3D Dirac semimetals: current materials, design principles and predictions of new materials (1411.0005v1)

Abstract: Design principles and novel predictions of new 3D Dirac semimetals are presented, along with the context of currently known materials. Current materials include those based on a topological to trivial phase transition, such as in TlBiSe${2-x}$S$_x$ and Hg${1-x}$Cd$x$Te, Bi${1-x}$Sb$x$, Bi${2-x}$In$x$Se$_3$, and Pb${1-x}$Sn$_x$Se. Some more recently revealed materials, Na$_3$Bi and Cd$_3$As$_2$, are 3D Dirac semimetals in their native composition. The different design principles presented each yield novel predictions for new candidates. For Case I, 3D Dirac semimetals based on charge balanced compounds, BaAgBi, SrAgBi, YbAuSb, PtBi$_2$ and SrSn$_2$As$_2$ are identified as candidates. For Case II, 3D Dirac semi-metals in analogy to graphene, BaGa$_2$ is identified as a candidate, and BaPt and Li$_2$Pt are discussed. For Case III, 3D Dirac semi-metals based on glide planes and screw axes, TlMo$_3$Te$_3$ and the AMo$_3$X$_3$ family in general (A=K, Na, In, Tl, X=Se,Te) as well as the Group IVb trihalides such as HfI$_3$ are identified as candidates. Finally we discuss conventional intermetallic compounds with Dirac cones, and identify Cr$_2$B as a potentially interesting material.

Overview of 3D Dirac Semimetals: Current Materials and Design Principles

This paper undertakes an extensive discussion on 3D Dirac semimetals, with an emphasis on current materials, design principles, and predictions of new candidates. It explores the electronic characteristics that define these materials, outlining both known and predicted 3D Dirac semimetals (DSMs) characterized by unique band crossings in their electronic structures. The main aim is to elucidate pathways for the identification and development of novel DSMs, highlighting the interplay between physics, chemistry, and crystallography.

Current Materials

Presently, the 3D DSM landscape is dominated by two intrinsic candidates: Na$_3$Bi and Cd$_3$As$_2$. Different from those systems in which DSM behavior is only situated at precise compositions within solid solutions—such as TlBiSe$_{2-x}$S$_x$—these materials possess crystalline symmetries that protect Dirac points without compositional tuning dependence. Na$_3$Bi features C$_3$ symmetry, while Cd$_3$As$_2$ utilizes C$_4$, facilitating robust 3D Dirac points.

Design Principles and Predicted New Materials

Case I: Charge Balanced Formulas

Predicted DSMs in charge balanced systems rely heavily on crystal symmetry to maintain degeneracy at specific k-points in the Brillouin zone. ZrBeSi type compounds such as BaAgBi demonstrate potential DSM behavior due to appropriate symmetry that allows band crossing unimpeded by SOC effects. Moreover, SrAgBi and other similar materials feature significant SOC that drives the band inversion necessary for Dirac points, albeit they face challenges due to the presence of additional bands. Similarly, the LiGaGe and pyrite family materials such as PtBi$_2$ encapsulate these principles to present novel implementations of 3D DSM electronic states.

Case II: Analogy to Graphene

Expanding on the analogy to 2D Dirac semimetals like graphene, materials such as BaGa$_2$ have been considered for their unique structural arrangements that mimic graphene's electronic properties in 3D systems. Despite challenges from interlayer coupling, BaGa$_2$ offers insights into the realization of quasi-2D Dirac states. Other compounds, including BaPt and Li$_2$Pt, attempt to leverage linear coordination and hexagonal arrangements to emulate graphene's properties in a 3D context.

Case III: Glide Planes and Screw Axes

The final avenue capitalizes on non-symmorphic symmetries that inherently necessitate band degeneracies, such as those exhibited by AMo$_3$X$_3$ cluster compounds. These utilize complex Mo configurations augmented by the presence of electron-donating elements to potentially access Dirac states. The exploration extends to group IVb trihalides like HfI$_3$, showcasing quasi-1D DSM characteristics attributed to their unique structural layout and electronic configurations.

Implications and Future Directions

Understanding these design principles enriches both theoretical knowledge and practical approaches to DSM discovery. The implications of these materials extend into applications demanding high electron mobility and potential topological protection. Moreover, unexplored areas such as DSMs with interacting electron systems—including superconducting or charge density wave properties—promise fascinating avenues for future research and applications in electronics, spintronics, and quantum computing.

In conclusion, this paper consolidates the underpinnings for identifying and realizing DSMs, laying the groundwork for exploration and experimentation. By leveraging the symmetry considerations, alongside the electronic characteristics inherent to these materials, researchers can better predict and synthesize new DSM candidates within emerging fields of condensed matter physics.