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Recently, a class of Dirac semimetals, such as textrm{Na}$_{mathrm{3}}% $textrm{Bi} and textrm{Cd}$_{mathrm{2}}$textrm{As}$_{mathrm{3}}$, are discovered to carry $mathbb{Z}_{2}$ monopole charges. We present an experimental mechanism to realize the $mathbb{Z}_{2}$ anomaly in regard to the $mathbb{Z}_{2}$ topological charges, and propose to probe it by magnetotransport measurement. In analogy to the chiral anomaly in a Weyl semimetal, the acceleration of electrons by a spin bias along the magnetic field can create a $mathbb{Z}_{2}$ charge imbalance between the Dirac points, the relaxation of which contributes a measurable positive longitudinal spin magnetoconductivity (LSMC) to the system. The $mathbb{Z}_{2}$ anomaly induced LSMC is a spin version of the longitudinal magnetoconductivity (LMC) due to the chiral anomaly, which possesses all characters of the chiral anomaly induced LMC. While the chiral anomaly in the topological Dirac semimetal is very sensitive to local magnetic impurities, the $mathbb{Z}_{2}$ anomaly is found to be immune to local magnetic disorder. It is further demonstrated that the quadratic or linear field dependence of the positive LMC is not unique to the chiral anomaly. Base on this, we argue that the periodic-in-$1/B$ quantum oscillations superposed on the positive LSMC can serve as a fingerprint of the $mathbb{Z}_{2}$ anomaly in topological Dirac semimetals.
Weyl semimetals (WSMs) host charged Weyl fermions as emergent quasiparticles. We develop a unified analytical theory for the anomalous positive longitudinal magnetoconductance (LMC) in a WSM, which bridges the gap between the classical and ultra-quan
We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect as emergent effects of the chiral anomaly in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It i
We report two theoretical discoveries for $mathbb{Z}_2$-topological metals and semimetals. It is shown first that any dimensional $mathbb{Z}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, wh
The manifestation of chiral anomaly in Weyl semimetals typically relies on the observation of longitudinal magnetoconductance (LMC) along with the planar Hall effect, with a specific magnetic field and angle dependence. Here we solve the Boltzmann eq
Type-II Weyl semimetals are characterized by the tilted linear dispersion in the low-energy excitations, mimicking Weyl fermions but with manifest violation of the Lorentz invariance, which has intriguing quantum transport properties. The magnetocond