Doubling theorem and boundary states of five-dimensional Weyl semimetal

Chen, Jing-Yuan; Lian, Biao; Zhang, Shou-Cheng

doi:10.1103/physrevb.100.075112

Title: Doubling theorem and boundary states of five-dimensional Weyl semimetal

Journal Article · Tue Aug 06 00:00:00 EDT 2019 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.100.075112· OSTI ID:1560630

^[1]; Lian, Biao ^[2]; Zhang, Shou-Cheng ^[3]

Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
Princeton Univ., NJ (United States). Princeton Center for Theoretical Science
Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics, and Stanford Center for Topological Quantum Physics

We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have nontrivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated doubling theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: GBMF4302; AC02-76SF00515

OSTI ID:: 1560630

Alternate ID(s):: OSTI ID: 1557345

Journal Information:: Physical Review B, Vol. 100, Issue 7; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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References (57)

Five-dimensional generalization of the topological Weyl semimetal Lian, Biao; Zhang, Shou-Cheng Physical Review B, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevB.94.041105	journal	July 2016
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Differential Topology of Semimetals Mathai, Varghese; Thiang, Guo Chuan Communications in Mathematical Physics, Vol. 355, Issue 2 https://doi.org/10.1007/s00220-017-2965-z	journal	July 2017
Band Topology and Linking Structure of Nodal Line Semimetals with $Z_{2}$ Monopole Charges Ahn, Junyeong; Kim, Dongwook; Kim, Youngkuk Physical Review Letters, Vol. 121, Issue 10 https://doi.org/10.1103/PhysRevLett.121.106403	journal	September 2018
Weyl electrons kiss Balents, Leon Physics, Vol. 4 https://doi.org/10.1103/Physics.4.36	journal	May 2011
Topological Classification and Stability of Fermi Surfaces Zhao, Y. X.; Wang, Z. D. Physical Review Letters, Vol. 110, Issue 24 https://doi.org/10.1103/PhysRevLett.110.240404	journal	June 2013
Chern-Simons theory and Wilson loops in the Brillouin zone Lian, Biao; Vafa, Cumrun; Vafa, Farzan Physical Review B, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevB.95.094512	journal	March 2017
Synthetic Gauge Fields in Synthetic Dimensions Celi, A.; Massignan, P.; Ruseckas, J. Physical Review Letters, Vol. 112, Issue 4 https://doi.org/10.1103/PhysRevLett.112.043001	journal	January 2014
Topological surface states in nodal superconductors Schnyder, Andreas P.; Brydon, Philip M. R. Journal of Physics: Condensed Matter, Vol. 27, Issue 24 https://doi.org/10.1088/0953-8984/27/24/243201	journal	May 2015
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
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 185, Issue 1 https://doi.org/10.1016/0550-3213(81)90361-8	journal	July 1981
Protected boundary states in gapless topological phases Matsuura, Shunji; Chang, Po-Yao; Schnyder, Andreas P. New Journal of Physics, Vol. 15, Issue 6 https://doi.org/10.1088/1367-2630/15/6/065001	journal	June 2013
Stability of Fermi Surfaces and $K$ Theory Hořava, Petr Physical Review Letters, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevLett.95.016405	journal	June 2005
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Momentum space topological invariants for the 4 D relativistic vacua with mass gap Zubkov, M. A.; Volovik, G. E. Nuclear Physics B, Vol. 860, Issue 2 https://doi.org/10.1016/j.nuclphysb.2012.03.002	journal	July 2012
Classification of reflection-symmetry-protected topological semimetals and nodal superconductors Chiu, Ching-Kai; Schnyder, Andreas P. Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.205136	journal	November 2014
Topological semimetals with a double-helix nodal link Chen, Wei; Lu, Hai-Zhou; Hou, Jing-Min Physical Review B, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevB.96.041102	journal	July 2017
Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon's knot, trefoil knot, and other linked nodal varieties Ezawa, Motohiko Physical Review B, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevB.96.041202	journal	July 2017
Nodal-link semimetals Yan, Zhongbo; Bi, Ren; Shen, Huitao Physical Review B, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevB.96.041103	journal	July 2017
Quantal Phase Factors Accompanying Adiabatic Changes Berry, M. V. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802 https://doi.org/10.1098/rspa.1984.0023	journal	March 1984
Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides Weng, Hongming; Fang, Chen; Fang, Zhong Physical Review X, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevX.5.011029	journal	March 2015
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
Weyl semimetals from noncentrosymmetric topological insulators Liu, Jianpeng; Vanderbilt, David Physical Review B, Vol. 90, Issue 15 https://doi.org/10.1103/PhysRevB.90.155316	journal	October 2014
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 98, Issue 10, Article No. 106803 https://doi.org/10.1103/PhysRevLett.98.106803	journal	March 2007
Weyl semimetal and topological phase transition in five dimensions Lian, Biao; Zhang, Shou-Cheng Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/PhysRevB.95.235106	journal	June 2017
