Double Andreev reflections at surface states of the topological insulators with hexagonal warping

doi:10.1007/s11467-019-0941-0

Front. Phys.

2020, Vol. 15

Issue (2) : 23602 https://doi.org/10.1007/s11467-019-0941-0

RESEARCH ARTICLE

Double Andreev reflections at surface states of the topological insulators with hexagonal warping

Chang-Yong Zhu^1,², Shi-Han Zheng¹, Hou-Jian Duan¹, Ming-Xun Deng¹(

), Rui-Qiang Wang¹(

)

¹. 1Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
². 2School of Physics and Mechanical and Electrical Engineering, Shaoguan University, Shaoguan 512005, China

Download: PDF(2377 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We study the Andreev reflection (AR) at the interface of the topological insulator with hexagonal warping and superconductor junction. Due to the hexagonal warping effect, the double ARs are found in a certain range of the incident angle, where for one incident electron beam, two beams of holes are reflected back. Interestingly, both the beams of holes are reflected as retro-AR on the same side of the normal line of the interface but with different reflection angles, different from the previously reported double AR with one retro-AR and one specular-AR. The double reflections owing to the warping effect show the optics-like property of the Dirac fermion and can stimulate the double reflections of light in anisotropic crystals. In addition, we find that the double ARs are dependent on the hexagonal warping parameter nonmonotonically, and in an intermediate strength the double AR phenomenon is prominent, providing a possibility to explore the warping parameter of topological insulators.

Keywords Andreev reflection topological insulator warping effect

Corresponding Author(s): Ming-Xun Deng,Rui-Qiang Wang

Issue Date: 22 November 2019

Cite this article:

Chang-Yong Zhu,Shi-Han Zheng,Hou-Jian Duan, et al. Double Andreev reflections at surface states of the topological insulators with hexagonal warping[J]. Front. Phys. , 2020, 15(2): 23602.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-019-0941-0
https://academic.hep.com.cn/fop/EN/Y2020/V15/I2/23602

