Electron-mediated anharmonicity and its role in the Raman spectrum of graphene
Source abstract
Abstract
Abstract The Raman active G mode in graphene exhibits a strong coupling to electrons, yet the comprehensive treatment of this interaction in the calculation of its temperature-dependent Raman spectrum remains incomplete. In this study, we calculate the temperature dependence of the G-mode frequency and linewidth, and successfully explain the experimental trend by accounting for the contributions arising from the first-order electron-phonon coupling, electron-mediated phonon-phonon coupling, and standard lattice anharmonicity. The generality of our approach enables its broad applicability to study phonon dynamics in materials where both electron-phonon coupling and anharmonicity are important.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Graphene research and applications · Boron and Carbon Nanomaterials Research · Diamond and Carbon-based Materials Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Giustino, F. Electron-phonon interactions from first principles. Rev. Mod. Phys. 89, 015003 (2017).10.1103/RevModPhys.89.015003 ↗
2. