[Paper Review] Anomalous Hall Effect in Type-II Weyl Semimetals

A. A. Zyuzin, Rakesh P. Tiwari|arXiv (Cornell University)|Jan 5, 2016

Graphene research and applications3 citations

TL;DR

This paper investigates the anomalous Hall effect (AHE) in type-II Weyl semimetals with a tilted conical spectrum using the Kubo formula. It shows that the AHE conductivity is not universal and can change sign depending on tilt parameters, even when Weyl points are degenerate, due to asymmetric tilting of the two cones.

ABSTRACT

Recently, a new type of Weyl semimetals called type-II Weyl semimetals has been proposed. Unlike the usual (type-I) Weyl semimetals, which have a point-like Fermi surface, this new type of Weyl semimetals have a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.

Motivation & Objective

• To understand the anomalous Hall effect in type-II Weyl semimetals, which feature a tilted conical spectrum around Weyl points.
• To investigate how the tilting of the Weyl cones—unlike in type-I Weyl semimetals—affects the Hall conductivity.
• To determine whether a finite anomalous Hall effect can emerge even when the Weyl points are at zero separation, provided the tilts are asymmetric.
• To assess the universality of the anomalous Hall conductivity in the presence of spectral tilting.

Proposed method

• The Kubo formula is employed to calculate the anomalous Hall conductivity in a system with a pair of Weyl points exhibiting a tilted conical spectrum.
• The calculation incorporates parameters quantifying the degree and direction of spectral tilting around each Weyl point.
• The model considers a two-cone system where the Weyl points may be separated or degenerate in momentum space.
• The analysis focuses on the dependence of the Hall conductivity on the tilting parameters, particularly the asymmetry between the two cones.
• The formalism accounts for the non-hermitian nature of the effective Hamiltonian due to tilting, using linearized band structure near the Weyl points.
• The results are derived analytically in the low-energy limit, assuming weak external fields and linear dispersion with tilt.

Experimental results

Research questions

• RQ1 How does the anomalous Hall conductivity in type-II Weyl semimetals depend on the degree and direction of spectral tilting?
• RQ2 Can a finite anomalous Hall effect persist when the Weyl points are at zero momentum separation, due to asymmetric tilting?
• RQ3 Is the anomalous Hall conductivity universal in type-II Weyl semimetals, or does it vary with material-specific parameters?
• RQ4 What is the role of cone asymmetry in generating or suppressing the anomalous Hall effect?

Key findings

• The anomalous Hall conductivity in type-II Weyl semimetals is not universal and depends explicitly on the parameters quantifying the tilting of the conical spectra.
• The Hall conductivity can change sign as a function of the tilting parameters, indicating a tunable and non-monotonic response.
• Even when the Weyl points are at zero separation in momentum space, a finite anomalous Hall effect can emerge if the tilts of the two cones are not identical.
• The non-universality of the AHE arises from the breaking of Lorentz invariance due to spectral tilting, which modifies the Berry curvature distribution.
• The sign and magnitude of the Hall response are sensitive to the relative orientation and strength of the tilts between the two Weyl cones.
• The results suggest that tilting alone—without Weyl point separation—can induce a non-zero anomalous Hall effect, challenging the conventional view of AHE as requiring momentum-space separation.