Weyl and Dirac Semimetals in Three Dimensional Solids (1705.01111v3)

Abstract: Weyl and Dirac semimetals are three dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and -- despite their gaplessness -- to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. Here we review the theoretical foundations of these phases, their proposed realizations in solid state systems, recent experiments on candidate materials, as well as their relation to other states of matter.

• The paper demonstrates how broken symmetries in 3D solids give rise to Weyl and Dirac fermions with robust topological protections.
• It uses numerical simulations and experimental data to reveal distinct signatures such as the chiral anomaly and negative magnetoresistance.
• The study underscores the importance of symmetry and topology in guiding material synthesis and advancing quantum phase research.

Overview of "Weyl and Dirac Semimetals in Three-Dimensional Solids"

The paper "Weyl and Dirac Semimetals in Three-Dimensional Solids" provides a comprehensive exploration into the theoretical underpinnings, experimental realizations, and potential implications of Weyl and Dirac semimetals. Semimetals represent a class of materials in which conduction and valence bands touch at discrete points, known as nodes, permitting unique electronic properties protected by the topology of the material's band structure. These properties often exhibit robust surface states and characteristic responses to external electromagnetic fields, thus sparking extensive interest in both condensed matter physics and materials science.

Theoretical Foundations

Central to the discussion is the Dirac equation, historically significant for unifying quantum mechanics with special relativity, and predicting phenomena such as antimatter. In condensed matter systems, particularly three-dimensional crystals, effective low-energy models can approximate the Dirac equation, manifesting as Weyl fermions and Dirac fermions with distinct chiral properties. Weyl semimetals (WSMs) emerge when inversion or time-reversal symmetry is broken, leading to split chiral nodes in the momentum space, which are characterized by topological invariants corresponding to their monopole-like Berry curvature.

Dirac and Weyl Semimetals

Dirac semimetals (DSMs) are particularly noteworthy because they require symmetry-protected degeneracy, which can be provided by space group symmetries. These systems often materialize as a point on the phase boundary between different topological phases, such as a topological insulator and a trivial insulator. In contrast, Weyl semimetals exhibit nodes that are robust against perturbations, generating fascinating surface phenomena such as Fermi arcs, which are discontinuous contours on the surface energy-momentum space topology.

Strong Numerical Results and Implications

The paper explores the distinct electronic responses of these semimetals to applied fields. A prominent effect is the "chiral anomaly," which, in Weyl semimetals, manifests as a non-conservation of chiral charge under the simultaneous application of parallel electric and magnetic fields, resulting in negative magnetoresistance—a potentially measurable signature. Weyl semimetals also give rise to an intrinsic anomalous Hall effect, where the conductivity is directly related to the separation of Weyl nodes in momentum space.

Experimental Realizations and Materials

The research surveys candidate materials, emphasizing the significance of symmetry considerations in realizing DSM and WSM phases. Practically, identifying Weyl semimetals often involves finding or synthesizing materials with appropriate topological protections, achieved through experimental conditions such as pressure, strain, or chemical doping. The paper details successful materials such as the TaAs family, which exhibits clear signatures of Weyl physics and has been extensively studied using methods like angle-resolved photoemission spectroscopy (ARPES) and quantum oscillations.

Future Directions and Considerations

The paper speculates on future research directions and applications. The interplay between topology and electron interactions presents possibilities for novel quantum phases. Further development of experimental probes could reveal finer details of Weyl semimetals, such as their interaction with light, which points to potential applications in optoelectronics and quantum computing. Moreover, the exploration of related concepts in non-electronic systems, like photonic and acoustic crystals, underscores the broader scientific relevance of topological phases beyond their manifestation in electronic materials.

Concluding Remarks

In summary, this paper articulates a solid framework for understanding Weyl and Dirac semimetals, emphasizing the interplay between symmetry, topology, and experimental realizations. It calls for a continued search for ideal materials and exploration beyond conventional electronic contexts. As the field evolves, these semimetals stand to play a prominent role in future advancements in technology and fundamental physics.