本篇論文研究第四族二維材料和缺陷相關系統的基本物理性質。爲研究庫侖激發、庫侖散射和磁量子化，利用廣義緊束縛模型結合隨機相位近似、介電函數、光學吸收函數和梯度近似等理論，對庫侖激發、庫侖散射和磁量子化進行了研究。豐富的物理特徵與平面或彎曲結構的晶格幾何、顯著的自旋軌道耦合、非均勻躍遷積分和原子軌域能量、客體原子的晶格位置和濃度以及外部場有關。由轉換動量的大小和方向、費米能量和柵極電壓不同，集體和單粒子的激發和激發是不同的。根據獨特的頻率和動量相圖，有不同種類的電漿子模式。根據準粒子狀態和費米能量的不同，去激發過程可以利用能帶內、能帶間單粒子激發和等離子體模態。石墨烯、矽烯和鍺烯在庫侖激發和散射的主要特徵上有很大不同。自旋軌道耦合和缺陷，特別是取代原子，極大地改變了第四族二維材料的電子性質，如能隙和各向異性行爲。矽摻雜石墨烯和雙層矽烯中的磁量子化藍道能級呈現出豐富而獨特的性質。它們在很大程度上取決於矽客體原子的不同晶格位置和濃度，或雙層矽烯的堆積幾何形狀。對於前者，根據機率分佈和振盪模式有四種不同的藍道能階。超晶格中Ai和Bi子晶格的非等價或等價性質所產生的不尋常的磁光選擇規則，清楚地反映了超晶格的主要特徵。AB-bt雙層矽烯由於不同的支配子晶格和自旋自由度，呈現出4個不同的類別。磁光激發除了由臨界電場操控外，不存在特定的選擇規則。

In this thesis, the essential physical properties of group-IV two-dimensional (2D) materials and defect-related systems are studied. The generalized tight-binding model in combination with appropriate theories of random-phase approximation, dielectric function, optical absorption function, and gradient approximation is used in order to investigate the Coulomb excitation, Coulomb scattering, and magnetic quantization. The feature-rich physical features are associated with the lattice geometries with plane or buckled structures, significant spin-orbit coupling, non-uniform hopping integrals and site energies, configuration and concentration of substituted atoms, and external fields. The collective and single-particle excitations and deexcitations are diversified by the magnitude and direction of transferred momentum, the Fermi energy and the gate voltage. There are different kinds of plasmon modes, according to the unique frequency- and momentum-dependent phase diagrams. The deexcitation processes might utilize the intraband single-particle excitations (SPEs), the interband SPEs, and the plasmon modes, depending on the quasiparticle states and the Fermi energies. Graphene, silicene, and germanene are quite different from one another in the main features of the Coulomb excitations and scattering. The spin-orbit couplings (SOC) and defect, specifically substituted atoms, drastically changes electronic properties of group-IV 2D materials, such as, inducing band gap and anisotropic behavior. The magnetic quantized Landau levels (LLs) in Si-doped graphene and bilayer silicene present the rich and unique properties. They strongly depends on various configurations and concentrations of Si guest atoms or stacking geometry in bilayer silicene. As for the former, there are four different kinds of LLs, based on the probability distributions and oscillation modes. The main characteristics of LLs are clearly reflected in the unusual magneto-optical selection rules which come from the non-equivalence or equivalence of the A$_i$ and B$_i$ sublattices in a supercell. AB-bt bilayer silicene exhibits four distinct groups of LLs due to different dominating sublattices and spin degree of freedom. The magneto-optical excitations do not obey a specific selection rule except that the Dirac-cone band structures are driven by the critical electric fields.

Chapter 1 REFERENCES
1. S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. C. Neto, and A. Lanzara, Nature Materials 6, 770 (2007).
2. I. Pletikosic, M. Kralj, P. Pervan, R. Brako, J. Coraux, A. T. NDiaye, C. Busse, and T. Michely, Phys. Rev. Lett. 102, 056808 (2009).
