Mixed Axial-Torsional Anomaly in Weyl Semimetals

Geometry, anomaly, topology, and transport in Weyl fermions

Weyl fermions are one of the simplest objects that link ideas in geometry and topology to high-energy physics and condensed matter physics. Although the existence of Weyl fermions as elementary particles remains dubious, there is mounting evidence of their existence as quasiparticles in certain condensed matter systems. Such systems are termed Weyl semimetals (WSMs). Needless to say, WSMs have emerged as a fascinating class of materials with unique electronic properties, offering a rich playground for both fundamental research and potential technological applications. This review examines recent advancements in understanding electron transport in WSMs. We begin with a pedagogical introduction to the geometric and topological concepts critical to understanding quantum transport in Weyl fermions. We then explore chiral anomaly, a defining feature of WSMs, and its impact on transport phenomena such as longitudinal magnetoconductance and planar Hall effect. The Maxwell-Boltzmann transport theory extended beyond the standard relaxation-time approximation is then discussed in the context of Weyl fermions, which is used to evaluate various transport properties. Attention is also given to the effects of strain-induced gauge fields and external magnetic fields in both time-reversal broken and inversion asymmetric inhomogeneous WSMs. The review synthesizes theoretical insights, experimental observations, and numerical simulations to provide a comprehensive understanding of the complex transport behaviors in WSMs, aiming to bridge the gap between theoretical predictions and experimental verification.

Spatiotemporal determination of photoinduced strain in a Weyl semimetal

The application of dynamic strain holds the potential to manipulate topological invariants in topological quantum materials. This study investigates dynamic structural deformation and strain modulation in the Weyl semimetal WTe2, focusing on the microscopic regions with static strain defects. The interplay of static strain fields, at local line defects, with dynamic strain induced from photo-excited coherent acoustic phonons results in the formation of local standing waves at the defect sites. The dynamic structural distortion is precisely determined utilizing ultrafast electron microscopy with nanometer spatial and gigahertz temporal resolutions. Numerical simulations are employed to interpret the experimental results and explain the mechanism for how the local strain fields are transiently modulated through light-matter interaction. This research provides the experimental foundation for investigating predicted phenomena such as the mixed axial-torsional anomaly, acoustogalvanic effect, and axial magnetoelectric effects in Weyl semimetals, and paves the road to manipulate quantum invariants through transient strain fields in quantum materials.

Antisymmetric Seebeck Effect in a Tilted Weyl Semimetal

Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co_{3}Sn_{2}S_{2}. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Momentum transport is anomalous in chiral p+ip superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semiclassical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticles which satisfy the conservation laws associated with local Lorentz symmetry restricted to the plane of uniaxial anisotropy of the superfluid (or superconductor). Moreover, we show that the anomalous Galilean momentum conservation is a consequence of the gravitational Nieh-Yan (NY) chiral anomaly the Weyl fermions experience on the background geometry. Notably, the NY anomaly coefficient features a nonuniversal ultraviolet cutoff scale Λ, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cutoff parameter Λ is determined by the normal state Fermi liquid and nonrelativistic uniaxial symmetry of the p-wave superfluid or superconductor.