1	A. F. Andreev, The thermal conductivity of the intermediate state in superconductors, Sov. Phys. JETP 19(5), 1228 (1964) [Zh. Eksp. Teor. Fiz. 46, 1823(1964)]
2	P. G. de Gennes, in: Superconductivity of Metals and Alloys, Benjamin, New York, 1966
3	J. Linder and J. W. A. Robinson, Superconducting spintronics, Nat. Phys. 11(4), 307 (2015) https://doi.org/10.1038/nphys3242
4	G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25(7), 4515 (1982) https://doi.org/10.1103/PhysRevB.25.4515
5	P. Lv, A. M. Guo, H. Y. Li, C. X. Liu, X. C. Xie, and Q. F. Sun, Spin-flip reflection at the normal metal-spin superconductor interface, Phys. Rev. B 95(10), 104516 (2017) https://doi.org/10.1103/PhysRevB.95.104516
6	C. W. J. Beenakker, Andreev reflection and Klein tunneling in graphene, Rev. Mod. Phys. 80(4), 1337 (2008) https://doi.org/10.1103/RevModPhys.80.1337
7	K. K. Li and Y. Y. Zhang, Spin-filtered and spatially distinguishable crossed Andreev reflection in a silicenesuperconductor junction, Phys. Rev. B 94(16), 165441 (2016) https://doi.org/10.1103/PhysRevB.94.165441
8	C. X. Bai, Y. L. Yang, and X. D. Zhang, Specular Andreev reflection and magnetoresistance in graphene-based ferromagnet-superconductor double junctions, Appl. Phys. Lett. 92(10), 102513 (2008) https://doi.org/10.1063/1.2894513
9	R. Q. Wang, L. Sheng, L. B. Hu, M. Yang, B. G. Wang, and D. Y. Xing, Generation of adjustable pure spin currents in negative-U systems, Front. Phys. 9(4), 477 (2014) https://doi.org/10.1007/s11467-014-0436-y
10	Z. M. Yu, Y. Liu, and S. A. Yang, Anomalous spatial shifts in interface electronic scattering, Front. Phys. 14(3), 33402 (2019) https://doi.org/10.1007/s11467-019-0882-7
11	B. Lv, C. Zhang, and Z. Ma, Specular Andreev reflection in the interface of a two-dimensional semiconductor with Rashba spin-orbit coupling and a d-wave superconductor, Phys. Rev. Lett. 108(7), 077002 (2012) https://doi.org/10.1103/PhysRevLett.108.077002
12	C. W. J. Beenakker, Specular Andreev reflection in graphene, Phys. Rev. Lett. 97(6), 067007 (2006) https://doi.org/10.1103/PhysRevLett.97.067007
13	Q. Y. Zhang, D. Y. Fu, B. G. Wang, R. Zhang, and D. Y. Xing, Signals for specular Andreev reflection, Phys. Rev. Lett. 101(4), 047005 (2008) https://doi.org/10.1103/PhysRevLett.101.047005
14	D. K. Efetov, L. Wang, C. Handschin, K. B. Efetov, J. Shuang, R. Cava, T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean, and P. Kim, Specular interband Andreev reflections at van der Waals interfaces between graphene and NbSe2, Nat. Phys. 12(4), 328 (2016) https://doi.org/10.1038/nphys3583
15	S. G. Cheng, Y. Xing, J. Wang, and Q. F. Sun, Controllable Andreev retroreflection and specular Andreev reflection in a four-terminal graphene-superconductor hybrid system, Phys. Rev. Lett. 103(16), 167003 (2009) https://doi.org/10.1103/PhysRevLett.103.167003
16	V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, The focusing of electron flow and a Veselago lens in graphene p-n junctions, Science 315(5816), 1252 (2007) https://doi.org/10.1126/science.1138020
17	S. Li, C. Wang, S. H. Zheng, R. Q. Wang, J. Li, and M. Yang, Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals, Front. Phys. 13(2), 137303 (2018) https://doi.org/10.1007/s11467-017-0742-2
18	F. Hassler, A. R. Akhmerov, and C. W. J. Beenakker, Flat-lens focusing of electrons on the surface of a topological insulator, Phys. Rev. B 82(12), 125423 (2010) https://doi.org/10.1103/PhysRevB.82.125423
19	H. Ren, L. Liu, D. Liu, and Z. Song, Double refraction and reflection of sequential crystal interfaces with arbitrary orientation of the optic axis and application to optimum design, J. Mod. Opt. 52(4), 529 (2005) https://doi.org/10.1080/09500340410001712364
20	J. F. Wu and C. M. Zhang, The double reflection on the interface of uniaxial crystals in the Savart polariscope, Sci. China Ser. G-Phys. Mech. Astron. 52(7), 1003 (2009) https://doi.org/10.1007/s11433-009-0147-5
21	Z. M. Yu, D. S. Ma, H. Pan, and Y. G. Yao, Double reflection and tunneling resonance in a topological insulator: Towards the quantification of warping strength by transport, Phys. Rev. B 96(12), 125152 (2017) https://doi.org/10.1103/PhysRevB.96.125152
22	Z. Hou and Q. F. Sun, Double Andreev reflections in type-II Weyl semimetal-superconductor junctions, Phys. Rev. B 96(15), 155305 (2017) https://doi.org/10.1103/PhysRevB.96.155305
23	X. S. Li, S. F. Zhang, X. R. Sun, and W. J. Gong, Double Andreev reflections and double electron transmissions in a normal-superconductor-normal junction based on type-II Weyl semimetal, New J. Phys. 20(10), 103005 (2018) https://doi.org/10.1088/1367-2630/aae280
24	L. Majidi and R. Asgari, Specular Andreev reflection in thin films of topological insulators, Phys. Rev. B 93(19), 195404 (2016) https://doi.org/10.1103/PhysRevB.93.195404
25	X. S. Li, C. Wang, M. X. Deng, H. J. Duan, P. H. Fu, R. Q. Wang, L. Sheng, and D. Y. Xing, Photoninduced Weyl half-metal phase and spin filter effect from topological Dirac semimetals, arxiv: 1910.06178 (2019)