3. Y. Liu and R. F. Willis, Phys. Rev. B 81, 081406 (2010).
4. I. D. Barcelos, A. R. Cadore, L. C. Campos, A. Malachias, K.Watanabe, T. Taniguchi,
F. C. B. Maia, R. Freitas, and C. Deneke, Nanoscale 7, 11620 (2015).
5. C.-C. Lee, Y. Yamada-Takamura, and T. Ozaki, J. Phys.: Condens. Matter 25, 345501 (2013).
6. Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, Phys. Rev. Lett. 98, 197403 (2007).
7. C.-L. Lin, R. Arafune, K. Kawahara, M. Kanno, N. Tsukahara, E. Minamitani, Y. Kim, M. Kawai, and N. Takagi, Phys. Rev. Lett. 110, 076801 (2013).
8. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, Solid State Communications 146, 351 (2008).
9. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass,
A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, Science 312, 1191 (2006).
10. C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, J. Phys. Chem. B 108, 19912 (2004).
11. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005).
12. C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, Nano Lett. 7, 2711 (2007).
13. E. Scalise, E. Cinquanta, M. Houssa, B. van den Broek, D. Chiappe, C. Grazianetti,
G. Pourtois, B. Ealet, A. Molle, M. Fanciulli, V. V. Afanasev, and A. Stesmans, Applied Surface Science 291, 113 (2014).
14. Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and P. Avouris, Science 327, 662 (2010).
15. L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, and D. Akinwande, Nature Nanotechnology 10, 227 (2015).
16. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
17. R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 46, 1804 (1992).
18. P. R. Wallace, Phys. Rev. 71, 622 (1947).
19. E. H. Hwang and S. Das Sarma, Phys. Rev. B 75, 205418 (2007).
20. E. H. Hwang, R. Sensarma, and S. Das Sarma, Phys. Rev. B 82, 195406 (2010).
21. Y. H. Lai, J. H. Ho, C. P. Chang, and M. F. Lin, Phys. Rev. B 77, 085426 (2008).
22. C.-Y. Lin, J.-Y. Wu, Y.-J. Ou, Y.-H. Chiu, and M.-F. Lin, Phys. Chem. Chem. Phys. 17, 26008 (2015).
23. E. H. Hwang, S. Adam, and S. D. Sarma, Phys. Rev. Lett. 98, 186806 (2007).
24. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
25. M. Tahir, A. Manchon, K. Sabeeh, and U. Schwingenschlgl, Appl. Phys. Lett. 102, 162412 (2013).
26. C.-C. Liu, W. Feng, and Y. Yao, Phys. Rev. Lett. 107, 076802 (2011).
27. M. Koshino and T. Ando, Phys. Rev. B 77, 115313 (2008).
28. C. L. Lu, C. P. Chang, Y. C. Huang, R. B. Chen, and M. L. Lin, Phys. Rev. B 73, 144427 (2006).
29. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
30. Y.-T. Wang, C.-W. Luo, A. Yabushita, K.-H. Wu, T. Kobayashi, C.-H. Chen, and L.-J. Li, Scientific Reports 5, 8289 (2015).
31. P. Tassin, T. Koschny, and C. M. Soukoulis, Science 341, 620 (2013).
32. H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, IEEE Journal of Selected Topics in Quantum Electronics 22, 98 (2016).
33. C. K. Chan, H. Peng, G. Liu, K. McIlwrath, X. F. Zhang, R. A. Huggins, and Y. Cui, Nature Nanotechnology 3, 31 (2008).
34. W. Zhang, J. Mao, S. Li, Z. Chen, and Z. Guo, J. Am. Chem. Soc. 139, 3316 (2017).
35. P. Song, X. Zhang, M. Sun, X. Cui, and Y. Lin, RSC Advances 2, 1168 (2012).
36. L. Dou, F. Cui, Y. Yu, G. Khanarian, S. W. Eaton, Q. Yang, J. Resasco, C. Schildknecht, K. Schierle-Arndt, and P. Yang, ACS Nano 10, 2600 (2016).
37. P. Xu, Y. Yang, D. Qi, S. D. Barber, J. K. Schoelz, M. L. Ackerman, L. Bellaiche, and P. M. Thibado, Phys. Rev. B 86, 085428 (2012).
