Dirac vs. Weyl in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena (1307.6990v1)

Abstract: Dirac metals (gapless semi-conductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of Weyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in Bi1-xSbx, we observe not only the weak anti-localization phenomenon in magnetoconductivity near zero magnetic fields (B < 0.4 T) but also its upturn above 0.4 T only for E // B. This incompatible coexistence between weak anti-localization and negative magnetoresistivity is attributed to the Adler-Bell-Jackiw anomaly (topological E B term) in the presence of weak anti-localization corrections.

• The paper demonstrates that longitudinal magnetoconductivity in Bi₁₋ₓSbₓ alloys is best explained by a semi-classical approach, contrasting with the ultra-quantum limit.
• The authors validate theoretical predictions by fitting experimental data to quadratic and linear magnetic field dependencies in conductivity.
• The study highlights reentrant magnetoconductivity downturns and Berry curvature effects, emphasizing the need for further exploration of anomalous transport in topological materials.

Analysis of the Adler-Bell-Jackiw Anomaly in Topological Insulators

The paper explores the transport phenomena in topological insulators, particularly focusing on the effects of the Adler-Bell-Jackiw (ABJ) anomaly within these materials. The objective is to discern the contributions of Dirac and Weyl electrons in such systems, specifically within the context of Bi$_{1-x}$Sb$_x$ alloys. The authors perform an in-depth analysis of longitudinal magnetoconductivity under various regimes and field limits, emphasizing the experimental verification of theoretical predictions related to the ABJ anomaly.

Adler-Bell-Jackiw Anomaly and Transport Regimes

The ABJ anomaly describes charge pumping between Weyl nodes of opposite chirality in presence of parallel electric and magnetic fields, influencing conductivity properties. Two regimes are explored: the semi-classical regime and the quantum regime. The semi-classical regime is characterized by negligible Landau level effects, while the quantum regime is defined by Landau-level quantization, where effectively one-dimensional chiral dynamics dominate.

In the semi-classical regime, the paper asserts that longitudinal magnetoconductivity can be expressed as $\sigma + \text{const. } B^2 \sigma$, where $B$ is the magnetic field and $\sigma$ is the Drude conductivity, primarily governed by intra-node scattering processes. Conversely, in the ultra-quantum limit, the conductivity showcases a linear $|B|$ dependence predominantly adjudicated by inter-node scattering.

Experimental Data and Ultra-Quantum Limit Analysis

The team scrutinized experimental data to affirm theoretical models. The attempt to fit experimental data of transverse and longitudinal magnetoconductivity to the parameters characterizing both semi-classical and quantum limits exhibits that the system resides closer to the semi-classical regime rather than the ultra-quantum limit. The discrepancies and the poor fits obtained for the ultra-quantum limit fitting underscore a higher Fermi level above the Weyl points, coherent with the band structure of Bi$_{1-x}$Sb$_x$ at $x \sim 3\%$.

Reentrant Downturn and Theoretical Implications

A critical observation is the "reentrant" downturn in magnetoconductivity beyond a magnetic field strength of approximately 4 T, coinciding with the theory of magnetic monopole pair annihilation or potential contributions from higher Landau levels in intermediate magnetic field ranges. Notably, the presence of Shubnikov-de Haas oscillations suggests onset of Landau level formation, hinting at a nuanced crossover regime. The implications of this downturn denote intricate dynamics in Weyl semimetals under external fields, yet definitive theoretical frameworks for this crossover remain unresolved, calling for further investigation.

Quantum Boltzmann Equation and Berry Curvature

The quantum Boltzmann equation is used to model the situation in the presence of an $\boldsymbol{E}\cdot\boldsymbol{B}$ term, with a specific interest in systems possessing Berry curvature anomalies. The paper incorporates Berry curvature effects into the semi-classical equations of motion to account for non-conventional transport dynamics in Weyl materials. These equations illuminate the integral role of Berry curvature in anomalous current contributions, further exhibiting the topological nature of transport phenomena.

Conclusion and Future Work

The paper substantiates the predominance of the semi-classical regime in the Bi$_{1-x}$Sb$_x$ system and demonstrates significant alignment between theoretical and experimental perspectives on the ABJ anomaly and transport properties of topological insulators. Future studies are anticipated to refine understanding within the crossover regime, necessitating comprehensive experimental and theoretical endeavors to elucidate behaviors beyond existing models. The insights presented could guide advancements in manipulating topological materials for technologies exploiting their unique transport properties.