The existence of pseudomagnetic helicons is predicted for strained Dirac and Weyl materials. The corresponding collective modes are reminiscent of the usual helicons in metals in strong magnetic fields but can exist even without a magnetic field due to a strain-induced background pseudomagnetic field. The properties of both pseudomagnetic and magnetic helicons are investigated in Weyl matter using the formalism of the consistent chiral kinetic theory. It is argued that the helicon dispersion relations are affected by the electric and chiral chemical potentials, the chiral shift, and the energy separation between the Weyl nodes. The effects of multiple pairs of Weyl nodes are also discussed. A simple setup for experimental detection of pseudomagnetic helicons is proposed.

We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. This finding suggests an efficient means of extracting the chiral shift parameter from the measurement of the plasma frequencies in Weyl materials. Introduction.-The study of the fundamental properties of magnetized relativistic matter attracted a lot of attention in recent years. The physical systems in question include the plasmas in the early Universe [1] and relativistic heavy-ion collisions [2,3], degenerate states of dense matter in compact stars [4], and a growing number of recently discovered three-dimensional Dirac and Weyl materials [5][6][7]. To large extent, the recent increased activity in the studies of magnetized relativistic matter is driven by the hope of detecting macroscopic implications of quantum anomalies. One of such implications is the celebrated chiral magnetic effect (CME) [8], which has been detected indirectly in the quark-gluon plasma created in heavy-ion collisions (for a review, see Ref.[3]), as well as in Dirac semimetals [9]. Note that the interpretation of the heavy-ion experiments is not without a controversy [10].

The complete set of Maxwell's and hydrodynamic equations for the chiral electrons in Weyl semimetals is presented. The formulation of the Euler equation takes into account the explicit breaking of the Galilean invariance by the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino) contributions should be added to the electric current and charge densities in Maxwell's equations that provide the information on the separation of Weyl nodes in energy and momentum. On the other hand, these topological contributions do not directly affect the Euler equation and the energy conservation relation for the electron fluid. By making use of the proposed consistent hydrodynamic framework, we show that the Chern-Simons contributions strongly modify the dispersion relations of collective modes in Weyl semimetals. This is reflected, in particular, in the existence of distinctive anomalous Hall waves, which are sustained by the local anomalous Hall currents.

By making use of a low-energy effective model of Weyl semimetals, we show that the Fermi arc transport is dissipative. The origin of the dissipation is the scattering of the surface Fermi arc states into the bulk of the semimetal. It is noticeable that the corresponding scattering rate is nonzero and can be estimated even in a perturbative theory, although in general the reliable calculations of transport properties necessitate a nonperturbative approach. Nondecoupling of the surface and bulk sectors in the low-energy theory of Weyl semimetals invalidates the usual argument of a nondissipative transport due to one-dimensional arc states. This property of Weyl semimetals is in drastic contrast to that of topological insulators, where the decoupling is protected by a gap in the bulk. Within the framework of the linear response theory, we obtain an approximate result for the conductivity due to the Fermi arc states and analyze its dependence on chemical potential, temperature, and other parameters of the model.

We demonstrate that the physical reason for nontrivial topological properties of Dirac semimetals A3Bi (A = Na, K, Rb) is connected with a discrete symmetry of the low-energy effective Hamiltonian. By making use of this discrete symmetry, we argue that all electron states can be split into two separate sectors of the theory. Each sector describes a Weyl semimetal with a pair of Weyl nodes and broken time-reversal symmetry. The latter symmetry is not broken in the complete theory because the time-reversal transformation interchanges states from different sectors. Our findings are supported by explicit calculations of the Berry curvature. In each sector, the field lines of the curvature reveal a pair of monopoles of the Berry flux at the positions of Weyl nodes. The Z2 Weyl semimetal nature is also confirmed by the existence of pairs of surface Fermi arcs, which originate from different sectors of the theory. Introduction. Three-dimensional (3D) Dirac semimetals whose conduction and valence bands touch only at discrete (Dirac) points in the Brillouin zone with the electron states described by the 3D masless Dirac equation are 3D analogs of graphene. Historically, bismuth 1 was the first material where it was shown that its low-energy quasiparticle excitations near the L point of the Brillouin zone are described by the 3D Dirac equation with a small mass 2 . Since the Dirac point is composed of two Weyl nodes of opposite chirality which overlap in momentum space, it can be gapped out. Therefore, even if the 3D Dirac point is obtained accidentally by fine tuning the spin-orbit coupling strength or chemical composition, it is, in general, not stable and is difficult to control.It was proposed in Refs. 3,4 that an appropriate crystal symmetry can protect and stabilize the 3D Dirac points if two bands which cross each other belong to different irreducible representations of the discrete crystal rotational symmetry. By using the first-principle calculations and effective model analysis, A 3 Bi (A=Na, K, Rb) and Cd 3 As 2 compounds were identified in Refs.5,6 as 3D Dirac semimetals protected by crystal symmetry. Various topologically distinct phases can be realized in these compounds by breaking time reversal and inversion symmetries. By making use of angle-resolved photoemission spectroscopy, Dirac semimetal band structure was indeed observed 7-9 in Cd 3 As 2 and Na 3 Bi opening the path toward experimental investigation of properties of 3D Dirac semimetals. For a recent review of 3D Dirac semimetals, see Ref.10 .