Pseudospin modes of surface acoustic wave and topologically protected sound transmission in phononic crystal

Wang Yi-He; Zhang Zhi-Wang; Cheng Ying; Liu Xiao-Jun

doi:10.7498/aps.68.20191363

Abstract

The manipulation of surface acoustic wave (SAW) in phononic crystal plays an important role in the applications of SAW. The introduction of topological acoustic theory has opened a new field for SAW in phononic crystals. Here we construct pseudospin modes of SAW and topological phase transition along the surface of phononic crystal. The local SAW propagation is realized by air cylindrical holes in honeycomb lattice arranged on rigid substrate, and the Dirac cone is formed at the K point of the first Brillouin zone. Furthermore, using the band-folding theory, double Dirac cones can be formed at the center Г_s point in the Brillouin zone of compound cell that contains six adjacent cylindrical air holes. The double Dirac cone can be broken to form two degenerated states and complete band gap by only shrinking or expanding the spacing of adjacent holes in the compound cell. It is found that the direction of energy is in a clockwise or counterclockwise direction, thus the pseudospin modes of SAW are constructed. The shrinkage-to-expansion of the compound cell leads to band inversion, and the system changes from trivial state to nontrivial state, accompanied by the phase transition. According to the bulk-boundary correspondence, the unidirectional acoustic edge states can be found at the interface between trivial system and nontrivial system. Then we can construct a topologically protected waveguide to realize the unidirectional transmission of surface waves without backscattering. This work provides a new possibility for manipulating the SAW propagating on the surface of phononic crystals and may be useful for making the acoustic functional devices based on SAW.

Keywords:

Authors and contacts

Institute of Acoustics, School of Physics, Nanjing University, Nanjing 210093, China

Corresponding author: Cheng Ying, chengying@nju.edu.cn ; Liu Xiao-Jun, liuxiaojun@nju.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303702), the National Natural Science Foundation of China (Grant Nos. 119224071, 11834008, 11874215, 11674172, 11574148), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160018)

