Magnetic field induces giant nonlinear optical response in Weyl semimetals

We study the second-order optical response of Weyl semimetals in the presence of a magnetic field. We consider an idealized model of a perfectly linear Weyl node and use the Kubo formula at zero temperature to calculate the intrinsic contribution to photocurrent and second harmonic generation conductivity components. We obtain exact analytical expressions applicable at arbitrary values of frequency, chemical potential, and magnetic field. Our results show that finite magnetic field significantly enhances the nonlinear optical response in semimetals, while magnetic resonances lead to divergences in nonlinear conductivity. In realistic systems, these singularities are regularized by a finite scattering rate, but result in pronounced peaks which can be detected experimentally, provided the system is clean and interactions are weak. We also perform a semiclassical calculation that complements and confirms our microscopic results at small magnetic fields and frequencies.Comment: 25 pages, 8 figure

Topological and superconducting properties of Weyl and Dirac metals

In this work we explore superconductivity and surface states in topological semimetals. We start from general overview of basic properties of topological semimetals. We review general concepts of Chern insulators, their surface states, and use it as a building block for construction of Weyl metals. We also construct double Weyl metals, which are protected both by topology and discrete rotational symmetry. In addition, we study Luttinger model of semimetals - it the simplest case, it is non-topological, but it can acquire topological Weyl points in the presence of non-zero Zeeman field. We present study of its surface states, and also consider its possible critical points. Next, we turn to the problem of superconductivity in Weyl metals. We demonstrate that Weyl metals are natural candidates for hosting unconventional superconductivity. Specifically, we consider two possible superconducting instabilities: unconventional finite momentum FFLO pairing, and zero momentum BCS pairing, which is also unconventional due to spin-momentum locking in Weyl metals. We demonstrate that its BCS phase is more favorable. In addition, we compute its anomalous Hall conductivity, and demonstrate that it is universal, i.e. not affected by the presence of superconductivity. Finally, we consider Dirac metals, which are protected solely by rotational symmetry. We point out, that mirror symmetry along its Dirac points plays special role. We demonstrate, that by breaking the rotational symmetry, it is possible to convert Dirac metal into a topological crystalline insulator, and Dirac metal itself can be viewed as a critical point between its different topological phases. We explore surface states spectrum in the resulting picture, and demonstrate, that this mechanism can be used to show that surface states in Dirac metal always terminate at Dirac points despite being not topologically protected

Weyl hydrodynamics in a strong magnetic field

We study the hydrodynamic transport of electrons in a Weyl semimetal in a strong magnetic field. Impurity scattering in a Weyl semimetal with two Weyl nodes is strongly anisotropic as a function of the direction of the field and is significantly suppressed if the field is perpendicular to the separation between the nodes in momentum space. This allows for convenient access to the hydrodynamic regime of transport, in which electron scattering is dominated by interactions rather than by impurities. In a strong magnetic field, electrons move predominantly parallel to the direction of the field, and the flow of the electron liquid in a Weyl-semimetal junction resembles the Poiseuille flow of a liquid in a pipe. We compute the viscosity of the Weyl liquid microscopically and find that it weakly depends on the magnetic field and has the temperature dependence $\eta(T)\propto T^2$. The hydrodynamic flow of the Weyl liquid can be generated by a temperature gradient. The hydrodynamic regime in a Weyl-semimetal junction can be probed via the thermal conductance $G_q(B,T)\propto B^2 T$ of the junction.Comment: 15 pages, 3 figure