| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
|
|
|
|
Inversion/Mirror Symmetry-Protected Dirac Cones in Distorted Ruby Lattices |
| Lei Sun1, Xiaoming Zhang1, Han Gao1, Jian Liu1, Feng Liu2, and Mingwen Zhao1,3* |
1School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
2Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
3Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
|
|
| Cite this article: |
|
Lei Sun, Xiaoming Zhang, Han Gao et al 2020 Chin. Phys. Lett. 37 127102 |
|
|
|
|
Abstract The exotic electronic band structures of Ruby and Star lattices, characterized by Dirac cone and nontrivial topology, offer a unique platform for the study of two-dimensional (2D) Dirac materials. In general, an ideal isotropic Dirac cone is protected by time reversal symmetry and inversion, so that its robustness against lattice distortion is not only of fundamental interest but also crucial to practical applications. Here we systematically investigate the robustness of Dirac cone in a Ruby lattice against four typical lattice distortions that break the inversion and/or mirror symmetry in the transition from Ruby to Star. Using a tight-binding approach, we show that the isotropic Dirac cones and their related topological features remain intact in the rotationally distorted lattices that preserve the inversion symmetry ($i$-Ruby lattice) or the in-plane mirror symmetry ($m$-Ruby lattice). On the other hand, the Dirac cones are gapped in the $a$- and $b$-Ruby lattices that break both these lattice symmetries or inversion. Furthermore, a rotational unitary matrix is identified to transform the original into the distorted lattice. The symmetry-protected Dirac cones were also verified in photonic crystal systems. The robust Dirac cones revealed in the non-mirror symmetric $i$-Ruby and non-centrosymmetric $m$-Ruby lattices provide a general guidance for the design of 2D Dirac materials.
|
|
|
Received: 17 September 2020
Published: 08 December 2020
|
|
| PACS: |
71.20.-b
|
(Electron density of states and band structure of crystalline solids)
|
| |
73.20.At
|
(Surface states, band structure, electron density of states)
|
| |
73.22.Gk
|
(Broken symmetry phases)
|
| |
42.70.Qs
|
(Photonic bandgap materials)
|
|
|
| Fund: Supported by the National Natural Science Foundation of China (Grant No. 11774201), and the Taishan Scholarship of Shandong Province. |
|
|
|
| [1] | Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666 |
| [2] | Yao Y, Ye F, Qi X L, Zhang S C and Fang Z 2007 Phys. Rev. B 75 041401 |
| [3] | Wang A Z, Zhao X R, Zhao M W, Zhang X M, Feng Y P and Liu F 2018 J. Phys. Chem. Lett. 9 614 |
| [4] | Hu J, Zhu Z and Wu R 2015 Nano Lett. 15 2074 |
| [5] | Qiao Z, Ren W, Chen H, Bellaiche L, Zhang Z, MacDonald A H and Niu Q 2014 Phys. Rev. Lett. 112 116404 |
| [6] | Haldane F D 1988 Phys. Rev. Lett. 61 2015 |
| [7] | Liu J, Meng S and Sun J T 2019 Nano Lett. 19 3321 |
| [8] | Liu H, Sun J T, Liu M and Meng S 2018 J. Phys. Chem. Lett. 9 6709 |
| [9] | Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801 |
| [10] | Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802 |
| [11] | Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802 |
| [12] | Sun K, Gu Z C, Katsura H and Sarma S D 2011 Phys. Rev. Lett. 106 236803 |
| [13] | Neupert T, Santos L, Chamon C and Mudry C 2011 Phys. Rev. Lett. 106 236804 |
| [14] | Jain J K and Jeon S 2005 Phys. Rev. B 72 201303 |
| [15] | Du X, Skachko I, Duerr F, Luican A and Andrei E Y 2009 Nature 462 192 |
| [16] | Read N and Green D 2000 Phys. Rev. B 61 10267 |
| [17] | Tang E, Mei J W and Wen X G 2011 Phys. Rev. Lett. 106 236802 |
| [18] | Bolotin K I, Ghahari F, Shulman M D, Stormer H L and Kim P 2009 Nature 462 196 |
| [19] | Zhang S et al. 2019 Phys. Rev. B 99 100404(R) |
| [20] | Jiang W, Kang M, Huang H, Xu H, Low T and Liu F 2019 Phys. Rev. B 99 125131 |
| [21] | Guo H M and Franz M 2009 Phys. Rev. B 80 113102 |
| [22] | Liu X Y and Yan W G 2013 Physica A 392 5615 |
| [23] | Hu X, Kargarian M and Fiete G A 2011 Phys. Rev. B 84 155116 |
| [24] | Lin K Y and Ma W J 1983 J. Phys. A 16 3895 |
| [25] | Lin K Y 1984 J. Phys. A 17 3201 |
| [26] | Chen M and Wan S 2012 J. Phys.: Condens. Matter 24 325502 |
| [27] | Owerre S A 2017 J. Phys.: Condens. Matter 29 185801 |
| [28] | Chen W C, Liu R, Wang Y F and Gong C D 2012 Phys. Rev. B 86 085311 |
| [29] | Neumann J V, Wigner W 1929 Z. Phys. 30 467 |
| [30] | Lifshitz E M and Landau L D 1981 Quantum Mechanics (Non-Relativistic Theory) 3rd edn (Oxford: Reed Educational and Professional Publishing Ltd) |
| [31] | Wang A, Zhang X and Zhao M 2014 Nanoscale 6 11157 |
| [32] | Yang B, Zhang X M, Wang A Z and Zhao M W 2019 J. Phys.: Condens. Matter 31 155001 |
| [33] | Yao Y, Kleinman L, MacDonald A H, Sinova J, Jungwirth T, Wang D S, Wang E and Niu Q 2004 Phys. Rev. Lett. 92 037204 |
| [34] | Takeda H, Takashima T and Yoshino K 2004 J. Phys.: Condens. Matter 16 6317 |
| [35] | Szameit A and Nolte S 2010 J. Phys. B 43 163001 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