FullText HTML : translate this paragraph

References

[1]	Ricca R L, Berger M A 1996 Phys. Today 49 28 Google Scholar
[2]	Vonklitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[3]	Thouless D J, Kohmoto M, Nightingale M P, Dennijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[4]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395 Google Scholar
[5]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[6]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[7]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[8]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[9]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[10]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[11]	Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904 Google Scholar
[12]	Raghu S, Haldane F D M 2008 Phys. Rev. A 78 033834 Google Scholar
[13]	Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2009 Nature 461 772 Google Scholar
[14]	Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2008 Phys. Rev. Lett. 100 013905 Google Scholar
[15]	Fang Y T, He H Q, Hu J X, Chen L K, Wen Z 2015 Phys. Rev. A 91 033827 Google Scholar
[16]	Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901 Google Scholar
[17]	Gao F, Xue H R, Yang Z J, Lai K F, Yu Y, Lin X, Chong Y D, Shvets G, Zhang B L 2018 Nat. Phys. 14 140 Google Scholar
[18]	Fleury R, Sounas D L, Sieck C F, Haberman M R, Alu A 2014 Science 343 516 Google Scholar
[19]	Yang Z J, Gao F, Shi X H, Lin X, Gao Z, Chong Y D, Zhang B L 2015 Phys. Rev. Lett. 114 114301 Google Scholar
[20]	Khanikaev A B, Fleury R, Mousavi S H, Alu A 2015 Nat. Commun. 6 8260 Google Scholar
[21]	Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L, Chen Y F 2015 New J. Phys. 17 053016 Google Scholar
[22]	Fleury R, Sounas D L, Alu A 2015 Phy. Rev. B 91 174306 Google Scholar
[23]	Fleury R, Khanikaev A B, Alu A 2016 Nat. Commun. 7 11744 Google Scholar
[24]	Wei Q, Tian Y, Zuo S Y, Cheng Y, Liu X J 2017 Phy. Rev. B 95 094305 Google Scholar
[25]	Zhang Z W, Wei Q, Cheng Y, Zhang T, Wu D J, Liu X J 2017 Phys. Rev. Lett. 118 084303 Google Scholar
[26]	He C, Ni X, Ge H, Sun X C, Chen Y B, Lu M H, Liu X P, Chen Y F 2016 Nat. Phys. 12 1124 Google Scholar
[27]	王健, 吴世巧, 梅军 2017 物理学报 66 224301 Google Scholar Wang J, Wu S Q, Mei J 2017 Acta Phys. Sin. 66 224301 Google Scholar
[28]	郑圣洁, 夏百战, 刘亭亭, 于德介 2017 物理学报 66 228101 Google Scholar Zheng S J, Xia B Z, Liu T T, Yu D J 2017 Acta Phys. Sin. 66 228101 Google Scholar
[29]	陈泽国, 吴莹 2017 物理学报 66 227804 Google Scholar Chen Z G, Wu Y 2017 Acta Phys. Sin. 66 227804 Google Scholar
[30]	Fan H Y, Xia B Z, Tong L, Meng S J, Yu D J 2019 Phys. Rev. Lett. 122 204301 Google Scholar
[31]	Zhang Z W, Tian Y, Cheng Y, Liu X J, Christense J 2017 Phy. Rev. B 96 241306 Google Scholar
[32]	Dai H Q, Qian M Y, Jiao J R, Xia B Z, Yu D J 2018 J. Appl. Phys. 124 175107 Google Scholar
[33]	Zhang Z W, Tian Y, Wang Y H, Gao S X, Cheng Y, Liu X J, Christensen J 2018 Adv. Mater. 30 1803229 Google Scholar
[34]	Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901 Google Scholar
[35]	Xia J P, Jia D, Sun H X, Yuan S Q, Ge Y, Si Q R, Liu X J 2018 Adv. Mater. 30 1805002 Google Scholar
[36]	Zhang Z W, Cheng Y, Liu X J, Christensen J 2019 Phy. Rev. B 99 224104 Google Scholar
[37]	Zhang Z W, Lopez M R, Cheng Y, Liu X J, Christensen J 2019 Phys. Rev. Lett. 122 195501 Google Scholar
[38]	Zhang Z W, Cheng Y, Liu X J 2018 Sci. Rep. 8 16784 Google Scholar
[39]	Zhang Z W, Tian Y, Cheng Y, Wei Q, Liu X J, Christensen J 2018 Phys. Rev. Appl. 9 034032 Google Scholar
[40]	Jia D, Sun H X, Xia J P, Yuan S Q, Liu X J, Zhang C 2018 New J. Phys. 20 093027 Google Scholar
[41]	Gao Z, Yang Z J, Gao F, Xue H R, Yang Y H, Dong J W, Zhang B L 2017 Phys. Rev. B 96 201402 Google Scholar
[42]	吴世巧 2018 博士学位论文 (广州: 华南理工大学) Wu S Q 2018 Ph. D. Dissertation(Guangzhou: South China University of Technology) (in Chinese)
[43]	Yang Y H, Gao Z, Xue H R, Zhang L, He M J, Yang Z J, Singh R, Chong Y D, Zhang B L, Chen H S 2019 Nature 565 622 Google Scholar
[44]	Ge H, Ni X, Tian Y, Gupta S K, Lu M H, Lin X, Huang W D, Chan C T, Chen Y F 2018 Phys. Rev. Appl. 10 014017 Google Scholar
[45]	He H L, Qiu C Y, Ye L P, Cai X X, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2018 Nature 560 61 Google Scholar
[46]	Yang Y H, Sun H X, Xia J P, Xue H R, Gao Z, Ge Y, Jia D, Yuan S Q, Chong Y D, Zhang B L 2019 Nat. Phys. 15 645 Google Scholar
[47]	Torrent D, Sánchez-Dehesa J 2012 Phys. Rev. Lett. 108 174301 Google Scholar
[48]	Ma C R, Gao S X, Cheng Y, Liu X J 2019 Appl. Phys. Lett. 115 053501 Google Scholar
[49]	孙晓晨 2017 博士学位论文 (南京: 南京大学) Sun X C 2017 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)

Cited By

图 1 (a)晶格在xy平面截面图及最小元胞(红色箭头)和复合胞(黄色箭头)的矢量表示; (b) 最小元胞的三维图; (c) 最小元胞第一布里渊区的能带图, 插图为晶格的第一布里渊区

