Session A55: Invited Session: Weyl and Dirac Semimetals: From Transport and Chiral Anomaly to Physical Realizations

Topological response in Weyl semimetals and metallic ferromagnets

Standard picture of a topologically-nontrivial phase of matter is an insulator with a bulk energy gap, but metallic surface states, protected by the bulk gap. Recent work has shown, however, that certain gapless systems may also be topologically nontrivial, in a precise and experimentally observable way. In this talk I will review our work on a class of such systems, in which the nontrivial topological properties arise from the existence of nondegenerate point band-touching nodes (Weyl nodes) in their electronic structure. Weyl nodes generally exist in any three-dimensional material with a broken time-reversal or inversion symmetry. Their effect is particularly striking, however, when the nodes coincide with the Fermi energy and no other states at the Fermi energy exist. Such ``Weyl semimetals'' have vanishing bulk density of states, but have gapless metallic surface states with an open (unlike in a regular two-dimensional metal) Fermi surface (``Fermi arc''). I will discuss our proposal to realize Weyl semimetal state in a heterostructure, consisting of alternating layers of topological and ordinary insulator, doped with magnetic impurities. I will further show that, apart from Weyl semimetals, even such ``ordinary'' materials as common metallic ferromagnets, in fact also possess Weyl nodes in the electronic structure, leading to a non-quantized contribution to their intrinsic anomalous Hall conductivity, which can not be attributed to the Fermi surface.   

Probing the chiral anomaly and transport in Weyl semimetals

The topological nature of Weyl semimetals is reflected in the Adler-Bell-Jackiw anomaly, an unusual bulk response where applying parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields pumps electrons between nodes of opposite chirality at a rate proportional to $\mathbf{E}\cdot\mathbf{B}$. We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal, and therefore serves as a test of the chiral anomaly. I will also comment on the possibility of observing similar physics in the three-dimensional Dirac semimetallic phase proposed to exist in Na$_3$Bi and Cd$_3$As$_2$, which have been the subject of recent photoemission and transport experiments. Reference: arXiv preprint 1306.1234 (2013).   

Three Dimensional Dirac Semimetals

Dirac points on the Fermi surface of two dimensional graphene are responsible for its unique electronic behavior. One can ask whether any three dimensional materials support similar pseudorelativistic physics in their bulk electronic spectra. This possibility has been investigated theoretically and is now supported by two successful experimental demonstrations reported during the last year. In this talk, I will summarize the various ways in which Dirac semimetals can be realized in three dimensions with primary focus on a specific theory developed on the basis of representations of crystal spacegroups. A three dimensional Dirac (Weyl) semimetal can appear in the presence (absence) of inversion symmetry by tuning parameters to the phase boundary separating a bulk insulating and a topological insulating phase. More generally, we find that specific rules governing crystal symmetry representations of electrons with spin lead to robust Dirac points at high symmetry points in the Brillouin zone. Combining these rules with microscopic considerations identifies six candidate Dirac semimetals. Another method towards engineering Dirac semimetals involves combining crystal symmetry and band inversion. Several candidate materials have been proposed utilizing this mechanism and one of the candidates has been successfully demonstrated as a Dirac semimetal in two independent experiments.   

Topological Semimetals in Realistic Compounds

Topological semimetal, characterized by Weyl/Dirac nodes in the bulk and Fermi arcs on the surfaces, is a new state of three-dimensional (3D) quantum matters, different from the 3D topological insulators. Weyl nodes are stable topological objects, and can be viewed as effective magnetic monopoles in the 3D momentum space. Its time-reversal invariant version --- 3D Dirac node, however, consists of two copies of distinct Weyl nodes with opposite chirality, and requires additional symmetry protection, such as the crystal symmetry. Novel properties, such as the giant diamagnetism and the linear quantum magnetoresistance can be expected for such semimetal states. In this talk, I will first present a general description of topological semimetal states, and then discuss its possible material realizations based on the first-principles calculations. We will show two theoretical predictions, Na$_3$Bi and Cd$_3$As$_2$, where the 3D Dirac cones are experimentally observed recently. \\[4pt] [1] G. Xu, H. M. Weng, Z. J. Wang, X. Dai, Z. Fang, Physical Review Letters 107, 186806 (2011). \\[0pt] [2] Z. J. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. M. Weng, X. Dai, Z. Fang, Phys. Rev. B 85, 195320 (2012).\\[0pt] [3] Z. J. Wang, H. M. Weng, Q. S. Wu, X. Dai, Z. Fang, Phys. Rev. B 88, 125427 (2013).   

Possible Weyl state near the metal-insulator boundary in pyrochlore iridates

Despite a rapidly growing theoretical literature on Weyl semi-metallic states, such states are proving elusive in real materials. Promising candidates, initially proposed by Wan et al.[1] and Witczak-Krempa et al. [2], are the pyrochlore iridate systems R$_2$Ir$_2$O$_7$, where $R$ is a rare earth. In this talk I will review experimental evidence for unconventional normal states near the metal-insulator boundary in these systems, focusing on Eu$_2$Ir$_2$O$_7$, where we have carried out transport measurements under pressure [3]. In measurements up to 12 GPa, we found a peculiar insulator-to-metal transition near 7 GPa. Across this pressure range magnetic order -- a prerequisite for a Weyl state in the pyrochlore lattice -- seems to be relatively unaffected, with $T_N \simeq 100-120$ K at all pressures. The normal state above 7 GPa is unusual, having a negative temperature derivative of resistance. Magnetoresistance measurements at 10 GPa down to 100 mK suggest the existence of small Fermi pockets. These behaviors may be consistent with a Weyl semi-metallic state near the metal-insulator boundary. Further transport measurements that could help to establish this are currently under way, and will be briefly described. \\[4pt] [1] X. Wan, A. M. Turner, A. Vishwanath and S. Y. Savrasov, Phys. Rev. B vol. 83 (2011) 205101.\\[0pt] [2] W. Witczack-Krempa and Y. B. Kim, Phys. Rev. B vol. 85 (2012) 045124.\\[0pt] [3] F. F. Tafti, J. J. Ishikawa, A. McCollam, S. Nakatsuji and S. R. Julian, Phys. Rev. B vol. 85 (2012) 205014.