26	I. Knez, R. R. Du, and G. Sullivan, Andreev reflection of helical edge modes in InAs/GaSb quantum spin Hall insulator, Phys. Rev. Lett. 109(18), 186603 (2012) https://doi.org/10.1103/PhysRevLett.109.186603
27	L. Fu, Hexagonal warping effects in the surface states of the topological insulator Bi2Te3, Phys. Rev. Lett. 103(26), 266801 (2009) https://doi.org/10.1103/PhysRevLett.103.266801
28	M. Z. Hasan and C. L. Kane, Topological insulators, Mod. Phys. 82(4), 3045 (2010) https://doi.org/10.1103/RevModPhys.82.3045
29	X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011) https://doi.org/10.1103/RevModPhys.83.1057
30	S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator, Phys. Rev. Lett. 106(21), 216803 (2011) https://doi.org/10.1103/PhysRevLett.106.216803
31	M. Nomura, S. Souma, A. Takayama, T. Sato, T. Takahashi, K. Eto, K. Segawa, and Y. Ando, Relationship between Fermi surface warping and out-of-plane spin polarization in topological insulators: A view from spin- and angle-resolved photoemission, Phys. Rev. B 89(4), 045134 (2014) https://doi.org/10.1103/PhysRevB.89.045134
32	Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5(6), 398 (2009) https://doi.org/10.1038/nphys1274
33	Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S. K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Experimental realization of a three-dimensional topological insulator, Bi2Te3, Science 325(5937), 178 (2009) https://doi.org/10.1126/science.1173034
34	K. Kuroda, M. Ye, A. Kimura, S. V. Eremeev, E. E. Krasovskii, E. V. Chulkov, Y. Ueda, K. Miyamoto, T. Okuda, K. Shimada, H. Namatame, and M. Taniguchi, Experimental realization of a three-dimensional topological insulator phase in ternary chalcogenide TlBiSe2, Phys. Rev. Lett. 105(14), 146801 (2010) https://doi.org/10.1103/PhysRevLett.105.146801
35	Z. Li and J. P. Carbotte, Hexagonal warping on spin texture, Hall conductivity, and circular dichroism of topological insulators, Phys. Rev. B 89(16), 165420 (2014) https://doi.org/10.1103/PhysRevB.89.165420
36	S. Roy, A. Soori, and S. Das, Tunnel magnetoresistance scan of a pristine three-dimensional topological insulator, Phys. Rev. B 91(4), 041109 (2015) https://doi.org/10.1103/PhysRevB.91.041109
37	Z. B. Siu, M. B. Jalil, and S. G. Tan, Topological state transport in topological insulators under the influence of hexagonal warping and exchange coupling to in-plane magnetizations, Sci. Rep. 4(1), 5062 (2015) https://doi.org/10.1038/srep05062
38	F. Hassler, A. R. Akhmerov, and C. W. J. Beenakker, Flat-lens focusing of electrons on the surface of a topological insulator, Phys. Rev. B 82(12), 125423 (2010) https://doi.org/10.1103/PhysRevB.82.125423
39	T. Habe and M. Koshino, Spin-dependent refraction at the atomic step of transition-metal dichalcogenides, Phys. Rev. B 91(20), 201407 (2015) https://doi.org/10.1103/PhysRevB.91.201407
40	P. Lv, N. Dai, and Q. F. Sun, Double refraction and spin splitter in normal-conductor/hexagonal-semiconductor junctions, Phys. Rev. B 97(23), 235425 (2018) https://doi.org/10.1103/PhysRevB.97.235425
41	D. Zhang, J. Wang, A. M. DaSilva, J. S. Lee, H. R. Gutierrez, M. H. W. Chan, J. Jain, and N. Samarth, Superconducting proximity effect and possible evidence for Pearl vortices in a candidate topological insulator, Phys. Rev. B 84(16), 165120 (2011) https://doi.org/10.1103/PhysRevB.84.165120
42	M. X. Wang, C. Liu, J. P. Xu, F. Yang, L. Miao, M. Y. Yao, C. L. Gao, C. Shen, X. Ma, X. Chen, Z. A. Xu, Y. Liu, S. C. Zhang, D. Qian, J. F. Jia, and Q. K. Xue, The coexistence of superconductivity and topological order in the Bi2Se3 thin films, Science 336(6077), 52 (2012) https://doi.org/10.1126/science.1216466
43	J. R. Williams, A. J. Bestwick, P. Gallagher, S. S. Hong, Y. Cui, A. S. Bleich, J. G. Analytis, I. R. Fisher, and D. Goldhaber-Gordon, Unconventional Josephson effect in hybrid superconductor-topological insulator devices, Phys. Rev. Lett. 109(5), 056803 (2012) https://doi.org/10.1103/PhysRevLett.109.056803
44	L. Galletti, S. Charpentier, M. Iavarone, P. Lucignano, D. Massarotti, R. Arpaia, Y. Suzuki, K. Kadowaki, T. Bauch, A. Tagliacozzo, F. Tafuri, and F. Lombardi, Influence of topological edge states on the properties of Al/Bi2Se3/Al hybrid Josephson devices, Phys. Rev. B 89(13), 134512 (2014) https://doi.org/10.1103/PhysRevB.89.134512
45	E. S. Tikhonov, D. V. Shovkun, M. Snelder, M. P. Stehno, Y. Huang, M. S. Golden, A. A. Golubov, A. Brinkman, and V. S. Khrapai, Andreev reflection in an s-type superconductor proximized 3D topological insulator, Phys. Rev. Lett. 117(14), 147001 (2016) https://doi.org/10.1103/PhysRevLett.117.147001
46	J. Wiedenmann, E. Liebhaber, J. Kübert, E. Bocquillon, P. Burset, C. Ames, H. Buhmann, T. M. Klapwijk, and L. W. Molenkamp, Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe, Phys. Rev. B 96(16), 165302 (2017) https://doi.org/10.1103/PhysRevB.96.165302