Figure 1. (a) Cross section of the phononic crystal lattice in xy-plane and the vector representation of the minimum cell (red arrows) and compound cell (yellow arrows); (b) three-dimensional view of the minimum cell; (c) band structure of the first Brillouin zone of the minimum cell. The inset shows the first Brillouin zone.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 复合胞的三维图; (b) 从Bz到Bz_s的折叠机制, 红色和黄色六边形区域代表了最小元胞和复合胞的第一布里渊区, 分别用Bz和Bz_{_s}表示; (c) 复合胞第一布里渊区的能带图

Figure 2. (a) Three-dimensional view of the compound cell; (b) the folding mechanism from Bz to Bz_{_s}. Red and yellow hexagon region represents the first Brillouin region of minimum cells and compound cells, respectively represented by Bz and Bz_{_s}; (c) band structure of the compound cell.

DownLoad: Full-Size Img PowerPoint

图 3 拓扑平庸　(a) R₁ = 0.32b和非平庸(c) R₁ = 0.345b复合胞的能带图; 插图给出了带隙频率下方能流顺时针流动时, 相应晶格在Г_s点附近的声压场分布. 拓扑平庸(b)和非平庸(d) 复合胞能带图中Г_s点两个双重简并态p态和d态的声压场分布图. 黑色箭头表示能流的运动方向. 能流顺时针转动, 对应向下赝自旋态, 用红色箭头表示; 能流逆时针转动, 对应向上赝自旋态, 用蓝色箭头表示

Figure 3. Band structure of the compound cell for the case of (a) topologically trivial R₁ = 0.32b and (c) topologically nontrivial R₁ = 0.345b. The insets show the pressure field below the band gap around Г_s in corresponding lattice when the energy flow rotating clockwise. The pressure filed of the double degenerated state at Г_s point in the band structure of topologically (b) trivial and (d) nontrivial compound cell. The black arrows indicate the direction of energy flow. The energy flow rotating clockwise (anticlockwise) corresponds to the pseudospin-down state (pseudospin-up) represented by red (blue) arrow.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 条状超胞示意图(xy平面)和能带图; 条状超胞是由中间的10个拓扑非平庸复合胞和上下各5个拓扑平庸复合胞构成的三明治结构, 能带图中灰色区域为体态, 蓝线和红线表示边界态; (b) 图(a)中A点与B点的声场分布图. 中间的四张菱形彩色图分别为A点和B点的两个边界态. 黑色箭头表示表面声波能流的运动方向

Figure 4. (a) Schematic diagram and band structure of the ribbon-shaped supercell (in xy-plane). The ribbon-shaped supercell is composed of 10 topologically nontrivial compound cells sandwiched by 5 topologically trivial compound cells on both sides. The gray areas in the band diagram represent the bulk modes and the blue and red lines indicate the edge modes; (b) pressure fields of points A and B in (a). The four diamond-shaped color graphs in the middle are the edge modes of point A and B, respectively. The black arrows indicate the direction of energy flow.

DownLoad: Full-Size Img PowerPoint

图 5 频率为7630 Hz时　(a)拓扑平庸声子晶体(结构Ⅰ), (b) 受拓扑保护的直线表面波波导(结构Ⅱ), (c) 弯曲型拓扑保护表面波波导(结构Ⅲ)的声压绝对值分布; 红色菱形框内为三种结构在z = L处的xy平面上绝对值声压分布图; (d)结构Ⅰ(黑色虚线), 结构Ⅱ(红色实线)和结构Ⅲ(蓝色点划线)中的声波传输系数, 阴影部分表示复合胞超元胞带隙频率范围

Figure 5. Absolute pressure field of (a) the topologically trivial phonon crystals (Structure Ⅰ), (b) linear type topologically protected surface wave waveguide (Structure Ⅱ), (c) bending type topologically protected surface wave waveguide (Structure Ⅲ) at f = 7630 Hz. The insets in red diamonds show the absolute pressure field of the three structures at z = L in xy-plane; (d) transmission coefficient of Structure Ⅰ (black dashed line), Structure Ⅱ (red solid line) and Structure Ⅲ(blue dotted line). The shaded areas represent the gap frequency range of the compound cell.

