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Chin. Phys. B, 2022, Vol. 31(7): 074101    DOI: 10.1088/1674-1056/ac4e03
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Goos-Hänchen and Imbert-Fedorov shifts in tilted Weyl semimetals

Shuo-Qing Liu(刘硕卿)1,†, Yi-Fei Song(宋益飞)1,†, Ting Wan(万婷)1, You-Gang Ke(柯友刚)1, and Zhao-Ming Luo(罗朝明)1,2,‡
1 Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communications, School of Information Science and Engineering, Hunan Institute of Science and Technology, Yueyang 414006, China;
2 School of Physics and Chemistry, Hunan First Normal University, Changsha 410205, China
Abstract  We establish the beam models of Goos-Hänchen (GH) and Imbert-Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-Ⅱ WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-Ⅱ WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-Ⅱ WSMs. By adjusting the chemical potential, the boundary between type-I and type-Ⅱ WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.
Keywords:  Goos-Hänchen shift      Imbert-Fedorov shift      Weyl cone tilting      chemical potential  
Received:  12 November 2021      Revised:  28 December 2021      Accepted manuscript online:  24 January 2022
PACS:  41.20.Jb (Electromagnetic wave propagation; radiowave propagation)  
  42.25.Dd (Wave propagation in random media)  
  78.20.Ci (Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity))  
  78.20.-e (Optical properties of bulk materials and thin films)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 62075060), the Natural Science Foundation of Hunan Province (Grant No. 2020JJ4033), the Research Foundation of Education Bureau of Hunan Province (Grant Nos. 20A218 and 19A198), Science and Technology Plan Project of Hunan Province (Grant No. 2019TP1014), and the Hunan Province Innovation Foundation for Postgraduate Grant (Grant No. CX20211185).
Corresponding Authors:  Zhao-Ming Luo     E-mail:  zhaomingluo@hnu.edu.cn

Cite this article: 

Shuo-Qing Liu(刘硕卿), Yi-Fei Song(宋益飞), Ting Wan(万婷), You-Gang Ke(柯友刚), and Zhao-Ming Luo(罗朝明) Goos-Hänchen and Imbert-Fedorov shifts in tilted Weyl semimetals 2022 Chin. Phys. B 31 074101

[1] Goos F and Hänchen H 1947 Ann. Phys 436 333
[2] Merano M, Aiello A, Van Exter M P and Woerdman J P 2009 Nat. Photon. 3 337
[3] Artmann K 1948 Ann. Phys. 437 87
[4] Fedorov F I 1955 Dokl. Akad. Nauk. SSSR 105 465
[5] Imbert C 1972 Phys. Rev. D 5 787
[6] Xie L G, Zhou X X, Qiu X D, Luo L, Liu X, Li Z X, He Y, Du J L, Zhang Z Y and Wang D Q 2018 Opt. Express 26 22934
[7] Shah M, Sajid M and Anwar M S 2021 Physica E 134 114819
[8] Wu H B, Luo Q L, Chen H J, Han Y, Yu X N and Liu S Y 2019 Phys. Rev. A 99 033820
[9] Abdipour P, Askarpour A N and Alú A 2019 IEEE Trans. Antenenas Propag. 68 1523
[10] Wong Y P, Miao Y, Skarda J and Solgaard O 2018 Opt. Lett. 43 2803
[11] Ma H, Ju C, Xi X and Wu R X 2020 Opt. Express 28 19916
[12] Zhen W M and Deng D M 2020 J. Phys. D:Appl. Phys. 53 255104
[13] Merano M 2016 Opt. Lett. 41 5780
[14] You Q, Jiang L Y, Dai X Y and Xiang Y J 2018 Chin. Phys. B 27 094211
[15] Zhou X, Liu S Q, Ding Y P, Min L and Luo Z M 2019 Carbon 149 604
[16] Tang T T, Li J, Zhu M, Luo L, Yao J Q, Li N X and Zhang P Y 2018 Carbon 135 29
[17] Shah M, Sajid M and Shah M 2021 J. Opt. Soc. Am. B 38 2736
[18] Shah M and Anwar M S 2020 OSA Continuum 3 878
[19] Wu W J, Chen S Z, Mi C Q, Zhang W S, Luo H L and Wen S C 2017 Phys. Rev. A 96 043814
[20] Chen M N and Chen W C 2021 Chin. Phys. B 30 110308
[21] Vazifeh M M and Franz M 2013 Phys. Rev. Lett. 111 027201
[22] Zhang C L, Yuan Z J, Jiang Q D, Tong B B, Zhang C, Xie X C and Jia S 2017 Phys. Rev. B 95 085202
[23] Jiang Q D, Jiang H, Liu H W, Sun Q F and Xie X C 2015 Phys. Rev. Lett. 115 156602
[24] Ye G Z, Zhang W S, Wu W J, Chen S Z, Shu W X, Luo H L and Wen S C 2019 Phys. Rev. A 99 023807
[25] Chen S Z, Mi C Q, Wu W J, Zhang W S, Shu W X, Luo H L and Wen S C 2018 New J. Phys. 20 103050
[26] Liu S Q, Shou Y C, Zhou X, Cheng W B and Luo Z M 2020 Opt. Express 28 10783
[27] Soluyanov A A, Gresch D, Wang Z J, Wu Q S, M. Troyer, Dai X and Bernevig B A 2015 Nature 527 495
[28] Li P, Wen Y, He X, Zhang Q, Xia C, Yu Z M, Yang S A, Zhu Z Y, Alshareef H N and Zhang X X 2017 Nat. Commun. 8 2150
[29] O'Brien T E, Diez M and Beenakker C W J 2016 Phys. Rev. Lett. 116 236401
[30] Halterman K, Alidoust M and Zyuzin A 2018 Phys. Rev. B 98 085109
[31] Sonowal K, Singh A and Agarwal A 2019 Phys. Rev. B 100 085436
[32] Jia G Y, Huang Z X, Ma Q Y and Li G 2020 Nanophotonics 9 715
[33] Xing Y, Shao Z B, Ge J, Luo J W, Wang J H, Zhu Z W, Liu J, Wang Y, Zhao Z Y, Yan J Q, Mandrus D, Yan B H, Liu X J, Pan M H and Wang J 2020 Natl. Sci. Rev. 7 579
[34] Liu S Q, Yang C F, Song Y F, Tang P, Ke Y G and Luo Z M 2020 J. Phys. D:Appl. Phys. 54 285108
[35] Lucarini V, Saarinen J J, Peiponen K E and Vartiainen E M 2005 Kramers-Kronig Relations in Optical Materials Research (New York:Springer) pp. 27-48
[36] Ahn S, Mele E J and Min H 2017 Phys. Rev. B 95 161112(R)
[37] Liu Z K, Yang L X, Sun Y, Peng H, Yang H F, Chen C, Zhang Y, Guo Y F, Prabhakaran D, Schmidt M, Hussain Z, Mo S -K, Felser C, Yan B and Chen Y L 2015 Nat. Mater. 15 27
[38] Wang Y J, Liu E F, Liu H M, Pan Y M, Zhang L Q, Zeng J W, Fu Y J, Wang M, Xu K, Huang Z, Wang Z L, Xing D Y, Wang B G, Wan X G and Miao F 2016 Nat. Commun. 7 13142
[39] Mehdi K, Mohit R and Nandini T 2015 Sci. Rep. 5 12683
[40] Onoda M, Murakami S and Nagaosa N 2004 Phys. Rev. Lett. 93 083901
[41] Hosten O and Kwiat P 2008 Science 319 787
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