[1]	Chen-Xiao Zhao (赵晨晓), Jin-Feng Jia (贾金锋). Stanene: A good platform for topological insulator and topological superconductor[J]. Front. Phys. , 2020, 15(5): 53201-.
[2]	Y. X. Zhao. Equivariant PT-symmetric real Chern insulators[J]. Front. Phys. , 2020, 15(1): 13603-.
[3]	Mengyun He, Huimin Sun, Qing Lin He. Topological insulator: Spintronics and quantum computations[J]. Front. Phys. , 2019, 14(4): 43401-.
[4]	Junjie Qi, Haiwen Liu, Hua Jiang, X. C. Xie. Dephasing effects in topological insulators[J]. Front. Phys. , 2019, 14(4): 43403-.
[5]	Hai-Peng Sun, Hai-Zhou Lu. Quantum transport in topological semimetals under magnetic fields (II)[J]. Front. Phys. , 2019, 14(3): 33405-.
[6]	Dingping Li, Baruch Rosenstein, B. Ya. Shapiro, I. Shapiro. Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator[J]. Front. Phys. , 2015, 10(3): 107402-.
[7]	Ming Yang, Xiao-Long Zhang, Wu-Ming Liu. Tunable topological quantum states in three- and two-dimensional materials[J]. Front. Phys. , 2015, 10(2): 108102-.
[8]	Yi-Bin Hu, Yong-Hong Zhao, Xue-Feng Wang. A computational investigation of topological insulator Bi₂Se₃ film[J]. Front. Phys. , 2014, 9(6): 760-767.
[9]	Ying Xing (邢颖), Yi Sun (孙祎), Meenakshi Singh, Yan-Fei Zhao (赵弇斐), Moses H. W. Chan, Jian Wang (王健). Electronic transport properties of topological insulator films and low dimensional superconductors[J]. Front. Phys. , 2013, 8(5): 491-508.
[10]	W. LiMing, Jia-Yun Luo, Xiao-Xue Cai, Ke Sha, Cheng-Ping Yin, Liang-Bin Hu. Andreev reflection and tunneling spectrum in a superlattice of metal-superconductor junctions[J]. Front. Phys. , 2013, 8(1): 50-54.
[11]	Jiajun Ouyang, W. LiMing, Liangbin Hu. Andreev reflection and tunneling spectrum on metal–superconductor–metal junctions[J]. Front. Phys. , 2012, 7(4): 449-452.
[12]	Hui Li (李辉), Hailin Peng (彭海琳), Wenhui Dang (党文辉), Lili Yu (余力立), Zhongfan Liu (刘忠范). Topological insulator nanostructures: Materials synthesis, Raman spectroscopy, and transport properties[J]. Front. Phys. , 2012, 7(2): 208-217.
[13]	Ivan Knez, Rui-Rui Du. Quantum spin Hall effect in inverted InAs/GaSb quantum wells[J]. Front. Phys. , 2012, 7(2): 200-207.
[14]	Jun-liang Zhang, Si-jia Zhang, Hong-ming Weng, Wei Zhang, Liu-xiang Yang, Qing-qing Liu, Pan-pan Kong, Jie Zhu, Shao-min Feng, Xian-cheng Wang, Ri-cheng Yu, Lie-zhao Cao, Shoucheng Zhang, Xi Dai, Zhong Fang, Chang-qing Jin. Superconductivity of topological matters induced via pressure[J]. Front. Phys. , 2012, 7(2): 193-199.
[15]	Yulin Chen. Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy[J]. Front. Phys. , 2012, 7(2): 175-192.

Viewed

Full text

Abstract

Cited

Shared

Discussed