexistence of helical Fermi arcs, which are often considered to be the smoking gun signatures of bulk topology. Finally, we outline a general recipe for computing bulk invariants of all Dirac materials from the winding of gaugeinvariant eigenvalues of planar Wilson loops, without relying on any nonuniversal properties of surface states. 
Monday, March 15, 2021 1:42PM  1:54PM Live 
B45.00012: HigherOrder Weyl Semimetals Sayed Ali Akbar Ghorashi, Tianhe Li, Taylor L Hughes We investigate higherorder Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higherorder topological invariant change. As a proof of concept we use a model of stacked higherorder quadrupole insulators (QI) to identify three types of WSM phases: $1st$order, $2nd$order, and hybridorder. The model can also realize typeII and hybridtilt WSMs with various surface and hinge arcs. Next, we discuss three remarkable results on various mechanisms of gapping out the $2nd$order Weyl nodes including (i) coupling to a $1st$order node as well as the nesting of nodes in presence of chargedensity wave (CDW) order in (ii) inversionsymmetric and (iii) timereversal symmetric models of HOWSMs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help to identify some classes of $2nd$ order WSMs. Finally, we show that periodic driving can be utilized as a way of generating HOWSMs. 
Monday, March 15, 2021 1:54PM  2:06PM Live 
B45.00013: Gapless Criterion for Crystals from Effective Axion Field Jiabin Yu, Zhida Song, Chaoxing Liu Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for threedimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetryrepresentation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals. 
Monday, March 15, 2021 2:06PM  2:18PM Live 
B45.00014: The Infinite Berry Curvature of Weyl Fermi Arcs Dennis Wawrzik, JhihShih You, Jorge I. Facio, Jeroen Van den Brink, Inti A Sodemann We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as 1/k^{2}, where k is the distance to a hotline in the surface Brillouin zone that connects the projection of Weyl nodes with opposite chirality but which is distinct from the Fermi arc itself. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally, and in particular leads to a surface Berry curvature dipole that grows linearly with the thickness of a slab of a Weyl semimetal material in the clean limit. This implies the emergence of a gigantic contribution to the nonlinear Hall effect in such devices. 
Monday, March 15, 2021 2:18PM  2:30PM Live 
B45.00015: Phonon induced Dirac and Weyl phases in topological insulator ZrTe_{5} Niraj Aryal, Xilian Jin, Alexei Tsvelik, Qiang Li, Weiguo Yin We study topological phase transitions induced by optical phononmode lattice distortions in ZrTe_{5}, a layered van der Waals topological insulating material, by using firstprinciples and effective Hamiltonian methods. We find that five of the six zonecentered A_{g} Raman phonon modes, which protect the crystalline symmetries, induce transition from strong to weak topological insulator with Dirac semimetallic state emerging at the transition point. Moreover, all zonecentered infrared phonon modes induce transition from topological insulating to the Weyl semimetallic phase by breaking the global inversion symmetry. Thus achieved Weyl phases are robust, tunable and in close proximity to the Fermi level.The experimental implications of our results are discussed. 
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