Type-II Weyl Semimetals (1507.01603v2)

Abstract: Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe$_2$, is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points.

• The paper introduces a Hamiltonian model showing how a significant tilt in Weyl cones creates open electron and hole pockets in type-II Weyl semimetals.
• It employs ab-initio calculations and Wannier-based tight-binding models to identify eight Weyl points with nontrivial Berry flux in WTe₂.
• The study predicts unique transport phenomena, including a direction-dependent chiral anomaly and anisotropic conductivity, opening new research avenues in topological materials.

Insights on Type II Weyl Semimetals

The paper presents a detailed theoretical analysis of a novel type of Weyl semimetal, christened as type II Weyl semimetals. Traditional Weyl semimetals (WSMs), now referred to as type I, are characterized by point-like Fermi surfaces (FS) at the Weyl points, a result of linearly crossing bands at the Fermi level. In contrast, type II Weyl semimetals differ fundamentally; their spectrum at the Weyl points includes a significant tilt, creating open electron and hole pockets, which results in a finite density of states at the crossing. This tilting leads to marked changes in their thermodynamic and transport responses.

Theoretical Framework and Predictions

The work lays down a Hamiltonian indicative of type II Weyl points, demonstrating the essential conditions under which such points can form. The presence of these Weyl points is signaled by an emergent mismatch between the kinetic term and the Weyl cone's potential term in the system's Hamiltonian. More critically, in type II WSMs, the axis along which the kinetic term dominates determines their distinct topological characterization. The categorical prediction is that the material WTe$_2$ hosts these type II Weyl fermions, occurring at nodes between electron and hole pockets, which is a departure from the expectation of point-like nodes that characterized earlier views on Weyl semimetals.

Numerical and Topological Analysis

The authors utilize ab-initio calculations and construct Wannier-based tight-binding models to provide numerical evidence of this new semimetallic phase in WTe$_2$. They identify a total of eight Weyl points, distributed along high-symmetry lines in the Brillouin zone, with their positions and separations sensitive to external factors like strain. The computation of Chern numbers associated with these nodes verifies their Weyl character. Extensive topological analyses confirm the distinctive nontrivial Berry flux and surface Fermi arcs, characteristic of topological Weyl points.

Implications and Theoretical Developments

The implication of type II Weyl semimetals is profound, particularly in terms of their transport properties. The material not only violates Lorentz invariance, a symmetry often preserved in high-energy physics, but also displays a unique chiral anomaly with constraints dictated by the direction of applied magnetic fields. This is in striking contrast to type I Weyl semimetals where chiral anomalies are observed universally under magnetic fields. These properties hint at novel electronic applications due to the anisotropic and angle-dependent conductivities in type II WSMs.

The introduction of a new categorization for Weyl semimetals by the tilt in Weyl cones challenges the current classification and augments the field's understanding of topological materials. It opens up avenues for potential research into the emergent phenomena such as direction-dependent anomalous transport and quantized thermal Hall conductivities.

Future Outlook and Conclusion

Looking forward, the paper sets the stage for experimental validation of the theoretical findings, which could decisively alter the synthesis and functionalities of topological materials. Investigating pressure and strain effects further reveals the potentially rich phase diagram in systems hosting type II Weyl fermions. This research represents a significant addition to the understanding of Weyl fermions in solid-state physics, promoting exploration into broader classes of materials that might exhibit these intriguing properties. Such investigations are crucial for advancing applications in quantum computing and novel electronic devices, exploiting the fundamentally different electronic and magnetic responses of these materials.