Quantum effects in graphene monolayers: Path-integral simulations

Journal of Chemical Physics

Volumn 145, Issue 22, 2016, Pages

  Herrero, Carlos P ^a   Ramírez, Rafael ^a  

^a INSTITUTO DE CIENCIA DE MATERIALES DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; GRAPHENE; MOLECULAR DYNAMICS; POTENTIAL ENERGY; QUANTUM ELECTRONICS; THERMAL EXPANSION;

CLASSICAL MOLECULAR DYNAMICS; INTER-ATOMIC DISTANCES; NUCLEAR QUANTUM EFFECTS; OUT-OF-PLANE DIRECTION; PATH-INTEGRAL MOLECULAR DYNAMICS; PATH-INTEGRAL SIMULATION; QUANTUM DELOCALIZATIONS; THERMAL EXPANSION COEFFICIENTS;

TEMPERATURE;

EID: 85003533176     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4971453     Document Type: Article

References (83)

1. A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007). 10.1038/nmat1849
2. G. W. Flynn, J. Chem. Phys. 135, 050901 (2011). 10.1063/1.3615063
3. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys.81.109
4. J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, Nature 446, 60 (2007). 10.1038/nature05545
5. A. Fasolino, J. H. Los, and M. I. Katsnelson, Nat. Mater. 6, 858 (2007). 10.1038/nmat2011
6. E.-A. Kim and A. H. Castro Neto, EPL 84, 57007 (2008). 10.1209/0295-5075/84/57007
7. B. Amorim, A. Cortijo, F. de Juan, A. G. Grushin, F. Guinea, A. Gutiérrez-Rubio, H. Ochoa, V. Parente, R. Roldán, P. San-Jose et al., Phys. Rep. 617, 1 (2016). 10.1016/j.physrep.2015.12.006
8. M. I. Katsnelson and A. K. Geim, Philos. Trans. R. Soc., A 366, 195 (2008). 10.1098/rsta.2007.2157
9. F. Guinea, M. I. Katsnelson, and M. A. H. Vozmediano, Phys. Rev. B 77, 075422 (2008). 10.1103/PhysRevB.77.075422
10. P. L. de Andres, F. Guinea, and M. I. Katsnelson, Phys. Rev. B 86, 144103 (2012). 10.1103/PhysRevB.86.144103
11. J. H. Warner, Y. Fan, A. W. Robertson, K. He, E. Yoon, and G. D. Lee, Nano Lett. 13, 4937 (2013). 10.1021/nl402902q
12. Y. Wei, B. Wang, J. Wu, R. Yang, and M. L. Dunn, Nano Lett. 13, 26 (2013). 10.1021/nl303168w
13. N. D. Mermin, Phys. Rev. 176, 250 (1968). 10.1103/PhysRev.176.250
14. S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison Wesley, New York, 1994).
15. D. Nelson, T. Piran, and S. Weinberg, Statistical Mechanics of Membranes and Surfaces (World Scientific, London, 2004).
16. P. Tarazona, E. Chacón, and F. Bresme, J. Chem. Phys. 139, 094902 (2013). 10.1063/1.4818421
17. E. Pop, V. Varshney, and A. K. Roy, MRS Bull. 37, 1273 (2012). 10.1557/mrs.2012.203
18. K. C. Fong, E. E. Wollman, H. Ravi, W. Chen, A. A. Clerk, M. D. Shaw, H. G. Leduc, and K. C. Schwab, Phys. Rev. X 3, 041008 (2013). 10.1103/physrevx.3.041008
19. B. Amorim, R. Roldan, E. Cappelluti, A. Fasolino, F. Guinea, and M. I. Katsnelson, Phys. Rev. B 89, 224307 (2014). 10.1103/PhysRevB.89.224307
20. P. Wang, W. Gao, and R. Huang, J. Appl. Phys. 119, 074305 (2016). 10.1063/1.4941987
21. F. Shimojo, R. K. Kalia, A. Nakano, and P. Vashishta, Phys. Rev. B 77, 085103 (2008). 10.1103/PhysRevB.77.085103
22. P. L. de Andres, F. Guinea, and M. I. Katsnelson, Phys. Rev. B 86, 245409 (2012). 10.1103/PhysRevB.86.245409
23. G. M. Chechin, S. V. Dmitriev, I. P. Lobzenko, and D. S. Ryabov, Phys. Rev. B 90, 045432 (2014). 10.1103/PhysRevB.90.045432