38. Y. I. Kurys, O. O. Ustavytska, V. G. Koshechko, and V. D. Pokhodenko, RSC Adv. 6, 36050 (2016).
39. L. Liu, H. Zhou, R. Cheng, W. J. Yu, Y. Liu, Y. Chen, J. Shaw, X. Zhong, Y. Huang, and X. Duan, ACS Nano 6, 8241 (2012).
40. R. K. Vijayaraghavan, C. Gaman, B. Jose, A. P. McCoy, T. Cafolla, P. J. McNally, and S. Daniels, ACS Appl. Mater. Interfaces 8, 4878 (2016).
41. 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).
42. L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, and D. Akinwande, Nature Nanotechnology 10, 227 (2015).
43. L. Li, S. Lu, J. Pan, Z. Qin, Y. Wang, Y. Wang, G. Cao, S. Du, and H.-J. Gao, Advanced Materials 26, 4820 (2014).
44. M. Derivaz, D. Dentel, R. Stephan, M.-C. Hanf, A. Mehdaoui, P. Sonnet, and C. Pirri, Nano Lett. 15, 2510 (2015).
45. C.-C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011).
46. M. Ezawa, New J. Phys. 14, 033003 (2012).
47. S.-M. Huang, S.-T. Lee, and C.-Y. Mou, Phys. Rev. B 89, 195444 (2014).
48. J. Zheng, F. Chi, and Y. Guo, J. Phys.: Condens. Matter 27, 295302 (2015).
49. V. O. zelik, E. Durgun, and S. Ciraci, J. Phys. Chem. Lett. 5, 2694 (2014).
50. N. B. M. Schrter, M. D. Watson, L. B. Duffy, M. Hoesch, Y. Chen, T. Hesjedal, and T. K. Kim, 2D Mater. 4, 031005 (2017).
51. C. Heske, R. Treusch, F. J. Himpsel, S. Kakar, L. J. Terminello, H. J. Weyer, and E. L. Shirley, Phys. Rev. B 59, 4680 (1999).
52. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, Nature Physics 3, 36
(2007).
53. W. Zhou, M. D. Kapetanakis, M. P. Prange, S. T. Pantelides, S. J. Pennycook, and J.-C. Idrobo, Phys. Rev. Lett. 109, 206803 (2012).
54. L. S. Panchakarla, K. S. Subrahmanyam, S. K. Saha, A. Govindaraj, H. R. Krishnamurthy, U. V. Waghmare, and C. N. R. Rao, Advanced Materials 21, 4726 (2009).
