Nexus fermions in topological symmorphic crystalline metals

Chang, Guoqing; Xu, Su-Yang; Huang, Shin-Ming; Sanchez, Daniel S.; Hsu, Chuang-Han; Bian, Guang; Yu, Zhi-Ming; Belopolski, Ilya; Alidoust, Nasser; Zheng, Hao; Chang, Tay-Rong; Jeng, Horng-Tay; Yang, Shengyuan A.; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

doi:10.1038/s41598-017-01523-8

Title: Nexus fermions in topological symmorphic crystalline metals

Journal Article · Wed May 10 00:00:00 EDT 2017 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-017-01523-8· OSTI ID:1423565

^[1]; Xu, Su-Yang ^[2];

^[3]; Sanchez, Daniel S. ^[2];

^[1];

^[2]; Yu, Zhi-Ming ^[4]; Belopolski, Ilya ^[2]; Alidoust, Nasser ^[2];

^[2]; Chang, Tay-Rong ^[5]; Jeng, Horng-Tay ^[6];

^[7];

^[8]; Lin, Hsin ^[1];

^[2]

National Univ. of Singapore (Singapore). Centre for Advanced 2D Materials and Graphene Research Centre and Dept. of Physics
Princeton Univ., NJ (United States). Dept. of Physics and Lab. for Topological Quantum Matter and Spectroscopy
National Sun Yat-sen Univ., Kaohsiung (Taiwan). Dept. of Physics
Beijing Inst. of Technology, Beijing (China). School of Physics; Singapore Univ. of Technology and Design (Singapore). Research Lab. for Quantum Materials
National Tsing Hua Univ., Hsinchu (Taiwan). Dept. of Physics
National Tsing Hua Univ., Hsinchu (Taiwan). Dept. of Physics; Academia Sinica, Taipei (Taiwan). Inst. of Physics
Singapore Univ. of Technology and Design (Singapore). Research Lab. for Quantum Materials
Princeton Univ., NJ (United States). Princeton Center for Theoretical Science; Univ. of Zurich (Switzerland). Dept. of Physics

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. It has been well-established that the known TMs can be classified by the dimensionality of the topologically protected band degeneracies. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM that goes beyond the above paradigms. It shows an exotic configuration of degeneracies without a well-defined dimensionality. Specifically, it consists of 0D nexus with triple-degeneracy that interconnects 1D lines with double-degeneracy. We show that, because of the novel form of band crossing, the new TM cannot be described by the established results that characterize the topology of the Dirac and Weyl nodes. Moreover, triply-degenerate nodes realize emergent fermionic quasiparticles not present in relativistic quantum field theory. We present materials candidates. Thus, our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National University of Singapore (Singapore); Singapore National Science Foundation; National Science Council (NSC) (Taiwan); National Center for High-performance Computing (NCHC) (Taiwan); National Center for Theoretical Sciences (NCTS) (Taiwan); National Energy Research Scientific Computing Center (NERSC); Gordon and Betty Moore Foundation

Grant/Contract Number:: FG02-05ER46200; NRFNRFF2013- 03; FG02-07ER46352; AC02-05CH11231; GBMF4547

OSTI ID:: 1423565

Journal Information:: Scientific Reports, Vol. 7, Issue 1; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 110 works

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References (43)