24. E. Cadelano, P. L. Palla, S. Giordano, and L. Colombo, Phys. Rev. Lett. 102, 235502 (2009). 10.1103/PhysRevLett.102.235502
25. C. P. Herrero and R. Ramírez, Phys. Rev. B 79, 115429 (2009). 10.1103/PhysRevB.79.115429
26. E. Akatyeva and T. Dumitrica, J. Chem. Phys. 137, 234702 (2012). 10.1063/1.4770002
27. G.-D. Lee, E. Yoon, N.-M. Hwang, C.-Z. Wang, and K.-M. Ho, Appl. Phys. Lett. 102, 021603 (2013). 10.1063/1.4775671
28. J. H. Los, M. I. Katsnelson, O. V. Yazyev, K. V. Zakharchenko, and A. Fasolino, Phys. Rev. B 80, 121405 (2009). 10.1103/PhysRevB.80.121405
29. H.-S. Shen, Y.-M. Xu, and C.-L. Zhang, Appl. Phys. Lett. 102, 131905 (2013). 10.1063/1.4799673
30. Y. Magnin, G. D. Foerster, F. Rabilloud, F. Calvo, A. Zappelli, and C. Bichara, J. Phys.: Condens. Matter 26, 185401 (2014). 10.1088/0953-8984/26/18/185401
31. J. H. Los, A. Fasolino, and M. I. Katsnelson, Phys. Rev. Lett. 116, 015901 (2016). 10.1103/PhysRevLett.116.015901
32. R. Ramírez, E. Chacón, and C. P. Herrero, Phys. Rev. B 93, 235419 (2016). 10.1103/PhysRevB.93.235419
33. M. J. Gillan, Philos. Mag. A 58, 257 (1988). 10.1080/01418618808205187
34. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). 10.1103/RevModPhys.67.279
35. B. G. A. Brito, L. Cândido, G.-Q. Hai, and F. M. Peeters, Phys. Rev. B 92, 195416 (2015). 10.1103/PhysRevB.92.195416
36. F. Calvo and Y. Magnin, Eur. Phys. J. B 89, 56 (2016). 10.1140/epjb/e2016-60839-6
37. N. Mounet and N. Marzari, Phys. Rev. B 71, 205214 (2005). 10.1103/PhysRevB.71.205214
38. T. Shao, B. Wen, R. Melnik, S. Yao, Y. Kawazoe, and Y. Tian, J. Chem. Phys. 137, 194901 (2012). 10.1063/1.4766203
39. W. Gao and R. Huang, J. Mech. Phys. Solids 66, 42 (2014). 10.1016/j.jmps.2014.01.011
40. C. P. Herrero and R. Ramírez, Phys. Rev. B 63, 024103 (2000). 10.1103/PhysRevB.63.024103
41. R. Ramírez, C. P. Herrero, and E. R. Hernández, Phys. Rev. B 73, 245202 (2006). 10.1103/PhysRevB.73.245202
42. C. P. Herrero and R. Ramírez, Phys. Rev. Lett. 99, 205504 (2007). 10.1103/PhysRevLett.99.205504
43. C. P. Herrero and R. Ramírez, Phys. Rev. B 82, 174117 (2010). 10.1103/PhysRevB.82.174117
44. Y. Kwon and D. M. Ceperley, Phys. Rev. B 85, 224501 (2012). 10.1103/PhysRevB.85.224501
45. R. P. Feynman, Statistical Mechanics (Addison-Wesley, New York, 1972).
46. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1990).
47. D. Chandler and P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981). 10.1063/1.441588
48. C. P. Herrero and R. Ramírez, J. Phys.: Condens. Matter 26, 233201 (2014). 10.1088/0953-8984/26/23/233201
49. J. H. Los and A. Fasolino, Phys. Rev. B 68, 024107 (2003). 10.1103/PhysRevB.68.024107
50. J. H. Los, L. M. Ghiringhelli, E. J. Meijer, and A. Fasolino, Phys. Rev. B 72, 214102 (2005). 10.1103/PhysRevB.72.214102
51. L. M. Ghiringhelli, C. Valeriani, J. H. Los, E. J. Meijer, A. Fasolino, and D. Frenkel, Mol. Phys. 106, 2011 (2008). 10.1080/00268970802077884
52. L. M. Ghiringhelli, J. H. Los, A. Fasolino, and E. J. Meijer, Phys. Rev. B 72, 214103 (2005). 10.1103/PhysRevB.72.214103
53. K. V. Zakharchenko, M. I. Katsnelson, and A. Fasolino, Phys. Rev. Lett. 102, 046808 (2009). 10.1103/PhysRevLett.102.046808
