Collective modes of type-II Weyl fermions with repulsive S-wave interaction

Three-dimensional type-II Weyl fermions possess overtilted conelike low-energy band dispersion. Unlike the closed ellipsoidal Fermi surface for type-I Weyl fermions, the Fermi surface is an open hyperboloid for type-II Weyl fermions. We evaluate the spin and density susceptibility of type-II Weyl fermions with repulsive S-wave interaction by means of Green’s functions. We obtain the particle-hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction, respectively. We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.

Nonadiabatic nonlinear optics and quantum geometry — Application to the twisted Schwinger effect

We study the tunneling mechanism of nonlinear optical processes in solids induced by strong coherent laser fields. The theory is based on an extension of the Landau-Zener model with nonadiabatic geometric effects. In addition to the rectification effect known previously, we find two effects, namely perfect tunneling and counterdiabaticity at fast sweep speed. We apply this theory to the twisted Schwinger effect, i.e., nonadiabatic pair production of particles by rotating electric fields, and find a nonperturbative generation mechanism of the opto-valley polarization and photo-current in Dirac and Weyl fermions.

Unravelling relativistic fermions in Weyl semimetal TaAs by magnetostriction measurements

In the topological semimetals, electrons in the vicinity of the Weyl or Dirac nodes behave like massless relativistic fermions that are of interest both for basic research and future electronic applications. Thus far, a detection of these Dirac or Weyl quasiparticles in topological semimetals is often elusive since in these materials, conventional charge carriers exist as well. Here, considering a prototype topological Weyl semimetal TaAs as an example, we show that when the massless quasiparticles reach the ultra-quantum limit, the magnetostriction of the semimetal is appreciably produced by the relativistic fermions. This field-induced expansion of TaAs measured along the [001] direction exhibits a weak dependence on the magnetic-field orientation and is in striking contrast to the magnetostriction measured along the [100] axis. The latter quantity experiences immense changes from large positive to large negative values with minute deviations of the applied field from the [001] direction. Employing a rigid-band approximation, we work out a theory of the magnetostriction for the Weyl semimetals and point out the features of this thermodynamic probe that can serve as hallmarks of the Weyl quasiparticles. Using the theory, we quantitatively describe a part of the obtained experimental data and find a number of the parameters characterizing TaAs. The derived dependence of the Fermi level on the magnetic field should be also relevant to understanding some other field-dependent properties of this topological semimetal, in particular, the negative longitudinal magnetoresistance. Our results illustrate how a magnetostriction may be used to unveil Weyl fermions in topological semimetals with a noncetrosymmetric crystal structure.

Perturbative and Non-Pertrubative Trace Anomalies

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.