Classification of stable three-dimensional Dirac semimetals with nontrivial topology

By Bohm-Jung Yang, N. Nagaosa. Nature Communications, 2014

742 citations recorded by the source corpus.

A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant. Three-dimensional Dirac semimetals are a recently discovered state of condensed matter considered as the 3D analogue of graphene. Here, Yang et al. propose a general framework to classify stable 3D Dirac semimetals in systems with time-reversal, inversion and uniaxial rotational symmetries.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/c480572074a5cc67031474a3ba8259c7753a62dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. N. P. Armitage
3. Y. Ando
4. E. Mele
5. Hsin Lin
6. Arun Bansil
7. D. Vanderbilt
8. Bogdan Andrei Bernevig

In Condensed Matter Physics

1. Ashvin Vishwanath
2. Y. Ando
3. Masatoshi Sato
4. Chen Fang
5. E. Witten
6. Liang Fu
7. X. Dai
8. H. Weng

In Materials Chemistry

1. Ashvin Vishwanath
2. Hsin Lin
3. N. P. Armitage
4. Arun Bansil
5. Y. Ando
6. E. Mele
7. M. Zahid Hasan
8. D. Vanderbilt

Citations in the corpus

• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, background): “The Dirac points are formed, since the Weyl points of opposite chirality are protected from gapping each other by a rotational symmetry [61, 160]: the two doublets crossing along Γ-A belong to different irreducible representations of the little group of the k-vectors k = (0, 0, u) (C6v).”
• Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions (2021, background): “[13] Bohm-Jung Yang and Naoto Nagaosa, “Classification of stable three-dimensional dirac”
• Topological Semimetals from First Principles (2018, background): “Yang and Nagaosa have systematically considered such accidental band crossings and classified the rotation symmetry-protected Dirac semimetals, finding that n-fold rotations Cn with n = 3, 4, 6 can stabilize band inversion induced Dirac points (66).”
• Experimental Tests of the Chiral Anomaly Magnetoresistance in the Dirac-Weyl Semimetals Na3Bi and GdPtBi (2018, background): “A crucial step in the search for 3D Dirac states was the realization that inclusion of point group symmetry [with time-reversal (TR) symmetry and inversion symmetry] allows Dirac nodes to be protected anywhere along symmetry axes, instead of being pinned to TR-invariant momenta on the Brillouin zone”
• Discovery of a Weyl fermion semimetal and topological Fermi arcs (2015, background): “d bulk Weyl nodes (26), which in this case is . Therefore, this property distinguishes the crescent Fermi arcs not only from any closed contour but also from the double Fermi arcs in Dirac semimetals (27, 28) because the bulk Dirac nodes do not carry any net chiral charges (26). After observing the ”