55. L. Qu, Y. Liu, J.-B. Baek, and L. Dai, ACS Nano 4, 1321 (2010).
56. S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu, H. K. Zhong, and Z. J. Xu, Nanoscale 8, 226 (2015).
57. M. Shahrokhi and C. Leonard, Journal of Alloys and Compounds 693, 1185 (2017).
58. P. Vogt et al., Phys. Rev. Lett. 108, 155501 (2012).
59. T. Li et al., Nat. Nanotech. 10, 227-231 (2015).
60. B. Mohan, A. Kumar, P. K. Ahluwalia, Physica E 53, 233-239 (2013).
61. H. S. Liu, N. Han and J. J. Zhao, J. Phys.: Condens. Matter 26, 475303 (2014).
62. J. J. Liu and W. Q. Zhang, RSC Adv. 3, 21943 (2013).
63. F. Liuy, C. C. Liuy, K. H. Wu, F. Yang, and Y. G. Yao, Phys. Rev. Lett. 111, 066804 (2013).
64. J. E. Padilha, and R. B. Pontes, J. Phys. Chem. C 119, 3818-3825 (2015).
65. Y. P. Lin, C. Y. Lin, Y. H. Ho, T. N. Do and M. F. Lin, PCCP 17, 15921 (2015).
66. H. X. Fu, J. Zhang, Z. J. Ding, H. Li, and S. Menga, Appl. Phys. Lett. 104, 131904 (2014).
67. R. Yaokawa, T. Ohsuna, T. Morishita, Y. Hayasaka, M. J. S. Spencer, and H. Nakano, Nat. Comm. 7, 10657 (2016).
Chapter 2 REFERENCES
1. S. J. Zhang, S. S. Lin, X. Q. Li, X. Y. Liu, H. A. Wu, W. L. Xu, P. Wang, Z. Q. Wu,
H. K. Zhong, and Z. J. Xu, Nanoscale 8, 226 (2015).
2. M. Shahrokhi and C. Leonard, Journal of Alloys and Compounds 693, 1185 (2017).
3. M. S. Dresselhaus and G. Dresselhaus, Advances in Physics 30, 139 (1981).
4. C.-C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011).
5. P. H. Shih, T. N. Do, B. L. Huang, G. Gumbs, D. Huang, and M. F. Lin, ArXiv:1808.10382 [Cond-Mat, Physics:Physics] (2018).
6. H. X. Fu, J. Zhang, Z. J. Ding, H. Li, and S. Menga, Appl. Phys. Lett. 104, 131904 (2014).
7. C. C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011).
8. X. Q. Wang and Z. G. Wu, Phys. Chem.Chem. Phys. 19, 2148 (2017).
9. S. C. Chen, J. Y. Wu, C. Y. Lin, and M. F. Lin, IOP Publishing 2017, 2053-2563, ISBN: 978-0-7503-1674-3.
10. M. Koshino, H. Aoki, K. Kuroki, S. Kagoshima and T. Osada, Phys. Rev. Lett. 86, 1062 (2001).
11. M. Tau, H. Eschrig and M. Richter, Phys. Rev. B 72, 165304 (2005).
12. Y. P. Lin, C. Y. Lin, Y. H. Ho, T. N. Do and M. F. Lin, PCCP 17, 15921 (2015).
13. D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
14. M. Kohmoto, Ann. Phys. 160, 343 (1985).
15. M. F. Lin and K. W.-K. Shung, Phys. Rev. B 50, 17744 (1994).
16. K. W.-K. Shung, Phys. Rev. B 34, 979 (1986).
17. G. D. Mahan, Springer US 2000, ISBN: 978-0-306-46338-9.
Chapter 3 REFERENCES
1. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
2. R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 46, 1804 (1992).
3. S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. C. Neto, and A. Lanzara, Nature Materials 6, 770 (2007).
4. P. R. Wallace, Phys. Rev. 71, 622 (1947).
5. [1]C.-C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011).
6. C. Lian and J. Ni, Phys. Chem. Chem. Phys. 17, 13366 (2015).
7. Z. Ni, Q. Liu, K. Tang, J. Zheng, J. Zhou, R. Qin, Z. Gao, D. Yu, and J. Lu, Nano Lett. 12, 113 (2012).
18. D. Van Tuan and N. Q. Khanh, Physica E: Low-Dimensional Systems and Nanostructures 54, 267 (2013).
9. M.-F. Lin and F.-L. Shyu, J. Phys. Soc. Jpn. 69, 607 (2000).
10. J.-Y. Wu, S.-C. Chen, O. Roslyak, G. Gumbs, and M.-F. Lin, ACS Nano 5, 1026 (2011).
11. J. H. Ho, C. L. Lu, C. C. Hwang, C. P. Chang, and M. F. Lin, Phys. Rev. B 74, 085406 (2006).
12. Y.-C. Chuang, J.-Y. Wu, and M.-F. Lin, Sci Rep 3, (2013).
13. E. J. G. Santos, Phys. Rev. B 87, 155440 (2013).
14. K. W.-K. Shung, Phys. Rev. B 34, 979 (1986).
15. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, New J. Phys. 8, 318 (2006).
