Weyl and Nodal Ring Magnons in Three-Dimensional Honeycomb Lattices
Kang-Kang Li1,2** , Jiang-Ping Hu1,2,3
1 Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 1001902 School of Physics, University of Chinese Academy of Sciences, Beijing 1000493 Collaborative Innovation Center of Quantum Matter, Beijing 100871
Abstract :We study the topological properties of magnon excitations in a wide class of three-dimensional (3D) honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The nodal ring degeneracy can be lifted by the Dzyaloshinskii–Moriya interactions to form two Weyl points with opposite charges. We explicitly discuss these physics in the simplest 3D honeycomb lattice and the hyperhoneycomb lattice, and show drumhead and arc surface states in the nodal ring and Weyl phases, respectively, due to the bulk-boundary correspondence.
收稿日期: 2017-04-17
出版日期: 2017-06-23
:
75.30.Ds
(Spin waves)
75.50.Dd
(Nonmetallic ferromagnetic materials)
75.70.Rf
(Surface magnetism)
75.90.+w
(Other topics in magnetic properties and materials)
[1] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801 [2] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802 [3] Wang J T et al 2016 Phys. Rev. Lett. 116 195501 [4] Takayama T et al 2015 Phys. Rev. Lett. 114 077202 [5] Biffin A et al 2014 Phys. Rev. B 90 205116 [6] Modic K A et al 2014 Nat. Commun. 5 4203 [7] Lee E K H et al 2014 Phys. Rev. B 89 205132 [8] Lee E K H et al 2014 Phys. Rev. B 89 045117 [9] Mullen K et al 2015 Phys. Rev. Lett. 115 026403 [10] Nasu J et al 2014 Phys. Rev. B 89 115125 [11] Nasu J et al 2015 J. Phys.: Conf. Ser. 592 012115 [12] Kimchi I et al 2014 Phys. Rev. B 90 205126 [13] Lee S B et al 2014 Phys. Rev. B 89 014424 [14] Hermanns M, OBrien K and Trebst S 2015 Phys. Rev. Lett. 114 157202 [15] Robert Schaffer, Lee E K H, Lu Y M and Kim Y B 2015 Phys. Rev. Lett. 114 116803 [16] Mandal S and Surendran N 2009 Phys. Rev. B 79 024426 [17] Phillips M and Aji V 2014 Phys. Rev. B 90 115111 [18] Xie L S, Schoop L M, Seibel E M, Gibson Q D, Xie W and Cava R J 2015 APL Mater. 3 083602 [19] Yu R, Weng H, Fang Z, Dai X and Hu X 2015 Phys. Rev. Lett. 115 036807 [20] Kim Y, Wieder B J, Kane C L and Rappe A M 2015 Phys. Rev. Lett. 115 036806 [21] Yamakage A, Yamakawa Y, Tanaka Y and Okamoto Y 2016 J. Phys. Soc. Jpn. 85 013708 [22] Weng H, Liang Y, Xu Q, Yu R, Fang Z, Dai X and Kawazoe Y 2015 Phys. Rev. B 92 045108 [23] Motohiko E 2016 Phys. Rev. Lett. 116 127202 [24] Roldán-Molina A, Nunez A S and Fernández-Rossier J 2016 New J. Phys. 18 045015 [25] Zhang L F, Ren J, Wang J S and Li B W 2013 Phys. Rev. B 87 144101 [26] Ryuichi S, Ryo M, Shuichi M and Jun-ichiro O 2013 Phys. Rev. B 87 174427 [27] Kim S K, Héctor O, Ricardo Z and Yaroslav T 2016 Phys. Rev. Lett. 117 227201 [28] Owerre S A 2016 J. Phys.: Condens. Matter 28 386001 [29] Owerre S A 2016 Phys. Rev. B 94 094405 [30] Li F Y, Li Y D, Kim Y B, Leon B, Yu Y and Chen G 2016 Nat. Commun. 7 12691 [31] Alexander M, Jürgen H and Ingrid M 2016 Phys. Rev. Lett. 117 157204 [32] Alexander M, Jürgen H and Ingrid M 2017 Phys. Rev. B 95 014418 [33] Li K K, Li C Y, Hu J P, Li Y and Fang C 2017 arXiv:1703.08545 [34] Hatsugai Y 1993 Phys. Rev. B 48 11851 [35] Hatsugai Y 1993 Phys. Rev. Lett. 71 3697 [36] Holstein T and Primakoff H 1940 Phys. Rev. 58 1098
[1]
. [J]. 中国物理快报, 2023, 40(2): 27502-.
[2]
. [J]. 中国物理快报, 2023, 40(2): 29902-.
[3]
. [J]. 中国物理快报, 2022, 39(12): 127501-.
[4]
. [J]. 中国物理快报, 2022, 39(5): 57501-057501.
[5]
. [J]. 中国物理快报, 2022, 39(2): 27501-027501.
[6]
. [J]. 中国物理快报, 2021, 38(11): 117101-.
[7]
. [J]. 中国物理快报, 2021, 38(4): 47501-.
[8]
. [J]. 中国物理快报, 2020, 37(10): 107502-.
[9]
. [J]. 中国物理快报, 2020, 37(7): 77501-.
[10]
. [J]. 中国物理快报, 2016, 33(07): 77503-077503.
[11]
. [J]. 中国物理快报, 2014, 31(1): 17502-017502.
[12]
DONG Zhan-Hai. 120° Ordered Phase of Triangular Lattice Antiferromagnetic Heisenberg Model with Long Range Couplings [J]. 中国物理快报, 2009, 26(10): 107503-107503.
[13]
LU Feng;SONG Yun;CHEN Dong-Meng;ZOU Liang-Jian. Orbital Order and Orbital Excitations in Degenerate Itinerant Electron Systems [J]. 中国物理快报, 2009, 26(9): 97501-097501.
[14]
WU Bao-Jian;GAO Xiang. Magnetostatic-Wave-Based Magneto-Optic Pulse Compression by Control of Phase Mismatching [J]. 中国物理快报, 2008, 25(11): 4006-4008.
[15]
WU Bao-Jian;QIU Kun. Magneto-Optic Coupling Theory for Guided Optical Waves and Magnetostatic Waves Using an Arbitrarily Tilted Bias Magnetic Field [J]. 中国物理快报, 2005, 22(9): 2396-2399.