**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 3DGraphene 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 et.al., 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(S |
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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) |
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Topology of the electronic structure of a crystal is manifested in its surface states. In topological insulators B |
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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 Cd |
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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). |
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Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd _{3}As_{2}. Published in M. Neupane, S.-Y. Xu, R. Sankar, et al., Nature Commun. 5, 4786 (2014). |
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Observation of a bulk 3D Dirac multiplet, Lifshitz transition, and nestled spin states in Na _{3}Bi. Published in S.-Y. Xu, C. Liu, S. K. Kushwaha, et al., arXiv:1312.7624 (2013). |
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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). |
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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). |
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Ultraquantum magnetoresistance in single-crystalline Ag2Se. Published in C. Zhang, H. Li, T.-R. Chang, et al., arXiv:1502.02324 (2015). |
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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). |
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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) |
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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) |
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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) |
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Topological Hopf-link semimetals (2017) | ||

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