16. C. W. Chiu, S. H. Lee, S. C. Chen, and M. F. Lin, Journal of Applied Physics 106, 113711 (2009).
17. F. L. Shyu and M. F. Lin, Phys. Rev. B 62, 8508 (2000).
18. J. Y. Wu, S. C. Chen, and M. F. Lin, New J. Phys. 16, 125002 (2014).
19. C. J. Tabert and E. J. Nicol, Phys. Rev. B 89, 195410 (2014).
20. J.-Y. Wu, C.-Y. Lin, G. Gumbs, and M.-F. Lin, RSC Adv. 5, 51912 (2015).
21. B. Van Duppen, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B 90, 035142 (2014).
22. H.-R. Chang, J. Zhou, H. Zhang, and Y. Yao, Phys. Rev. B 89, 201411 (2014).
23. V. Despoja, D. Novko, K. Dekanic, M. Łunjic, and L. Maruic, Phys. Rev. B 87, 075447 (2013).
24. S. Y. Shin, C. G. Hwang, S. J. Sung, N. D. Kim, H. S. Kim, and J. W. Chung, Phys. Rev. B 83, 161403 (2011).
25. J. Lu, K. P. Loh, H. Huang, W. Chen, and A. T. S. Wee, Phys. Rev. B 80, 113410 (2009).
26. T. Eberlein, U. Bangert, R. R. Nair, R. Jones, M. Gass, A. L. Bleloch, K. S. Novoselov, A. Geim, and P. R. Briddon, Phys. Rev. B 77, 233406 (2008).
27. P. Wachsmuth, R. Hambach, M. K. Kinyanjui, M. Guzzo, G. Benner, and U. Kaiser, Phys. Rev. B 88, 075433 (2013).
28. C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rmmeli, M. Knupfer, J. Fink,
B. Bchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V.
Olevano, A. G. Marinopoulos, and T. Pichler, Phys. Rev. Lett. 100, 196803 (2008).
29. C. T. Pan, R. R. Nair, U. Bangert, Q. Ramasse, R. Jalil, R. Zan, C. R. Seabourne, and A. J. Scott, Phys. Rev. B 85, 045440 (2012).
30. M. Houssa, G. Pourtois, V. V. Afanasev, and A. Stesmans, Appl. Phys. Lett. 97, 112106 (2010).
31. M. A. Eriksson, A. Pinczuk, B. S. Dennis, S. H. Simon, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 82, 2163 (1999).
32. D. Richards, Phys. Rev. B 61, 7517 (2000).
33. T. P. Devereaux and R. Hackl, Rev. Mod. Phys. 79, 175 (2007).
34. A. F. Garca-Flores, H. Terashita, E. Granado, and Y. Kopelevich, Phys. Rev. B 79, 113105 (2009).
35. T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).
36. C.-H. Park, F. Giustino, C. D. Spataru, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 102, 076803 (2009).
37. 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).
38. 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).
39. S. Huang, W. Kang, and L. Yang, Appl. Phys. Lett. 102, 133106 (2013).
Chapter 4 REFERENCES
1. E. H. Hwang and S. Das Sarma, Phys. Rev. B 75, 205418 (2007).
2. J. H. Ho, C. L. Lu, C. C. Hwang, C. P. Chang, and M. F. Lin, Phys. Rev. B 74, 085406 (2006).
3. C. J. Tabert and E. J. Nicol, Phys. Rev. B 89, 195410 (2014).
4. H.-R. Chang, J. Zhou, H. Zhang, and Y. Yao, Phys. Rev. B 89, 201411 (2014).
5. P.-H. Shih, Y.-H. Chiu, J.-Y. Wu, F.-L. Shyu, and M.-F. Lin, Scientific Reports 7, 40600 (2017).
6. N. B. M. Schrter, M. D. Watson, L. B. Duffy, M. Hoesch, Y. Chen, T. Hesjedal, and T. K. Kim, 2D Mater. 4, 031005 (2017).
7. C. Heske, R. Treusch, F. J. Himpsel, S. Kakar, L. J. Terminello, H. J. Weyer, and E. L. Shirley, Phys. Rev. B 59, 4680 (1999).
8. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, Nature Physics 3, 36 (2007).
