Dirac Semimetals in Two Dimensions (1504.07977v2)

Abstract: Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are \emph{not} gapped by spin-orbit interactions, and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases, and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of non-symmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.

• The paper introduces a theoretical framework using a two-site tight-binding model to reveal symmetry-protected Dirac semimetals in two dimensions.
• The paper shows that nonsymmorphic symmetries stabilize multiple Dirac points, preventing the SOC-induced gap commonly observed in graphene.
• The paper discusses how breaking specific symmetries induces transitions to insulating or Weyl semimetal phases, paving the way for novel electronic applications.

Symmetry-Protected Two-Dimensional Dirac Semimetals

The paper "Dirac Semimetals in Two Dimensions" by Steve M. Young and Charles L. Kane investigates a class of materials that host two-dimensional (2D) Dirac fermions. These materials differ fundamentally from known systems such as graphene, which, while possessing Dirac-like properties, manifests a gap due to spin-orbit coupling (SOC) that turns it into a quantum spin Hall insulator. The focus of this work is on symmetry-protected Dirac semimetals that retain Dirac points in the presence of SOC, a feature not previously identified in two dimensions.

The authors utilize a theoretical framework based on a two-site tight-binding model to elucidate the formation and stability of these Dirac semimetal phases under various symmetry conditions. Key to their analysis is the role of nonsymmorphic symmetries, which involve symmetry operations combining point group transformations with fractional lattice translations. These symmetries are shown to dictate band-touching conditions necessary for forming Dirac points, placing the system at the boundary between topological and trivial insulating phases without the SOC-induced gap observed in systems like graphene.

In 2D Dirac semimetals identified in this work, pairs or triplets of Dirac points emerge due to the preservation of certain symmetry operations, such as nonsymmorphic space group symmetries in combination with time-reversal invariance. These Dirac points are located at high-symmetry points within the Brillouin zone (BZ), and their stability against SOC is attributed to the projective representations of the little groups at these points, ensuring band degeneracy and crossing.

Three distinct Dirac semimetal phases are characterized:

1. A pair of symmetry-equivalent Dirac points protected by specific mirror and glide plane symmetries.
2. Two symmetry-inequivalent Dirac points stabilized by separate glide or screw symmetries.
3. Three Dirac points protected by combined C4 rotation and additional symmetries.

The authors also establish the impossibility of a solitary symmetry-protected Dirac point in two dimensions due to the need for such a point to serve as a boundary between topologically distinct phases. This necessitates symmetry-induced mapping between multiple band touchings.

In addition to identifying these semimetal phases, the paper discusses the transition to other phases, such as insulating or Weyl semimetal phases, by breaking specific symmetries. For instance, the introduction of inversion symmetry violation can lead to Weyl points or nodal lines, signifying a pathway to varied electronic behavior depending on the symmetry constraints imposed or removed.

The practical implications of this research are significant for the development of materials that might leverage the robust electronic properties of Dirac fermions for applications in quantum computing and advanced electronic devices. The authors suggest that certain transition metal dichalcogenides and artificially layered structures, such as iridium oxide superlattices, are promising candidates for experimental realization.

Future perspectives of the research point towards creating novel 2D materials with customizable electronic properties by engineered symmetry breaking. The critical understanding of symmetry in dictating electronic states could drive the precise control of electronic transport phenomena, potentially contributing to the advent of novel topological devices.