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Register a new userEntropy wave instability in Dirac and Weyl semimetals
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Hydrodynamic instabilities driven by a direct current are analyzed in 2D and 3D relativisticlike systems with the Dyakonov-Shur boundary conditions supplemented by a boundary condition for the temperature. Besides the conventional Dyakonov-Shur instability for plasmons, we find an entropy wave instability in both 2D and 3D systems. The entropy wave instability is a manifestation of the relativisticlike nature of electron quasiparticles and a nontrivial role of the energy current in such systems. These two instabilities occur for the opposite directions of fluid flow. While the Dyakonov-Shur instability is characterized by the plasma frequency in 3D and the system size in 2D, the frequency of the entropy wave instability is tunable by the system size and the flow velocity.
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Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number L retains its usual value L_0. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, L exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatial-inversion symmetry. We show that, while the former will follow the same behaviour as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.
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.
Weyl semimetals expand research on topologically protected transport by adding bulk Berry monopoles with linearly dispersing electronic states and topologically robust, gapless surface Fermi arcs terminating on bulk node projections. Here, we show how the Nernst effect, combining entropy with charge transport, gives a unique signature for the presence of Dirac bands. The Nernst thermopower of NbP (maximum of 800 microV K-1 at 9 T, 109 K) exceeds its conventional thermopower by a hundredfold and is significantly larger than the thermopower of traditional thermoelectric materials. The Nernst effect has a pronounced maximum near T_M=90 +/- 20 K=mu_0/kB (mu_0 is chemical potential at T=0 K). A self-consistent theory without adjustable parameters shows that this results from electrochemical potential pinning to the Weyl point energy at T>=TM, driven by charge neutrality and Dirac band symmetry. Temperature and field dependences of the Nernst effect, an even function of the charge polarity, result from the intrinsically bipolar nature of the Weyl fermions. Through this study, we offer an understanding of the temperature dependence of the position of the electrochemical potential vis-a-vis the Weyl point, and we show a direct connection between topology and the Nernst effect, a potentially robust experimental tool for investigating topological states and the chiral anomaly.
We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high temperatures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.
Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl semimetals exhibit strong SHG upon application of finite current. Our experimental estimation for a Dirac semimetal Cd$_3$As$_2$ and a magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ suggests that the induced susceptibility $chi^{(2)}$ for practical applied current densities can reach $10^5~mathrm{pm}cdotmathrm{V}^{-1}$ with mid-IR or far-IR light. This value is 10$^2$-10$^4$ times larger than those of typical nonlinear optical materials. We also discuss experimental approaches to observe the current-induced SHG and comment on current-induced SHG in other topological semimetals in connection with recent experiments.
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