9. A. V. Chaplik, J. Exp. Theor. Phys. 33, 977 (1971).
10. G. F. Giuliani and J. J. Quinn, Phys. Rev. B 26, 4421 (1982).
11. T. Ando, J. Phys. Soc. Jpn. 75, 074716 (2006).
12. O. Roslyak, G. Gumbs, and D. Huang, Journal of Applied Physics 109, 113721 (2011).
13. Q. Li and S. Das Sarma, Phys. Rev. B 87, 085406 (2013).
14. E. H. Hwang, B. Y.-K. Hu, and S. Das Sarma, Phys. Rev. B 76, 115434 (2007).
15. L. Algharagholy, S. W. D. Bailey, T. Pope, and C. J. Lambert, Phys. Rev. B 86, 075427 (2012).
16. Z. Ni, E. Minamitani, Y. Ando, and S. Watanabe, Phys. Chem. Chem. Phys. 17, 19039 (2015).
17. C. W. Chiu, S. H. Lee, S. C. Chen, and M. F. Lin, Journal of Applied Physics 106, 113711 (2009).
18. M. E. Dvila, L. Xian, S. Cahangirov, A. Rubio, and G. L. Lay, New J. Phys. 16, 095002 (2014).
19. M. Derivaz, D. Dentel, R. Stephan, M.-C. Hanf, A. Mehdaoui, P. Sonnet, and C. Pirri, Nano Lett. 15, 2510 (2015).
20. V. O. zelik, E. Durgun, and S. Ciraci, J. Phys. Chem. Lett. 5, 2694 (2014).
21. G. D. Mahan, Springer US 2000, ISBN: 978-0-306-46338-9.
22. C.-H. Park, F. Giustino, C. D. Spataru, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 102, 189904 (2009).
23. L. Hung, F. H. da Jornada, J. Souto-Casares, J. R. Chelikowsky, S. G. Louie, and S. gt, Phys. Rev. B 94, 085125 (2016).
Chapter 5 REFERENCES
1. L.-J. Yin, K.-K. Bai, W.-X. Wang, S.-Y. Li, Y. Zhang, and L. He, Front. Phys. 12, 127208 (2017).
2. T.-N. Do, P.-H. Shih, G. Gumbs, D. Huang, C.-W. Chiu, and M.-F. Lin, Phys. Rev. B 97, 125416 (2018).
3. J. L. Lado and J. Fernndez-Rossier, 2D Mater. 3, 035023 (2016).
4. R. Stepniewski, K. Pastor, and M. Grynberg, J. Phys. C: Solid State Phys. 13, 5783 (1980).
5. S. Gopalan, J. K. Furdyna, and S. Rodriguez, Phys. Rev. B 32, 903 (1985).
6. J.-Y.Wu, S.-C. Chen, T.-N. Do,W.-P. Su, and G. Gumbs, ArXiv:1712.09508 [Cond-Mat] (2017).
7. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (2005).
8. K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Falko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, Nature Physics 2, 177 (2006).
9. T.-N. Do, C.-P. Chang, P.-H. Shih, J.-Y. Wu, and M.-F. Lin, Phys. Chem. Chem. Phys. 19, 29525 (2017).
10. R. John and B. Merlin, Journal of Physics and Chemistry of Solids 110, 307 (2017).
11. M.Weinberg, C. Staarmann, C. lschlger, J. Simonet, and K. Sengstock, 2D Mater. 3, 024005 (2016).
12. T.-N. Do, P.-H. Shih, C.-P. Chang, C.-Y. Lin, and M.-F. Lin, Phys. Chem. Chem.
Phys. 18, 17597 (2016).
13. P.-H. Shih, C.-W. Chiu, J.-Y. Wu, T.-N. Do, and M.-F. Lin, Phys. Rev. B 97, 195302 (2018).
14. K. J. Lee, D. Kim, B. C. Jang, D.-J. Kim, H. Park, D. Y. Jung, W. Hong, T. K. Kim,
Y.-K. Choi, and S.-Y. Choi, Advanced Functional Materials 26, 5093 (2016).
