Role of acoustic phonons in Bi2Se3 topological insulator slabs: A quantum transport investigation

Physical Review B - Condensed Matter and Materials Physics

Volumn 89, Issue 24, 2014, Pages

  Gupta, Gaurav ^a   Lin, Hsin ^a,b   Bansil, Arun ^b   Jalil, Mansoor Bin Abdul ^a   Liang, Gengchiau ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84902665530     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.89.245419     Document Type: Article

References (52)

1. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803 (Pubitemid 46393379)
2. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.3045
3. D. Pesin and A. H. MacDonald, Nat. Mater. 11, 409 (2012). 10.1038/nmat3305
4. C. W. J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013). 10.1146/annurev-conmatphys-030212-184337
5. D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London) 460, 1101 (2009). 10.1038/nature08234
6. L. A. Wray, S. Y. Xu, Y. Q. Xia, D. Hsieh, A. V. Fedorov, Y. S. Hor, R. J. Cava, A. Bansil, H. Lin, and M. Z. Hasan, Nat. Phys. 7, 32 (2011). 10.1038/nphys1838
7. 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, Nat. Phys. 5, 398 (2009). 10.1038/nphys1274
8. S. Cho, N. P. Butch, J. Paglione, and M. S. Fuhrer, Nano Lett. 11, 1925 (2011). NALEFD 1530-6992 10.1021/nl200017f
9. J. G. Checkelsky, Y. S. Hor, R. J. Cava, and N. P. Ong, Phys. Rev. Lett. 106, 196801 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.196801
10. D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, Nat. Phys. 8, 460 (2012). 10.1038/nphys2286
11. N. Bansal, Y. S. Kim, M. Brahlek, E. Edrey, and S. Oh, Phys. Rev. Lett. 109, 116804 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.116804
12. D. Kim, Q. Li, P. Syers, N. P. Butch, J. Paglione, S. D. Sarma, and M. S. Fuhrer, Phys. Rev. Lett. 109, 166801 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.166801
13. S. S. Hong, J. J. Cha, D. S. Kong, and Y. Cui, Nat. Commun. 3, 757 (2012). 10.1038/ncomms1771
14. J. G. Analytis, R. D. McDonald, S. C. Riggs, J.-H. Chu, G. S. Boebinger, and I. R. Fisher, Nat. Phys. 6, 960 (2010). 10.1038/nphys1861
15. B. Skinner, T. R. Chen, and B. I. Shklovskii, Phys. Rev. Lett. 109, 176801 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.176801
16. Z. Ren, A. A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Phys. Rev. B 84, 075316 (2011). PRBMDO 0163-1829 10.1103/PhysRevB.84.075316
17. H. Chi, W. Liu, K. Sun, X. Su, G. Wang, P. Lošt'ák, V. Kucek, C. Drašar, and C. Uher, Phys. Rev. B 88, 045202 (2013). PRBMDO 0163-1829 10.1103/PhysRevB.88.045202
18. F. Yang, A. A. Taskin, S. Sasaki, K. Segawa, Y. Ohno, K. Matsumoto, and Y. Ando, Appl. Phys. Lett. 104, 161614 (2014). 10.1063/1.4873397
19. S. Giraud and R. Egger, Phys. Rev. B 83, 245322 (2011). PRBMDO 0163-1829 10.1103/PhysRevB.83.245322
20. S. Giraud, A. Kundu, and R. Egger, Phys. Rev. B 85, 035441 (2012). PRBMDO 0163-1829 10.1103/PhysRevB.85.035441
21. X. T. Zhu, L. Santos, C. Howard, R. Sankar, F. C. Chou, C. Chamon, and M. El-Batanouny, Phys. Rev. Lett. 108, 185501 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.185501
22. S. R. Park, W. S. Jung, G. R. Han, Y. K. Kim, C. Kim, D. J. Song, Y. Y. Koh, S. Kimura, K. D. Lee, N. Hur, J. Y. Kim, B. K. Cho, J. H. Kim, Y. S. Kwon, J. H. Han, and C. Kim, New J. Phys. 13, 013008 (2011). NJOPFM 1367-2630 10.1088/1367-2630/13/1/013008
23. Z. H. Pan, A. V. Fedorov, D. Gardner, Y. S. Lee, S. Chu, and T. Valla, Phys. Rev. Lett. 108, 187001 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108. 187001
24. P. Thalmeier, Phys. Rev. B 83, 125314 (2011). PRBMDO 0163-1829 10.1103/PhysRevB.83.125314
25. L. Barreto, M. Bianchi, D. Guan, R. Hatch, J. Mi, B. B. Iversen, and P. Hofmann, Phys. Status Solidi Rapid Res. Lett. 7, 136 (2012). 10.1002/pssr.201206407
26. C. W. Luo, H. J. Wang, S. A. Ku, H. J. Chen, T. T. Yeh, J. Y. Lin, K. H. Wu, J. Y. Juang, B. L. Young, T. Kobayashi, C. M. Cheng, C. H. Chen, K. D. Tsuei, R. Sankar, F. C. Chou, K. A. Kokh, O. E. Tereshchenko, E. V. Chulkov, Y. M. Andreev, and G. D. Gu, Nano Lett. 13, 5797 (2013). NALEFD 1530-6992 10.1021/nl4021842
27. L. Fu and E. Berg, Phys. Rev. Lett. 105, 097001 (2010). 10.1103/PhysRevLett.105.097001
28. L. Fu, Phys. Rev. Lett. 103, 266801 (2009). 10.1103/PhysRevLett.103. 266801