The Crystal Structure of WC Type ZrTe. Advantages in Chemical Bonding as Contrasted to NiAs Type ZrTe Örlygsson, Gissur; Harbrecht, Bernd Zeitschrift für Naturforschung B, Vol. 54, Issue 9 https://doi.org/10.1515/znb-1999-0906	journal	September 1999
Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya Nature Physics, Vol. 11, Issue 9 https://doi.org/10.1038/nphys3437	journal	August 2015
Classification of stable three-dimensional Dirac semimetals with nontrivial topology Yang, Bohm-Jung; Nagaosa, Naoto Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5898	journal	September 2014
Experimental observation of Weyl points Lu, L.; Wang, Z.; Ye, D. Science, Vol. 349, Issue 6248 https://doi.org/10.1126/science.aaa9273	journal	July 2015
The tungsten carbide and nickel arsenide structures Schönberg, Nils Acta Metallurgica, Vol. 2, Issue 3 https://doi.org/10.1016/0001-6160(54)90062-0	journal	May 1954
Type-II Weyl Semimetals Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun arXiv https://doi.org/10.48550/arxiv.1507.01603	text	January 2015
Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal Zhang, Cheng-Long; Xu, Su-Yang; Belopolski, Ilya Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10735	journal	February 2016
Notizen: Hochdruckreaktionen von CuAlS2 und CuAlSe2 / High Pressure Reactions of CuAlS2 and CuAlSe2 Range, Klaus-Jürgen; Engert, Gerd; Zabel, Manfred Zeitschrift für Naturforschung B, Vol. 29, Issue 11-12 https://doi.org/10.1515/znb-1974-11-1224	journal	December 1974
First-principles study of ground-state properties and phase stability of vanadium nitrides Ravi, Chinnappan Calphad, Vol. 33, Issue 3 https://doi.org/10.1016/j.calphad.2009.03.001	journal	September 2009
Reciprocal-space and real-space neutron investigation of nanostructured Mo2C and WC Page, Katharine; Li, Jun; Savinelli, Robert Solid State Sciences, Vol. 10, Issue 11 https://doi.org/10.1016/j.solidstatesciences.2008.03.018	journal	November 2008
Kristallstruktur von AuCd.r Alasafi, K. M.; Schubert, K. Journal of the Less Common Metals, Vol. 55, Issue 1 https://doi.org/10.1016/0022-5088(77)90255-7	journal	September 1977
Quantum spin-valley Hall effect in AB-stacked bilayer silicene Lee, Kyu Won; Lee, Cheol Eui Scientific Reports, Vol. 9, Issue 1 https://doi.org/10.1038/s41598-019-55927-9	journal	December 2019
The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal Nielsen, H. B.; Ninomiya, Masao Physics Letters B, Vol. 130, Issue 6 https://doi.org/10.1016/0370-2693(83)91529-0	journal	November 1983
Time-reversal-invariant topological superconductivity in doped Weyl semimetals Hosur, Pavan; Dai, Xi; Fang, Zhong Physical Review B, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevB.90.045130	journal	July 2014
A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8373	journal	June 2015
Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs Xu, Su-Yang; Belopolski, Ilya; Alidoust, Nasser arXiv https://doi.org/10.48550/arxiv.1502.03807	text	January 2015
Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals Kargarian, Mehdi; Randeria, Mohit; Trivedi, Nandini Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep12683	journal	August 2015
Probing unconventional superconductivity in inversion-symmetric doped Weyl semimetal Kim, Youngseok; Park, Moon Jip; Gilbert, Matthew J. Physical Review B, Vol. 93, Issue 21 https://doi.org/10.1103/PhysRevB.93.214511	journal	June 2016
Synthesis and properties of two novel line phases that contain linear scandium chains, lithium scandium iodide (LiScI3) and sodium scandium iodide (Na0.5ScI3) Lachgar, Abdessedek.; Dudis, Douglas S.; Dorhout, Peter K. Inorganic Chemistry, Vol. 30, Issue 17 https://doi.org/10.1021/ic00017a019	journal	August 1991
Observation of Fermi arc surface states in a topological metal Xu, S. -Y.; Liu, C.; Kushwaha, S. K. Science, Vol. 347, Issue 6219 https://doi.org/10.1126/science.1256742	journal	December 2014
The electronic properties of bilayer graphene McCann, Edward; Koshino, Mikito Reports on Progress in Physics, Vol. 76, Issue 5 https://doi.org/10.1088/0034-4885/76/5/056503	journal	April 2013
Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks Hasan, M. Zahid; Xu, Su-Yang; Bian, Guang Physica Scripta, Vol. T164 https://doi.org/10.1088/0031-8949/2015/T164/014001	journal	September 2015
Evidence for the chiral anomaly in the Dirac semimetal Na3Bi Xiong, J.; Kushwaha, S. K.; Liang, T. Science, Vol. 350, Issue 6259 https://doi.org/10.1126/science.aac6089	journal	September 2015
Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl Fermion semimetal Zhang, Chenglong; Xu, Su-Yang; Belopolski, Ilya arXiv https://doi.org/10.48550/arxiv.1601.04208	text	January 2016
Predicted Unusual Magnetoresponse in Type-II Weyl Semimetals Yu, Zhi-Ming; Yao, Yugui; Yang, Shengyuan A. Physical Review Letters, Vol. 117, Issue 7 https://doi.org/10.1103/PhysRevLett.117.077202	journal	August 2016
Type-II Weyl semimetals Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun Nature, Vol. 527, Issue 7579 https://doi.org/10.1038/nature15768	journal	November 2015
Notizen: Darstellung und Struktur der Phase Li2Sb / Preparation and Crystal Structure of Li2Sb Müller, Wiking Zeitschrift für Naturforschung B, Vol. 32, Issue 3 https://doi.org/10.1515/znb-1977-0326	journal	March 1977
Double Dirac Semimetals in Three Dimensions Wieder, Benjamin J.; Kim, Youngkuk; Rappe, A. M. Physical Review Letters, Vol. 116, Issue 18 https://doi.org/10.1103/PhysRevLett.116.186402	journal	May 2016
Discovery of a Weyl fermion semimetal and topological Fermi arcs Xu, S. -Y.; Belopolski, I.; Alidoust, N. Science, Vol. 349, Issue 6248 https://doi.org/10.1126/science.aaa9297	journal	July 2015
Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals Potter, Andrew C.; Kimchi, Itamar; Vishwanath, Ashvin Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6161	journal	October 2014
On the crystal structure of the nitrides of silicon and germanium Ruddlesden, S. N.; Popper, P. Acta Crystallographica, Vol. 11, Issue 7 https://doi.org/10.1107/S0365110X58001304	journal	July 1958
Nexus and Dirac lines in topological materials Heikkila, T. T.; Volovik, G. E. arXiv https://doi.org/10.48550/arxiv.1505.03277	text	January 2015
Berry phase in Magnetic Superconductors Murakami, Shuichi; Nagaosa, Naoto arXiv https://doi.org/10.48550/arxiv.cond-mat/0209001	text	January 2002
Time-reversal invariant topological superconductivity in doped Weyl semimetals Hosur, Pavan; Dai, Xi; Fang, Zhong arXiv https://doi.org/10.48550/arxiv.1405.4299	text	January 2014
Nexus and Dirac lines in topological materials Heikkilä, T. T.; Volovik, G. E. New Journal of Physics, Vol. 17, Issue 9 https://doi.org/10.1088/1367-2630/17/9/093019	journal	September 2015
The electronic properties of bilayer graphene McCann, Edward; Koshino, Mikito arXiv https://doi.org/10.48550/arxiv.1205.6953	text	January 2012
X-Ray, infrared, and magnetic studies of α- and β-ruthenium trichloride Fletcher, J. M.; Gardner, W. E.; Fox, A. C. J. Chem. Soc. A, Vol. 0, Issue 0 https://doi.org/10.1039/J19670001038	journal	January 1967
Berry Phase in Magnetic Superconductors Murakami, Shuichi; Nagaosa, Naoto Physical Review Letters, Vol. 90, Issue 5 https://doi.org/10.1103/physrevlett.90.057002	journal	February 2003
A reinvestigation of the structure of ε-tantalum nitride Christensen, A. N.; Lebech, B. Acta Crystallographica Section B, Vol. 34, Issue 1 https://doi.org/10.1107/s0567740878002733	journal	January 1978
Classification of stable three-dimensional Dirac semimetals with nontrivial topology Yang, Bohm-Jung; Nagaosa, Naoto arXiv https://doi.org/10.48550/arxiv.1404.0754	text	January 2014
Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya arXiv https://doi.org/10.48550/arxiv.1501.00755	text	January 2015
Experimental observation of Weyl points Lu, Ling; Wang, Zhiyu; Ye, Dexin arXiv https://doi.org/10.48550/arxiv.1502.03438	text	January 2015
Discovery of a Weyl Fermion semimetal state in NbAs Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya arXiv https://doi.org/10.48550/arxiv.1504.01350	text	January 2015

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