15. F. Liu, S. Song, D. Xue, and H. Zhang, Advanced Materials 24, 1089 (2012).
16. Optical Properties of Graphene in Magnetic and Electric Fields (n.d.).
17. S. H. Jhang, M. F. Craciun, S. Schmidmeier, S. Tokumitsu, S. Russo, M. Yamamoto,
Y. Skourski, J. Wosnitza, S. Tarucha, J. Eroms, and C. Strunk, Phys. Rev. B 84, 161408 (2011).
18. R. B. Pontes, R. H. Miwa, A. J. R. da Silva, A. Fazzio, and J. E. Padilha, Phys. Rev. B 97, 235419 (2018).
19. S. Zhao, Y. Lv, and X. Yang, Nanoscale Res Lett 6, 498 (2011).
20. A. Mostofizadeh, Y. Li, B. Song, and Y. Huang, Journal of Nanomaterials (2011).
21. V. Meunier, A. G. Souza Filho, E. B. Barros, and M. S. Dresselhaus, Rev. Mod. Phys. 88, 025005 (2016).
22. E. E. Krasovskii, J. Phys.: Condens. Matter 27, 493001 (2015).
23. S. Wang, Phys. Chem. Chem. Phys. 13, 11929 (2011).
24. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
25. S. Park and H.-S. Sim, Phys. Rev. B 77, 075433 (2008).
26. D. L. Miller, K. D. Kubista, G. M. Rutter, M. Ruan, W. A. de Heer, P. N. First, and J. A. Stroscio, Science 324, 924 (2009).
27. Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, Phys. Rev. Lett. 98, 197403 (2007).
28. S. C. Chen, J. Y. Wu, C. Y. Lin, and M. F. Lin, IOP Publishing 2017, 2053-2563, ISBN: 978-0-7503-1674-3.
29. G. M. Rutter, S. Jung, N. N. Klimov, D. B. Newell, N. B. Zhitenev, and J. A. Stroscio, Nature Physics 7, 649 (2011).
30. G. Li and E. Y. Andrei, Nature Physics 3, 623 (2007).
31. M. Orlita, C. Faugeras, J. Borysiuk, J. M. Baranowski, W. Strupinski, M. Sprinkle,
C. Berger, W. A. de Heer, D. M. Basko, G. Martinez, and M. Potemski, Phys. Rev. B 83, 125302 (2011).
32. P. Plochocka, C. Faugeras, M. Orlita, M. L. Sadowski, G. Martinez, M. Potemski,
M. O. Goerbig, J.-N. Fuchs, C. Berger, and W. A. de Heer, Phys. Rev. Lett. 100, 087401 (2008).
33. P. Plochocka, P. Y. Solane, R. J. Nicholas, J. M. Schneider, B. A. Piot, D. K. Maude, O. Portugall, and G. L. J. A. Rikken, Phys. Rev. B 85, 245410 (2012).
34. R. J. Nicholas, P. Y. Solane, and O. Portugall, Phys. Rev. Lett. 111, 096802 (2013).
Chapter 6 REFERENCES
1. P. Vogt et al., Phys. Rev. Lett. 108, 155501 (2012).
2. Y. K. Huang, S. C. Chen, Y. H. Ho, C. Y. Lin, M. F. Lin, Sci. Rep. 4, 7509-7519 (2014).
3. G. H. Li, A. Luican, and E. Y. Andrei, Phys. Rev. Lett. 102, 176804 (2009).
4. L. J. Yin, Y. Zhang, J. B. Qiao, S. Y. Li, and L. He, Phys. Rev. B 93, 125422 (2016).
5. Y. Borensztein, G. Prevot, and L. Masson, Phys. Rev. B 89, 245410 (2014).
6. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim et al., Nat. Phys. 4 (7), 532-5 (2008).