DownLoad: Full-Size Img PowerPoint

[1]	Ricca R L, Berger M A 1996 Phys. Today 49 28 Google Scholar
[2]	Vonklitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[3]	Thouless D J, Kohmoto M, Nightingale M P, Dennijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[4]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395 Google Scholar
[5]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[6]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[7]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[8]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[9]	Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61 Google Scholar
[10]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[11]	Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904 Google Scholar
[12]	Raghu S, Haldane F D M 2008 Phys. Rev. A 78 033834 Google Scholar
[13]	Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2009 Nature 461 772 Google Scholar
[14]	Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2008 Phys. Rev. Lett. 100 013905 Google Scholar
[15]	Fang Y T, He H Q, Hu J X, Chen L K, Wen Z 2015 Phys. Rev. A 91 033827 Google Scholar
[16]	Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901 Google Scholar
[17]	Gao F, Xue H R, Yang Z J, Lai K F, Yu Y, Lin X, Chong Y D, Shvets G, Zhang B L 2018 Nat. Phys. 14 140 Google Scholar
[18]	Fleury R, Sounas D L, Sieck C F, Haberman M R, Alu A 2014 Science 343 516 Google Scholar
[19]	Yang Z J, Gao F, Shi X H, Lin X, Gao Z, Chong Y D, Zhang B L 2015 Phys. Rev. Lett. 114 114301 Google Scholar
[20]	Khanikaev A B, Fleury R, Mousavi S H, Alu A 2015 Nat. Commun. 6 8260 Google Scholar
[21]	Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L, Chen Y F 2015 New J. Phys. 17 053016 Google Scholar
[22]	Fleury R, Sounas D L, Alu A 2015 Phy. Rev. B 91 174306 Google Scholar
[23]	Fleury R, Khanikaev A B, Alu A 2016 Nat. Commun. 7 11744 Google Scholar
[24]	Wei Q, Tian Y, Zuo S Y, Cheng Y, Liu X J 2017 Phy. Rev. B 95 094305 Google Scholar
[25]	Zhang Z W, Wei Q, Cheng Y, Zhang T, Wu D J, Liu X J 2017 Phys. Rev. Lett. 118 084303 Google Scholar
[26]	He C, Ni X, Ge H, Sun X C, Chen Y B, Lu M H, Liu X P, Chen Y F 2016 Nat. Phys. 12 1124 Google Scholar
[27]	王健, 吴世巧, 梅军 2017 物理学报 66 224301 Google Scholar Wang J, Wu S Q, Mei J 2017 Acta Phys. Sin. 66 224301 Google Scholar
[28]	郑圣洁, 夏百战, 刘亭亭, 于德介 2017 物理学报 66 228101 Google Scholar Zheng S J, Xia B Z, Liu T T, Yu D J 2017 Acta Phys. Sin. 66 228101 Google Scholar
[29]	陈泽国, 吴莹 2017 物理学报 66 227804 Google Scholar Chen Z G, Wu Y 2017 Acta Phys. Sin. 66 227804 Google Scholar
[30]	Fan H Y, Xia B Z, Tong L, Meng S J, Yu D J 2019 Phys. Rev. Lett. 122 204301 Google Scholar
[31]	Zhang Z W, Tian Y, Cheng Y, Liu X J, Christense J 2017 Phy. Rev. B 96 241306 Google Scholar
[32]	Dai H Q, Qian M Y, Jiao J R, Xia B Z, Yu D J 2018 J. Appl. Phys. 124 175107 Google Scholar
[33]	Zhang Z W, Tian Y, Wang Y H, Gao S X, Cheng Y, Liu X J, Christensen J 2018 Adv. Mater. 30 1803229 Google Scholar
[34]	Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901 Google Scholar
[35]	Xia J P, Jia D, Sun H X, Yuan S Q, Ge Y, Si Q R, Liu X J 2018 Adv. Mater. 30 1805002 Google Scholar
[36]	Zhang Z W, Cheng Y, Liu X J, Christensen J 2019 Phy. Rev. B 99 224104 Google Scholar
[37]	Zhang Z W, Lopez M R, Cheng Y, Liu X J, Christensen J 2019 Phys. Rev. Lett. 122 195501 Google Scholar
[38]	Zhang Z W, Cheng Y, Liu X J 2018 Sci. Rep. 8 16784 Google Scholar
[39]	Zhang Z W, Tian Y, Cheng Y, Wei Q, Liu X J, Christensen J 2018 Phys. Rev. Appl. 9 034032 Google Scholar
[40]	Jia D, Sun H X, Xia J P, Yuan S Q, Liu X J, Zhang C 2018 New J. Phys. 20 093027 Google Scholar
[41]	Gao Z, Yang Z J, Gao F, Xue H R, Yang Y H, Dong J W, Zhang B L 2017 Phys. Rev. B 96 201402 Google Scholar
[42]	吴世巧 2018 博士学位论文 (广州: 华南理工大学) Wu S Q 2018 Ph. D. Dissertation(Guangzhou: South China University of Technology) (in Chinese)
[43]	Yang Y H, Gao Z, Xue H R, Zhang L, He M J, Yang Z J, Singh R, Chong Y D, Zhang B L, Chen H S 2019 Nature 565 622 Google Scholar
[44]	Ge H, Ni X, Tian Y, Gupta S K, Lu M H, Lin X, Huang W D, Chan C T, Chen Y F 2018 Phys. Rev. Appl. 10 014017 Google Scholar
[45]	He H L, Qiu C Y, Ye L P, Cai X X, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2018 Nature 560 61 Google Scholar
[46]	Yang Y H, Sun H X, Xia J P, Xue H R, Gao Z, Ge Y, Jia D, Yuan S Q, Chong Y D, Zhang B L 2019 Nat. Phys. 15 645 Google Scholar
[47]	Torrent D, Sánchez-Dehesa J 2012 Phys. Rev. Lett. 108 174301 Google Scholar
[48]	Ma C R, Gao S X, Cheng Y, Liu X J 2019 Appl. Phys. Lett. 115 053501 Google Scholar
[49]	孙晓晨 2017 博士学位论文 (南京: 南京大学) Sun X C 2017 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)

