Recent developments in transport phenomena in Weyl semimetals (original) (raw)
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3 Recent developments in transport phenomena in Weyl semimetals
2016
The last decade has witnessed great advancements in the science and engineering of systems with unconventional band structures, seeded by studies of graphene and topological insulators. While the band structure of graphene simulates massless relativistic electrons in two dimensions, topological insulators have bands that wind non-trivially over momentum space in a certain abstract sense. Over the last couple of years, enthusiasm has been burgeoning in another unconventional and topological (although, not quite in the same sense as topological insulators) phase-the Weyl Semimetal. In this phase, electrons mimic Weyl fermions that are well-known in high-energy physics, and inherit many of their properties, including an apparent violation of charge conservation known as the Chiral Anomaly. In this review, we recap some of the unusual transport properties of Weyl semimetals discussed in the literature so far, focusing on signatures whose roots lie in the anomaly. We also mention several proposed realizations of this phase in condensed matter systems, since they were what arguably precipitated activity on Weyl semimetals in the first place.
Charge Transport in Weyl Semimetals
Physical Review Letters, 2012
We study transport in three dimensional Weyl semimetals with N isotropic Weyl nodes in the presence of Coulomb interactions or disorder at temperature T . In the interacting clean limit, we determine the conductivity by solving a quantum Boltzmann equation within a 'leading log' approximation and find it to be proportional to T , upto logarithmic factors arising from the flow of couplings. In the noninteracting disordered case, we compute the finite-frequency Kubo conductivity and show that it exhibits distinct behaviors for ω ≪ T and ω ≫ T : in the former regime we recover the results of a previous analysis, of a finite conductivity and a Drude width that vanishes as N T 2 ; in the latter, we find a conductivity that vanishes linearly with ω whose leading contribution as T → 0 is the same as that of the clean, non-interacting system σ(ω, T = 0) = N e 2 12h |ω| v F . We compare our results to experimental data on Y2Ir2O7 and also comment on the possible relevance to recent transport data on Eu2Ir2O7.
Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals
2017
In the presence of parallel electric and magnetic fields, the violation of separate number conservation laws for the three dimensional left and right handed Weyl fermions is known as the chiral anomaly. The recent discovery of Weyl and Dirac semimetals has paved the way for experimentally testing the effects of chiral anomaly via longitudinal magneto-transport measurements. More recently, a type-II Weyl semimetal (WSM) phase has been proposed, where the nodal points possess a finite density of states due to the touching between electron- and hole- pockets. It has been suggested that the main difference between the two types of WSMs (type-I and type-II) is that in the latter, chiral anomaly and the associated longitudinal magneto-resistance are strongly anisotropic, vanishing when the applied magnetic field is perpendicular to the direction of tilt of Weyl fermion cones in a type-II WSM. We analyze chiral anomaly in a type-II WSM in quasiclassical Boltzmann framework, and find that t...
Magnetotransport of Weyl semimetals with ℤ2 topological charge and chiral anomaly
Journal of High Energy Physics
We calculate the magnetoconductivity of the Weyl semimetal with ℤ2 topological charge and chiral anomaly utilizing the recently developed hydrodynamic theory. The system in question will be influenced by magnetic fields connected with ordinary Maxwell and the second U(1)-gauge field, which couples to the anomalous topological charge. The presence of chiral anomaly and ℤ2 topological charge endow the system with new transport coefficients. We start with the linear perturbations of the hydrodynamic equations and calculate the magnetoconductivity of this system. The holographic approach in the probe limit is implemented to obtain the explicit dependence of the longitudinal magneto-conductivities on the magnetic fields.
Magnetotransport phenomena related to the chiral anomaly in Weyl semimetals
Physical Review B, 2016
We present a theory of magnetotransport phenomena related to the chiral anomaly in Weyl semimetals. We show that conductivity, thermal conductivity, thermoelectric and the sound absorption coefficients exhibit strong and anisotropic magnetic field dependencies. We also discuss properties of magneto-plasmons and magneto-polaritons, whose existence is entirely determined by the chiral anomaly. Finally, we discuss the conditions of applicability of the quasi-classical description of electron transport phenomena related to the chiral anomaly.
From graphene and topological insulators to Weyl semimetals
Symmetry, Spin Dynamics and the Properties of Nanostructures, 2015
Here we present a short introduction into physics of Dirac materials. In particular we review main physical properties of various two-dimensional crystals such as graphene, sil-icene, germanene and others. We comment on the origin of their buckled two-dimensional shape, and address the issues created by Mermin-Wagner theorem prohibiting the existence of strictly two-dimensional, flat crystals. Then we describe main ideas which were leading to the discovery of two and three-dimensional topological insulators and Weyl fermions. We describe some of their outstanding electronic properties which have been originating due to the existence of the Dirac gapless spectrum. We also compare simplest devices made of Dirac materials. Analogies and differences between Dirac materials and optics are also discussed.
Arxiv preprint arXiv: …, 2011
We study transport in three dimensional Weyl semimetals in the presence of Coulomb interactions or disorder. We consider N Weyl nodes with isotropic dispersion at temperature T. In the clean limit, including Coulomb interactions, we determine the conductivity by solving a quantum Boltzmann equation within a 'leading log' approximation. The conductivity is found to be proportional to T , upto logarithmic factors arising from the flow of couplings. In the disordered case, we use the Kubo formula to compute conductivity of non-interacting electrons in the presence of impurities. Here, the finite-frequency conductivity exhibits distinct behaviors, depending on whether ω ≪ T or ω ≫ T : in the former regime we recover the results of a previous analysis, of a finite conductivity and a Drude width that vanishes as N T 2 ; however, in the latter case, we find a conductivity that vanishes linearly with ω whose leading contribution as T → 0 is the same as that of the clean, non-interacting system σ(ω, T = 0) = N e 2 12h |ω| v F. A comparison is made with existing dc transport data in a pyrochlore iridate, which is predicted to have N = 24 Weyl nodes.
Weyl semi-metals : a short review
Cornell University - arXiv, 2016
We begin this review with an introduction and a discussion of Weyl fermions as emergent particles in condensed matter systems, and explain how high energy phenomena like the chiral anomaly can be seen in low energy experiments. We then explain the current interest in the field due to the recent discovery of real materials which behave like Weyl semi-metals. We then describe a simple lattice model of a topological insulator, which can be turned into a Weyl semi-metal on breaking either time-reversal or inversion symmetry, and show how flat bands or Fermi arcs develop. Finally, we describe some new phenomena which occur due to the chiral nature of the Weyl nodes and end with possible future prospects in the field, both in theory and experiment.
Chiral Anomaly as the Origin of the Planar Hall Effect in Weyl Semimetals
Physical review letters, 2017
In condensed matter physics, the term "chiral anomaly" implies the violation of the separate number conservation laws of Weyl fermions of different chiralities in the presence of parallel electric and magnetic fields. One effect of the chiral anomaly in the recently discovered Dirac and Weyl semimetals is a positive longitudinal magnetoconductance. Here we show that chiral anomaly and nontrivial Berry curvature effects engender another striking effect in Weyl semimetals, the planar Hall effect (PHE). Remarkably, the PHE manifests itself when the applied current, magnetic field, and the induced transverse "Hall" voltage all lie in the same plane, precisely in a configuration in which the conventional Hall effect vanishes. In this work we treat the PHE quasiclassically, and predict specific experimental signatures for type-I and type-II Weyl semimetals that can be directly checked in experiments.