7. L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao and M. C. Martin, Phys. Rev. B 78 (23), 235408 (2008).
8. J. Y. Wu, S. C. Chen, O. Roslyak, G. Gumbs and M. F. Lin, ACS Nano 5 (2), 1026-1032 (2011).
9. C. Y. Lin, J. Y. Wu, Y. J. Ou, Y. H. Chiu, and M. F. Lin, Phys. Chem. Chem. Phys. 17, 26008-26035 (2015).
10. Y. J. Song, A. F. Otte, Y. Kuk, Y. K. Hu, D. B. Torrance, P. N. First, et al., Nature 467, 185 (2010).
11. W. X. Wang, L. J. Yin, J. B. Qiao, T. Cai, S. Y. Li, R. F. Dou, et al., Phys. Rev. B 92, 165420 (2015).
12. G. M. Rutter, S. Jung, N. N. Klimov, D. B. Newell, N. B. Zhitenev, J. A. Stroscio, Nat. Phys. 7, 649 (2011).
13. L. J. Yin, S. Y. Li, J. B. Qiao, J. C. Nie, and L. He, Phys. Rev. B 91, 115405 (2015).
14. G. H. Li, and E. Y. Andrei, Nat. Phys. 3, 623 (2007).
15. T. Taychatanapat, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, Nat. Phys. 7, 621 (2008).
16. K. F. Mak, J. Shan, T. F. Heinz, Phys. Rev. Lett 104, 176404 (2010).
17. C. Y. Lin, T. N. Do, Y. K. Huang and M. F. Lin, IOP e-book, Online ISBN: 978-0-7503-1566-1 (2017).
18. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim et al., Nat. Phys. 4 (7), 532-5 (2008).
19. L. M. Zhang, Z. Q. Li, D. N. Basov, M. M. Fogler, Z. Hao and M. C. Martin, Phys. Rev. B 78 (23), 235408 (2008).
20. K. F. Mak, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 104, 176404 (2010).
21. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer et al., Phys. Rev. Lett. 102, 037403 (2009).
22. Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim et al., Phys. Rev. Lett. 98, 197403 (2007).
23. P. Plochocka, C. Faugeras, M. Orlita, M. L. Sadowski, G. Martinez, M. Potemski et al., Phys. Rev. Lett. 100, 087401 (2008).
24. K. F. Mak, C. H. Lui, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 102, 256405 (2009).
25. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui C, J. A. Misewich, and T. F. Heinz, Phys. Rev. Lett. 101, 196405 (2008).
26. P. Plochocka, P. Y. Solane, R. J. Nicholas, J. M. Schneider, B. A. Piot, D. K. Maude et al., Phys. Rev. B 85, 245410 (2012).
27. R. J. Nicholas, P. Y. Solane, and O. Portugall, Phys. Rev. Lett. 111, 096802 (2013).
28. M. Orlita, C. Faugeras, J. Borysiuk, J. M. Baranowski, W. Strupinski, M. Sprinkle et al., Phys. Rev. B 83, 125302 (2011).
29. J.-Y. Wu, S.-C. Chen, T.-N. Do, W.-P. Su, G. Gumbs, and M.-F. Lin, Scientific Reports 8, 13303 (2018).

Chapter 7 REFERENCES
1. L. Liu, H. Zhou, R. Cheng, W. J. Yu, Y. Liu, Y. Chen, et al. ACS Nano. 2012; 6:8241.
2. S. Trivedi, A. Srivastava, and R. Kurchania. J. Comput. Theor. Nanosci. 2014; 11: 1-8.
3. C. Y. Lin, J. Y. Wu, Y. H. Chiu, C. P. Chang, and M. F. Lin. Phys. Rev. B 2014; 90: 205434.
4. M. Ezawa. J. Phys. Soc. Jpn. 2012; 81: 064705.
5. M. Tahir and U. Schwingenschlgl. Sci. Rep. 2013; 3: 1075.
6. C. J. Tabert and E. J. Nicol. Phys. Rev. B 2013; 88: 085434.
7. S. A. Yang, H. Pan, and F. Zhang. RSC Adv. 2015; 5: 83350.
8. S. C. Chen, C. L. Wu, J. Y. Wu, and M. F. Lin. Phys. Rev. B 2016; 94: 045410.
9. C. Cobaleda, E. Diez, M. Amado, S. Pezzini, F. Rossella, V. Bellani, et al. Journal of Physics: Conference Series 2013; 456: 012006.
10. K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, et al. Nat. Phys. 2006; 2: 177-180.
11. L. Zhang, Y. Zhang, J. Camacho, M. Khodas, and I. Zaliznyak. Nature Physics 2011; 7: 953-957.
12. C. J. Tabert et al. Phys. Rev. Lett. 2013; 110: 197402.
13. Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, et al. Phys. Rev. Lett. 2007; 98: 197403.
14. C. Faugeras, S. Berciaud, P. Leszczynski, Y. Henni, K. Nogajewski, M. Orlita, et al. Phys. Rev. Lett. 2015; 114: 126804.