[1]	Lin Ji-Yan, Chen Cheng, Guo Lin-Wei, Li Yao, Lin Shu-Yu, Sun Jiao-Xia, Xu Jie. Research on acoustic control of coupled vibration system of transducers using acoustic surface and topological defect structures. Acta Physica Sinica, 2024, 73(22): 224301. doi: 10.7498/aps.73.20241199
[2]	Ji Yu-Xuan, Zhang Ming-Kai, Li Yan. Dual-band semi-Dirac cones in two-dimensional photonic crystal and zero-index material. Acta Physica Sinica, 2024, 73(18): 181101. doi: 10.7498/aps.73.20240800
[3]	Luan Jia-Qi, Zhang Ya-Jie, Chen Yu, Gao Ding-Shan, Li Pei-Li, Li Jia-Qi, Li Jia-Qi. Genetic algorithm based terahertz multifunctional reconfigurable Dirac semi-metallic coded metasurface. Acta Physica Sinica, 2024, 73(14): 144204. doi: 10.7498/aps.73.20240225
[4]	Wei Rui, Zhou Hou-Bing, Wang Si-Cheng, Ding Bing, Qiang Yun-Hua, Jia Chen-Xu, Chen Hong-Xing, Guo Song, C.M. Petrache, D. Mengoni, A. Astier, E. Dupont, Lü Bing-Feng, D. Bazzacco, A. Boso, A. Goasduff, F. Recchia, D. Testov, F. Galtarossa, G. Jaworski, D.R. Napoli, S. Riccetto, M. Siciliano, J.J. Valiente-Dobon, C. Andreoiu, F.H. Garcia, K. Ortner, K. Whitmore, A. Ataç-Nyberg, T. Bäck, B. Cederwall, E.A. Lawrie, I. Kuti, D. Sohler, T. Marchlewski, J. Srebrny, A. Tucholski. Exotic collective excitation patterns in triaxially deformed ¹³¹Ba. Acta Physica Sinica, 2024, 73(11): 112301. doi: 10.7498/aps.73.20240212
[5]	Sun Bin, Zhao Li-Chen, Liu Jie. Dirac magnetic monopoles potential in the nonlinear double-soliton interference. Acta Physica Sinica, 2023, 72(10): 100501. doi: 10.7498/aps.72.20222416
[6]	Liu Xiang-Lian, Li Kai-Zhou, Li Xiao-Qiong, Zhang Qiang. Coexistence of quantum spin and valley hall effect in two-dimensional dielectric photonic crystals. Acta Physica Sinica, 2023, 72(7): 074205. doi: 10.7498/aps.72.20221814
[7]	Li Yin-Ming, Kong Peng, Bi Ren-Gui, He Zhao-Jian, Deng Ke. Valley topological states in double-surface periodic elastic phonon crystal plates. Acta Physica Sinica, 2022, 71(24): 244302. doi: 10.7498/aps.71.20221292
[8]	Yao Hai-Yun, Yan Xin, Liang Lan-Ju, Yang Mao-Sheng, Yang Qi-Li, Lü Kai-Kai, Yao Jian-Quan. Terahertz dynamic multidimensional modulation at Dirac point based on patterned graphene/gallium nitride hybridized with metasurfaces. Acta Physica Sinica, 2022, 71(6): 068101. doi: 10.7498/aps.71.20211845
