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.

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and highlights the importance of the Berry curvature in the effective mass approximation.The effective mass approximation provides a simple yet extremely useful tool to understand a wide variety of electronic properties of semiconductors [1]. Within this approximation, electrons behave almost like free particles in response to external fields, provided that one replaces the bare electron mass with an effective mass derived from the band dispersion. Much of our intuition on electron transport is based on this semiclassical picture. However, it has been shown that such a picture is actually incomplete, and one must include the Berry curvature of the Bloch states [2]. Essentially, the Berry curvature modifies the electron dynamics through an anomalous term in the group velocity of the Bloch electrons [3,4], i.e.,where ε n (k) is the band energy, V (r) is the external potential, and Ω n (k) = i ∇ k u nk | × |∇ k u nk is the Berry curvature defined in terms of the periodic part u nk (r) of the Bloch function. The importance of the Berry curvature has been well established in a number of transport phenomena such as the anomalous Hall effect [5][6][7] and the spin Hall effect [8][9][10]. In this Letter we consider another type of problems for which the effective mass approximation must be modified to include the Berry curvature, namely, the bound state problem of Bloch electrons. To be specific, we will consider the energy spectrum of an exciton, even though our result should be equally applicable to other problems such as shallow impurity states. Our motivation is two fold. First, giant exciton binding energies (about a few hundred meV) have recently been observed in monolayers of transition metal dichalcogenides [11][12][13][14][15][16][17][18][19][20], in which the low-energy carriers behave like massive Dirac fermions with nonzero Berry curvature [21]. Thus, the detailed experimental study of excitons in the presence of the Berry curvature appears to be feasible. Secondly, there have been a few calculations of the exciton energy spectrum in these materials [18,[22][23][24][25][26][27], but the role of the Berry curvature is not explicitly discussed. We will show that, at the level of the effective mass approximation, the Berry curvature is essential to understand the exciton energy spectrum.Our main results are summarized below. We show that, quite generally, the Berry curvatu...

We show that an effective magnetic field acting on phonons naturally emerges in the phonon dynamics of magnetic solids, giving rise to the phonon Hall effect. A general formula for the intrinsic phonon Hall conductivity is derived by using the corrected Kubo formula with the energy magnetization contribution incorporated properly. We thus establish a direct connection between the phonon Hall effect and the intrinsic phonon band structure, i.e., the phonon Berry curvature and phonon dispersion. Based on the formalism, we predict that phonons could also display the quantum Hall effect in certain topological phonon systems. In the low-temperature regime, we predict that the phonon Hall conductivity is proportional to T 3 for ordinary phonon systems, while that for the topological phonon system has a linear T dependence with a quantized temperature coefficient.

The total reciprocal space magnetic flux threading through a closed Fermi surface is a topological invariant for a three-dimensional metal. For a Weyl metal, the invariant is non-zero for each of its Fermi surfaces. We show that such an invariant can be related to magneto-valley-transport effect, in which an external magnetic field can induce a valley current. We further show that a strain field can drive an electric current, and the effect is dictated by a second class Chern invariant. These connections open the pathway to observe the hidden topological invariants in metallic systems.

In most of natural montmorillonites, Na + and Ca 2+ ions commonly coexist in the interlayer space as compensation ions. Molecular dynamics simulations have been performed to investigate the swelling properties, hydration behaviors, and mobility of the interlayer species of (Na x , Ca y )-montmorillonites with different water contents. Nine montmorillonites with different Na + /Ca 2+ ratio were selected as model clay frameworks, and the content of interlayer water was set within a range from 0 to 486 mg water /g clay . The results show that the montmorillonites with coexisting of Na + and Ca 2+ present slightly different swelling curves, hydration energies, and immersion energies from Na-or Camontmorillonite. The double-layered hydrates are the thermodynamically stable states for all montmorillonites in the regime of crystalline swelling. A total of 170 mg water /g clay is found as the threshold water content for the complexing modes of interlayer Ca 2+ and Na + ions switching from inner-sphere complexes to outer-sphere ones. The self-confusion coefficient of interlayer species obviously reveals the confining effects of clay surfaces. In all montmorillonites, the mobility of Na + is always much greater than that of Ca 2+ due to their different hydration shells. According to the water residence time in typical Na + and Ca 2+ hydration complexes, Ca 2+ hydration complexes is pronounced more stable than those of Na + , and in montmorillonites with high Ca 2+ /Na + ratio, the inhibitory effects of Ca 2+ hydration complexes on the mobility of Na + is clearly revealed.