54. K. V. Zakharchenko, J. H. Los, M. I. Katsnelson, and A. Fasolino, Phys. Rev. B 81, 235439 (2010). 10.1103/PhysRevB.81.235439
55. K. V. Zakharchenko, A. Fasolino, J. H. Los, and M. I. Katsnelson, J. Phys.: Condens. Matter 23, 202202 (2011). 10.1088/0953-8984/23/20/202202
56. L. M. Ghiringhelli, J. H. Los, E. J. Meijer, A. Fasolino, and D. Frenkel, Phys. Rev. Lett. 94, 145701 (2005). 10.1103/PhysRevLett.94.145701
57. A. Politano, A. R. Marino, D. Campi, D. Farías, R. Miranda, and G. Chiarello, Carbon 50, 4903 (2012). 10.1016/j.carbon.2012.06.019
58. P. Lambin, Appl. Sci. 4, 282 (2014). 10.3390/app4020282
59. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992). 10.1063/1.463137
60. M. E. Tuckerman and A. Hughes, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. F. Coker (Word Scientific, Singapore, 1998), p. 311.
61. G. J. Martyna, A. Hughes, and M. E. Tuckerman, J. Chem. Phys. 110, 3275 (1999). 10.1063/1.478193
62. M. E. Tuckerman, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, edited by J. Grotendorst, D. Marx, and A. Muramatsu (NIC, FZ Jülich, 2002), p. 269.
63. G. J. Martyna, M. E. Tuckerman, D. J. Tobias, and M. L. Klein, Mol. Phys. 87, 1117 (1996). 10.1080/00268979600100761
64. C. P. Herrero, R. Ramírez, and E. R. Hernández, Phys. Rev. B 73, 245211 (2006). 10.1103/PhysRevB.73.245211
65. C. P. Herrero and R. Ramírez, J. Chem. Phys. 134, 094510 (2011). 10.1063/1.3559466
66. M. F. Herman, E. J. Bruskin, and B. J. Berne, J. Chem. Phys. 76, 5150 (1982). 10.1063/1.442815
67. R. Ramírez, N. Neuerburg, M. V. Fernández-Serra, and C. P. Herrero, J. Chem. Phys. 137, 044502 (2012). 10.1063/1.4737862
68. M. J. Gillan, in Computer Modelling of Fluids, Polymers and Solids, edited by C. R. A. Catlow, S. C. Parker, and M. P. Allen (Kluwer, Dordrecht, 1990), p. 155.
69. H. B. Callen, Thermodynamics (John Wiley, New York, 1960).
70. D. C. Wallace, Thermodynamics of Crystals (John Wiley, New York, 1972).
71. M. Pozzo, D. Alfè, P. Lacovig, P. Hofmann, S. Lizzit, and A. Baraldi, Phys. Rev. Lett. 106, 135501 (2011). 10.1103/PhysRevLett.106.135501
72. T. Yamanaka, S. Morimoto, and H. Kanda, Phys. Rev. B 49, 9341 (1994). 10.1103/PhysRevB.49.9341
73. A. K. Ramdas, S. Rodriguez, M. Grimsditch, T. R. Anthony, and W. F. Banholzer, Phys. Rev. Lett. 71, 189 (1993). 10.1103/PhysRevLett.71.189
74. A. Kazimorov, J. Zegenhagen, and M. Cardona, Science 282, 930 (1998). 10.1126/science.282.5390.930
75. E. Chacón, P. Tarazona, and F. Bresme, J. Chem. Phys. 143, 034706 (2015). 10.1063/1.4926938
76. K. R. Hahn, C. Melis, and L. Colombo, J. Phys. Chem. C 120, 3026 (2016). 10.1021/acs.jpcc.5b11556
77. K. H. Michel, S. Costamagna, and F. M. Peeters, Phys. Status Solidi B 252, 2433 (2015). 10.1002/pssb.201552286
78. A. Giansanti and G. Jacucci, J. Chem. Phys. 89, 7454 (1988). 10.1063/1.455276
79. C. P. Herrero and R. Ramírez, Phys. Rev. B 51, 16761 (1995). 10.1103/PhysRevB.51.16761
80. C. P. Herrero, Phys. Rev. B 65, 014112 (2002). 10.1103/PhysRevB.65.014112
81. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon, Oxford, 1980).
82. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed. (Pergamon, Oxford, 1965).
83. K. H. Michel, S. Costamagna, and F. M. Peeters, Phys. Rev. B 91, 134302 (2015). 10.1103/PhysRevB.91.134302