[9]	Sui Wen-Jie, Zhang Yu, Zhang Zi-Rui, Wang Xiao-Long, Zhang Hong-Fang, Shi Qiang, Yang Bing. Unidirectional propagation control of helical edge states in topological spin photonic crystals. Acta Physica Sinica, 2022, 71(19): 194101. doi: 10.7498/aps.71.20220353
[10]	Zhao Li-Li, Wu Meng-Meng, Lin Wen-Lu, Liu Yang. Contactless transport method of two-dimensional electron system studies. Acta Physica Sinica, 2022, 71(12): 127303. doi: 10.7498/aps.71.20220246
[11]	Yang Jun-Tao, Xiong Yong-Chen, Huang Hai-Ming, Luo Shi-Jun. Half-metallic magnetism and electronic structures of CrPSe₃ monolayers with multiple Dirac cones（withdraw）. Acta Physica Sinica, 2020, 69(24): 247101. doi: 10.7498/aps.69.20200960
[12]	Fang Yun-Tuan, Wang Zhang-Xin, Fan Er-Pan, Li Xiao-Xue, Wang Hong-Jin. Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states. Acta Physica Sinica, 2020, 69(18): 184101. doi: 10.7498/aps.69.20200415
[13]	Wang Yan-Lan, Li Yan. Pseudospin states and topological phase transitions in two-dimensional photonic crystals made of dielectric materials. Acta Physica Sinica, 2020, 69(9): 094206. doi: 10.7498/aps.69.20191962
[14]	Zhang Zhi-Mo, Zhang Wen-Hao, Fu Ying-Shuang. Scanning tunneling microscopy study on two-dimensional topological insulators. Acta Physica Sinica, 2019, 68(22): 226801. doi: 10.7498/aps.68.20191631
[15]	Li Chun-Xi, Shi Zhi-Xian, Zhuang Li-Yu, Ye Xue-Min. Effect of surfactants on thin film spreading under influence of surface acoustic wave. Acta Physica Sinica, 2019, 68(21): 214703. doi: 10.7498/aps.68.20190791
[16]	Shen Qing-Wei, Xu Lin, Jiang Jian-Hua. Topological phase transitions in core-shell gyromagnetic photonic crystal. Acta Physica Sinica, 2017, 66(22): 224102. doi: 10.7498/aps.66.224102
[17]	Wang Jian, Wu Shi-Qiao, Mei Jun. Topological phase transitions caused by a simple rotational operation in two-dimensional acoustic crystals. Acta Physica Sinica, 2017, 66(22): 224301. doi: 10.7498/aps.66.224301
[18]	Huang Xue-Qin, Chan Che-Ting. Dirac-like cones at k=0. Acta Physica Sinica, 2015, 64(18): 184208. doi: 10.7498/aps.64.184208
[19]	Lu Xiao-Bo, Zhang Guang-Yu. Graphene/h-BN Moiré superlattice. Acta Physica Sinica, 2015, 64(7): 077305. doi: 10.7498/aps.64.077305
[20]	Gao Hong-Lei, Li Ling, Gao Jie. Calculation of acoustoelectric current in a quasi-one-dimensional electron channel. Acta Physica Sinica, 2004, 53(10): 3504-3509. doi: 10.7498/aps.53.3504

Catalog

Vol. 68, Issue 22 - 2019-11-20

Metrics

Abstract views: 12683
PDF Downloads: 422
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板