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Nature News (Homepage, July 2017) : ..Topology Reshaping Physics

Ideas borrowed from graphene and topological insulators allow one to generalize to talk about a 3D Dirac Semimetal and there can be many different types of 2D and 3D Dirac Semimetals with their experimental realizations in non-Bi or Bi-based spin-orbit materials :
For recent developments in topological materials see talks at
KITP program on topological materials..
and Inst. for Advanced Study (IAS, Princeton) School on Topological Matter Reading List

FOCUS issue on "Topological Semimetals" by Nature Materials (Collection of Articles)

Dirac Semimetals in 2D and 3D

Graphene is an example of 2D Dirac semimetal. Another example of Dirac Semimetal is the surface states of topological insulators while Fermi level is tuned to lie at the Dirac point inside the bulk gap of the semiconductor (see, "A tunable topological insulator in the spin helical Dirac transport regime"; Hsieh, Xia, Wray, Nature 460, 1101 (2009)).

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S1-xSex)2, in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum–locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.


3D Dirac semimetals appear at the critical point between a conventional insulator and a 3D topological insulator (see papers below)

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator.
S.-Y. Xu, Y. Xia, L. A. Wray et al.;
Science 332, 560 (2011)


Topology of the electronic structure of a crystal is manifested in its surface states. In topological insulators B1-xSbx and Bi2Se3 or topological crystalline insulators such as the Pb1-xSnxTe(Se), the bulk has a full insulating energy gap, whereas the surface possesses an odd or even number of spin polarized surface or edge states. It is the 2D surface state or 1D edge state properties that carry the signature of topology, which is the key focus of experiments on all topological states of matter. Very recently, the possibility of realizing new topological states beyond insulators, such as metals or semimetals, has attracted much attention. Unlike insulators, semimetals are materials, whose bulk conduction and valence bands have small but finite overlap. Thus there does not exist a full band gap irrespective of the choice of the chemical potential. Since the definition of bulk topological number for topological insulators strictly requires a full bulk energy gap, a topological state that might exist in a semimetal should be fundamentally distinct from the topological states studied in insulating materials.

Recently, a distinct topological state has been proposed in metals or semimetals whose spin-orbit band structure features three-dimensional Dirac quasiparticles. We use angle-resolved photoemission spectroscopy to experimentally observe a pair of spin-polarized Fermi arc surface states on the surface of the Dirac semimetal Na3Bi at its native chemical potential. Our systematic results collectively identify a topological phase in a gapless material. The observed Fermi arc surface states open research frontiers in fundamental physics and possibly in spintronics.


Symmetry-broken three-dimensional (3D) topological Dirac semimetal systems with strong spin-orbit coupling can host many exotic Hall-like phenomena and Weyl fermion quantum transport. Using high-resolution angle-resolved photoemission spectroscopy, we performed systematic electronic structure studies on Cd3As2 and Na3Bi which have been predicted to be the parent material, from which many unusual topological phases can be derived. We experimentally verified their 3D nature.


Observation of Fermi Arc Surface States in a Topological Metal.
Published in S.-Y. Xu, C. Liu, S. Kushwaha, et al., Science 347, 294 (2014).

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2.
Published in M. Neupane, S.-Y. Xu, R. Sankar, et al., Nature Commun. 5, 4786 (2014).

Observation of a bulk 3D Dirac multiplet, Lifshitz transition, and nestled spin states in Na3Bi.
Published in S.-Y. Xu, C. Liu, S. K. Kushwaha, et al., arXiv:1312.7624 (2013).

Lifshitz transition and van Hove singularity in a 3D Topological Dirac Semimetal.
Published in S.-Y. Xu, C. Liu, I. Belopolski, et al., arXiv:1502.06917 (2015).

Bulk crystal growth and electronic characterization of the 3D Dirac Semimetal Na3Bi.
Published in S. K. Kushwaha, J. W. Krizan, B. E. Feldman, et al., Phys. Rev. B 92, 075115 (2015).

Ultraquantum magnetoresistance in single-crystalline Ag2Se.
Published in C. Zhang, H. Li, T.-R. Chang, et al., arXiv:1502.02324 (2015).

Surface Versus Bulk Dirac States Tuning in a Three-Dimensional Topological Dirac Semimetal.
Published in M. Neupane, S.-Y. Xu, N. Alidoust, et al., Phys. Rev. B 91, 241114(R) (2015).

A strongly robust type II topological Weyl fermion semimetal state in Ta3S2

Guoqing Chang, Su-Yang Xu, Daniel S. Sanchez, Shin-Ming Huang, Chi-Cheng Lee, Tay-Rong Chang, Guang Bian, Hao Zheng, Ilya Belopolski, Nasser Alidoust, Horng-Tay Jeng, Arun Bansil, Hsin Lin, and M. Zahid Hasan
Science Adv. e1600295 (2016)

Type-II Symmetry Protected Topological Dirac Semimetals

Tay-Rong Chang, Su-Yang Xu, Daniel S. Sanchez, Wei-Feng Tsai, Shin-Ming Huang, Guoqing Chang, Chuang-Han Hsu, Guang Bian, Ilya Belopolski, Zhi-Ming Yu, Shengyuan A. Yang, Titus Neupert, Horng-Tay Jeng, Hsin Lin, and M. Zahid Hasan
Physical Review Letters 119, 026404 (2017)

Mirror-protected Dirac fermions on Weyl Semimetal Surfaces (2017)

(Theoretical prediction and experimental observation of) "Mirror Protected Dirac Fermions on a Weyl Semimetal NbP Surface"
Hao Zheng, Guoqing Chang, Shin-Ming Huang, Cheng Guo, Xiao Zhang, Songtian Zhang, Jiaxin Yin, Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Daniel S. Sanchez, Guang Bian, Tay-Rong Chang, Titus Neupert, Horng-Tay Jeng, Shuang Jia, Hsin Lin, and M. Zahid Hasan
Phys. Rev. Lett. 119, 196403 (2017)

Topological Hopf-link semimetals (2017)

"Topological Hopf-link semimetals"
G. Chang, S.-Y. Xu,
"Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa"
Phys. Rev. Lett. 119, 156401 (2017)