Probing the topological phase transition via density oscillations in silicene and germanene

Physical Review B - Condensed Matter and Materials Physics

Volumn 89, Issue 20, 2014, Pages

  Chang, Hao Ran ^a   Zhou, Jianhui ^b   Zhang, Hui ^c   Yao, Yugui ^d  

^a SICHUAN NORMAL UNIVERSITY   (China)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c OHIO UNIVERSITY   (United States)

^d BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84902151591     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.89.201411     Document Type: Article

References (40)

1. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 (Pubitemid 41776999)
2. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006). SCIEAS 0036-8075 10.1126/science.1133734 (Pubitemid 44969083)
3. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007). SCIEAS 0036-8075 10.1126/science.1148047 (Pubitemid 351411764)
4. J. Friedel, Nuovo Cimento Suppl. 7, 287 (1958). NUCIAD 0029-6341 10.1007/BF02751483
5. G. G. Guzman-Verri and L. C. Lew Yan Voon, Phys. Rev. B 76, 075131 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.075131
6. S. Cahangirov, M. Topsakal, E. Aktürk, H. Åahin, and S. Ciraci, Phys. Rev. Lett. 102, 236804 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.236804
7. Because of the similarity between the germanene and the silicene, for the remainder of this Rapid Communication, we will not mention the germanene unless it is necessary.
8. M. Ezawa, Phys. Rev. Lett. 109, 055502 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.055502
9. W. F. Tsai, C. Y. Huang, T. R. Chang, H. Lin, H. T. Jeng, and A. Bansil, Nat. Commun. 4, 1500 (2013). 2041-1723 10.1038/ncomms2525
10. H. Z. Lu, W. Yao, D. Xiao, and S. Q. Shen, Phys. Rev. Lett. 110, 016806 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.016806
11. H. Pan, Z. Li, C.-C. Liu, G. Zhu, Z. Qiao, and Y. Yao, Phys. Rev. Lett. 112, 106802 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.106802
12. F. Liu, C.-C. Liu, K. Wu, F. Yang, and Y. Yao, Phys. Rev. Lett. 111, 066804 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.066804
13. W. Wan, Y. Ge, F. Yang, and Y. Yao, Europhys. Lett. 104, 36001 (2013). EULEEJ 0295-5075 10.1209/0295-5075/104/36001
14. L. Zhang, F. Yang, and Y. Yao, arXiv:1309.7347.
15. C.-C. Liu, W. X. Feng, and Y. G. Yao, Phys. Rev. Lett. 107, 076802 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.076802
16. L. Chen, C.-C. Liu, B. Feng, X. He, P. Cheng, Z. Ding, S. Meng, Y. Yao, and K. Wu, Phys. Rev. Lett. 109, 056804 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.056804
17. P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.155501
18. A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang, and Y. Yamada-Takamura, Phys. Rev. Lett. 108, 245501 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.245501
19. L. Meng, Y. Wang, L. Zhang, S. Du, R. Wu, L. Li, Y. Zhang, G. Li, H. Zhou, W. A. Hofer, and H.-J. Gao, Nano Lett. 13, 685 (2013). NALEFD 1530-6984 10.1021/nl304347w
20. Y. P. Wang and H. P. Cheng, Phys. Rev. B 87, 245430 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.245430
21. C. C. Liu, H. Jiang, and Y. G. Yao, Phys. Rev. B 84, 195430 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.195430
22. The effective dielectric constant (Equation presented) is the average screening contribution of any dielectrics above (Equation presented) and below (Equation presented) the sample. The different values of (Equation presented) do not modify the qualitative behavior.
23. K. W.-K. Shung, Phys. Rev. B 34, 979 (1986). PRBMDO 0163-1829 10.1103/PhysRevB.34.979
24. F. Stern, Phys. Rev. Lett. 18, 546 (1967). PRLTAO 0031-9007 10.1103/PhysRevLett.18.546
25. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, New J. Phys. 8, 318 (2006). NJOPFM 1367-2630 10.1088/1367-2630/8/12/318 (Pubitemid 44927392)
26. E. H. Hwang and S. Das Sarma, Phys. Rev. B 75, 205418 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.205418
27. M. Polini, R. Asgari, G. Borghi, Y. Barlas, T. Pereg-Barnea, and A. H. MacDonald, Phys. Rev. B 77, 081411 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.77. 081411
28. X. F. Wang and T. Chakraborty, Phys. Rev. B 75, 033408 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.033408
29. P. K. Pyatkovskiy, J. Phys.: Condens. Matter 21, 025506 (2009). JCOMEL 0953-8984 10.1088/0953-8984/21/2/025506
30. A. Scholz, T. Stauber, and J. Schliemann, Phys. Rev. B 86, 195424 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.195424
31. M. J. Lighthill, Introduction to Fourier Analysis and Generalized Functions (Cambridge University Press, Cambridge, U.K., 1958).
32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.89.201411 for a detailed derivation of the oscillatory part of the screened potential.
33. T. Ando, T. Nakanishi, and R. Saito, J. Phys. Soc. Jpn. 67, 2857 (1998). JUPSAU 0031-9015 10.1143/JPSJ.67.2857
34. In our numerical calculation, we take (Equation presented), (Equation presented), and (Equation presented).
35. B. Feng, H. Li, C.-C. Liu, T.-N. Shao, P. Cheng, Y. Yao, S. Meng, L. Chen, and K. Wu, ACS Nano 7, 9049 (2013). 1936-0851 10.1021/nn403661h
36. A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012). 1749-4885 10.1038/nphoton.2012.262
37. Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, Nano Lett. 11, 4701 (2011). NALEFD 1530-6984 10.1021/nl202362d
38. A. Bostwick, F. Speck, T. Seyller, K. Hom, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, Science 328, 999 (2010). SCIEAS 0036-8075 10.1126/science.1186489
39. In our simulations, the UPM's frequency is in the order of 10-100 meV, and within this region, one simple calculation within classical electromagnetic theory gives the same order amplitude in the absorption resonance of germanene compared with the background spectra of the Ag substrate. Also, when the absorption peak occurs at larger than 50 meV, the plasmon resonance would not be damped by the Ag substrate due to the small relaxation time of Ag (50 fs corresponds to 12 meV). Furthermore, usually the energies of the surface and bulk plasmon resonances of the metallic substrate lie in the order 1 eV (Ag is 3 eV while Au is (Equation presented) eV), and they are far away from that of germanene, with the result that the interference between the plasmon resonances of the substrate and germanene is nearly impossible. All three factors make the plasmon resonances of germanene observable in experiments, even in an Ag substrate.
40. C. J. Tabert and E. J. Nicol, Phys. Rev. B 89, 195410 (2014). 10.1103/PhysRevB.89.195410