Weyl semimetals are one kind of three-dimensional gapless semimetal with nontrivial topology in the momentum space. The chiral anomaly in Weyl semimetals manifests as a charge imbalance between the Weyl nodes of opposite chiralities induced by parallel electric and magnetic fields. We investigate the chiral anomaly effect on the plasmon mode in both intrinsic and doped Weyl semimetals within the random phase approximation. We prove that the chiral anomaly gives rise to a different plasmon mode in intrinsic Weyl semimetals. We also find the chiral anomaly leads to some exotic properties in the plasmon dispersion in doped Weyl semimetals. Consequently, the unconventional plasmon mode acts as a signature of the chiral anomaly in Weyl semimetals, by which the spectrum of plasmon provides a proper way to detect the Lifshitz transition.

We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results provide an alternative scheme to engineer topological SMs and shed new light on the application of Dirac and Weyl SMs in spintronics.

We theoretically investigated two kinds of density oscillations, the Friedel oscillation and collective excitation in the silicene and germanene within the random phase approximation, and found that the tunable spin-valley coupled band structure could lead to some exotic properties in these two phenomena. Based on an exact analytical and numerical analysis, we demonstrated that the beating of the screened potential as well as the undamped plasmon mode can be taken as fingerprints of a topological phase transition in doped silicene and doped germanene. Thus our proposal here establishes the connection between the topological phase transition and the density oscillations that can be accessed by a variety of experimental techniques.The quantum spin Hall effect (QSHE) [1, 2] has been studied extensively in both theoretical and experimental aspects. It is well known that topologically protected helical edge states are a distinct feature which characterizes the QSHE [3]. The transport measurement of edge states requires that the bulk state must be insulating. In practice, the system is usually metallic resulting from defects, self-doping and charge transfer from metallic substrates, and thus the detection of the topological phase transition (TPT) when the bulk is metallic becomes urgent and important in two-dimensional systems. In this Rapid Communication, we connect the TPT with two kinds of density oscillations: Friedel oscillation [4] and collective excitation in silicene and germanene.Silicene [5,6], a single layer of silicon atoms forming a two-dimensional (2D) buckled honeycomb lattice, can be regarded as the silicon-based counterpart of graphene [7]. The buckled honeycomb structure gives rise to a tunable spin-valley coupled band structure, which accounts for many exotic transport and superconducting phenomena [8][9][10][11][12][13][14] and makes silicene a promising candidate for the QSHE [15]. So far silicene or its superstructure has only been synthesized on metallic surfaces [16][17][18][19], hence the transport measurement of the helical edge states is prevented due to the metallic bulk state. On the other hand, it has been claimed that a Dirac-like spectrum does exist in silicene from experimental observations [16,17]. Although there is some debate about the origin of the linear dispersion [20], it is still highly worthwhile to examine whether or not silicene hosts the QSH state.In this Rapid Communication, we propose a detection method of TPT by employing both the Friedel oscillation and collective excitation in silicene, and show how to extract the information about the TPT from these two * Electronic address: jhzhou@andrew.cmu.edu effects. First, the screened potential of charged impurities has a beating structure of Friedel oscillations (the interference pattern of two branches of density waves of electrons). As one band gap decreases (for example, the spin-up gap in Fig. 1), the beating of the screened potential gradually becomes faint and eventually vanishes at the TPT point. Second, the undamped pl...