Topological response in Weyl semimetals and the chiral anomaly (1206.1868v3)

Abstract: We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a $\theta$-term in the action for the electromagnetic field, where $\theta$ is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the $\theta$-term and the corresponding topological response survive for sufficiently weak translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes.

• The paper provides a unified description of the anomalous Hall and chiral magnetic effects in Weyl semimetals through the framework of the chiral anomaly.
• It employs a multilayer heterostructure model and Fujikawa’s method to derive a dynamic theta-term linking electromagnetic responses to chiral fermion anomalies.
• The study shows that topological robustness persists despite symmetry-breaking perturbations, ensuring reliable transport properties even when gaps emerge.

Topological Response in Weyl Semimetals and the Chiral Anomaly

The paper by A.A. Zyuzin and A.A. Burkov discusses the nuanced behavior of Weyl semimetals, a recently characterized topological phase of matter. These materials are notable for their bulk gapless states and protected surface states. Central to their paper is the interplay between the anomalous Hall effect (AHE) and the chiral magnetic effect (CME), both of which are tied to the phenomenon of the chiral anomaly—a prominent concept initially established in high-energy physics.

Conceptual Framework and Theoretical Formalism

Weyl semimetals, which lack a bulk energy gap, exhibit topologically protected phenomena owing to the separation of Weyl nodes with distinct chiralities in momentum space. This separation necessitates breaking time-reversal or inversion symmetries. The authors argue that topological transport phenomena in these materials are unified under the chiral anomaly framework. This is effectively captured through the introduction of a dynamical $\theta$-term into the electromagnetic action. Unlike topological insulators, where $\theta$ is constant, in Weyl semimetals, it depends linearly on space-time coordinates.

Methodology

The authors employ a model based on a multilayer heterostructure that combines topological and normal insulators. This configuration simplifies the band structure to two Weyl nodes of opposite chirality, facilitating the exploration of fundamental properties. They derive the $\theta$-term using Fujikawa’s method, a technique originally developed for studying anomalies in quantum field theories. This approach highlights how electromagnetic responses in these systems relate directly to anomalies in chiral fermion conservation laws.

Key Findings

1. Unified Description: The AHE and CME are shown to arise from a common underlying topological structure. The CME, manifesting as an equilibrium current induced by a magnetic field, parallels the AHE induced by transverse electric fields.
2. Robustness to Gapping: The topological response mechanism persists despite translational symmetry-breaking perturbations, which can introduce spectral gaps. This indicates that topological robustness in Weyl semimetals extends beyond the mere presence of gapless Weyl fermions.
3. Chiral Anomaly Manifestation: The paper rigorously demonstrates that the chiral anomaly yields nontrivial transport properties even when conventional notions of topological protection through gapless states are destabilized by symmetry-breaking effects.

Implications and Future Directions

These findings deepen the understanding of how Weyl semimetals can be utilized in practical applications such as electronic transistors and sensors, where robust conductivity properties may be vital under various symmetry-breaking scenarios. The generalization of these results might influence investigations into other topological materials where chiral anomalies play a central role.

Looking forward, experimental validation of these theoretical insights, particularly the persistence of topological phenomena under gap conditions, would be critical. Furthermore, exploring the role of disorder and interactions in these systems could reveal additional layers of complexity in topological materials science.

Conclusion

This paper provides a consolidated framework that connects Weyl semimetals' unique transport properties with the chiral anomaly, emphasizing the persistence of topological robustness even in gapped scenarios. This expands the theoretical landscape for potential applications and future explorations of topological phases in condensed matter systems.