29. H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Nat. Phys. 5, 438 (2009). 10.1038/nphys1270
30. K. Kuroda, M. Arita, K. Miyamoto, M. Ye, J. Jiang, A. Kimura, E. E. Krasovskii, E. V. Chulkov, H. Iwasawa, T. Okuda, K. Shimada, Y. Ueda, H. Namatame, and M. Taniguchi, Phys. Rev. Lett. 105, 076802 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.076802
31. For operation in surface bands, transport is independent of slab thickess [Phys. Rev. Lett. 109, 116804 (2012) PRLTAO 0031-9007 10.1103/PhysRevLett.109. 116804], although percentage contribution through individual layers will change accordingly. However, computational time scales exponentially with slab thickness and becomes especially demanding for acoustic phonons, with an insignificant effect on data and discussion presented in this paper.
32. 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, Science 325, 178 (2009). SCIEAS 0036-8075 10.1126/science.1173034
33. Z. Alpichshev, J. G. Analytis, J. H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik, Phys. Rev. Lett. 104, 016401 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.016401
34. S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005).
35. M. P. L. Sancho, J. M. L. Sancho, and J. Rubio, J. Phys. F 14, 1205 (1984). 10.1088/0305-4608/14/5/016
36. M. P. Anantram, M. S. Lundstrom, and D. E. Nikonov, Proc. IEEE 96, 1511 (2008). 10.1109/JPROC.2008.927355
37. S. R. Park, W. S. Jung, C. Kim, D. J. Song, C. Kim, S. Kimura, K. D. Lee, and N. Hur, Phys. Rev. B 81, 041405 (2010). 10.1103/PhysRevB.81.041405
38. Device was simulated only up to 250 K as similar physics seems to be at play from experimental studies between 250 K to 300 K. Also, simulating higher temperatures, becomes increasing more compute-intensive, requiring long time for the self-energy in NEGF to converge.
39. M. V. Costache, I. Neumann, J. F. Sierra, V. Marinova, M. M. Gospodinov, S. Roche, and S. O. Valenzuela, Phys. Rev. Lett. 112, 086601 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.086601
40. M. Buttiker, Phys. Rev. B 46, 12485 (1992). PRBMDO 0163-1829 10.1103/PhysRevB.46.12485
41. D. S. Kong, J. C. Randel, H. L. Peng, J. J. Cha, S. Meister, K. J. Lai, Y. L. Chen, Z. X. Shen, H. C. Manoharan, and Y. Cui, Nano Lett. 10, 329 (2010). NALEFD 1530-6992 10.1021/nl903663a
42. For example, disorder scattering effectively broadens energy levels in alloys, see A. Bansil, Phys. Rev. B 20, 4025 (1979); PRBMDO 0163-1829 10.1103/PhysRevB.20.4025
43. A. Bansil, Phys. Rev. B 20, 4035 (1979); PRBMDO 0163-1829 10.1103/PhysRevB.20.4035
44. A. Bansil, Zeitschrift Naturforschung A 48, 165 (1993).
45. We emphasize that this approach only qualitatively characterizes the temperature dependency of relative decrease in the surface current, i.e. as the Fermi-level moves away from the Dirac-point, the differences in slopes expected for greatly differing strengths of the electron-phonon coupling. The measured magnitudes of the variation will depend on the sample quality, bias, dimensions (length and sample thickness) and specific values of λ.
46. S. Datta, Lessons from Nanoelectronics: A New Perspective on Transport (World Scientific, Singapore, 2012).
47. R. Venugopal, M. Paulsson, S. Goasguen, S. Datta, and M. S. Lundstrom, J. Appl. Phys. 93, 5613 (2003). JAPIAU 0021-8979 10.1063/1.1563298
48. We would like to note that since interlayer scattering due to van der Waals forces are weaker than in-plane scattering. Therefore, using the same λ for interlayer scattering might lead to a marginal overestimation of the net effect of scattering between the layers.
49. W. Zhang, R. Yu, H.-J. Zhang, X. Dai, and Z. Fang, New J. Phys. 12, 065013 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/6/065013
50. Y. H. Zhao, Y. B. Hu, L. Liu, Y. Zhu, and H. Guo, Nano Lett. 11, 2088 (2011). NALEFD 1530-6992 10.1021/nl200584f
51. C.-Y. Moon, J. Han, H. Lee, and H. J. Choi, Phys. Rev. B 84, 195425 (2011). PRBMDO 0163-1829 10.1103/PhysRevB.84.195425
52. Y. Zhang, K. He, C. Z. Chang, C. L. Song, L. L. Wang, X. Chen, J. F. Jia, Z. Fang, X. Dai, W. Y. Shan, S. Q. Shen, Q. Niu, X. L. Qi, S. C. Zhang, X. C. Ma, and Q. K. Xue, Nat. Phys. 6, 584 (2010). 10.1038/nphys1689