Topological response in Weyl semimetals and the chiral anomaly Zyuzin, A. A.; Burkov, A. A. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115133	journal	September 2012
MANIFOLD-SPLITTING REGULARIZATION, SELF-LINKING, TWISTING, WRITHING NUMBERS OF SPACE-TIME RIBBONS and POLYAKOV’S PROOF OF FERMI-BOSE TRANSMUTATIONS Tze, Chia-Hsiung International Journal of Modern Physics A, Vol. 03, Issue 08 https://doi.org/10.1142/S0217751X88000825	journal	August 1988
Chiral gauge field and axial anomaly in a Weyl semimetal Liu, Chao-Xing; Ye, Peng; Qi, Xiao-Liang Physical Review B, Vol. 87, Issue 23 https://doi.org/10.1103/PhysRevB.87.235306	journal	June 2013
A Four-Dimensional Generalization of the Quantum Hall Effect Zhang, S. -C. Science, Vol. 294, Issue 5543 https://doi.org/10.1126/science.294.5543.823	journal	October 2001
Chiral anomaly and classical negative magnetoresistance of Weyl metals Son, D. T.; Spivak, B. Z. Physical Review B, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevB.88.104412	journal	September 2013
Topological Hopf and Chain Link Semimetal States and Their Application to ${Co}_{2} Mn G a$ Chang, Guoqing; Xu, Su-Yang; Zhou, Xiaoting Physical Review Letters, Vol. 119, Issue 15 https://doi.org/10.1103/PhysRevLett.119.156401	journal	October 2017
Topological field theory of time-reversal invariant insulators Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 78, Issue 19, Article No. 195424 https://doi.org/10.1103/PhysRevB.78.195424	journal	November 2008
Double Helix Nodal Line Superconductor Sun, Xiao-Qi; Lian, Biao; Zhang, Shou-Cheng Physical Review Letters, Vol. 119, Issue 14 https://doi.org/10.1103/PhysRevLett.119.147001	journal	October 2017
Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase New Journal of Physics, Vol. 9, Issue 9 https://doi.org/10.1088/1367-2630/9/9/356	journal	September 2007
Noncentrosymmetric Superconductors Yip, Sungkit Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133912	journal	March 2014
Global topology of Weyl semimetals and Fermi arcs Mathai, Varghese; Thiang, Guo Chuan Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 11 https://doi.org/10.1088/1751-8121/aa59b2	journal	February 2017
Absence of neutrinos on a lattice Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 193, Issue 1 https://doi.org/10.1016/0550-3213(81)90524-1	journal	December 1981
Fermi-Bose Transmutations Induced by Gauge Fields Polyakov, A. M. Modern Physics Letters A, Vol. 03, Issue 03 https://doi.org/10.1142/S0217732388000398	journal	February 1988
Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin Physical Review B, Vol. 83, Issue 20 https://doi.org/10.1103/PhysRevB.83.205101	journal	May 2011
Topological insulators and superconductors: tenfold way and dimensional hierarchy Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira New Journal of Physics, Vol. 12, Issue 6 https://doi.org/10.1088/1367-2630/12/6/065010	journal	June 2010
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
Absence of neutrinos on a lattice: Proof by homotopy theory Nielsen, H. B.; Ninomiya, M. Nuclear Physics B, Vol. 195, Issue 3, p. 541-542 https://doi.org/10.1016/0550-3213(82)90011-6	journal	February 1982
Fermi-Bose Transmutations Induced by Gauge Fields Polyakov, A. M. Modern Physics Letters B, Vol. 01, Issue 11n12 https://doi.org/10.1142/s0217984988001557	journal	February 1988
Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase Murakami, Shuichi New Journal of Physics, Vol. 10, Issue 2 https://doi.org/10.1088/1367-2630/10/2/029802	journal	February 2008
Topological Field Theory of Time-Reversal Invariant Insulators Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng arXiv https://doi.org/10.48550/arxiv.0802.3537	text	January 2008
Synthetic gauge fields in synthetic dimensions Celi, A.; Massignan, P.; Ruseckas, J. arXiv https://doi.org/10.48550/arxiv.1307.8349	text	January 2013
Classification of reflection symmetry protected topological semimetals and nodal superconductors Chiu, Ching-Kai; Schnyder, Andreas P. arXiv https://doi.org/10.48550/arxiv.1408.4642	text	January 2014
Weyl semimetals from noncentrosymmetric topological insulators Liu, Jianpeng; Vanderbilt, David arXiv https://doi.org/10.48550/arxiv.1409.6399	text	January 2014
Weyl semimetal phase in non-centrosymmetric transition metal monophosphides Weng, Hongming; Fang, Chen; Fang, Zhong arXiv https://doi.org/10.48550/arxiv.1501.00060	text	January 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
A Five Dimensional Generalization of the Topological Weyl Semimetal Lian, Biao; Zhang, Shou-Cheng arXiv https://doi.org/10.48550/arxiv.1604.07459	text	January 2016
Chern-Simons Theory and Wilson Loops in the Brillouin Zone Lian, Biao; Vafa, Cumrun; Vafa, Farzan arXiv https://doi.org/10.48550/arxiv.1610.05810	text	January 2016
Weyl Semimetal and Topological Phase Transition in Five Dimensions Lian, Biao; Zhang, Shou-Cheng arXiv https://doi.org/10.48550/arxiv.1702.07982	text	January 2017
Topological semimetals with double-helix nodal link Chen, Wei; Lu, Hai-Zhou; Hou, Jing-Min arXiv https://doi.org/10.48550/arxiv.1703.10886	text	January 2017
Nodal-link semimetals Yan, Zhongbo; Bi, Ren; Shen, Huitao arXiv https://doi.org/10.48550/arxiv.1704.00655	text	January 2017
Nodal-knot semimetals Bi, Ren; Yan, Zhongbo; Lu, Ling arXiv https://doi.org/10.48550/arxiv.1704.06849	text	January 2017
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0607699	text	January 2006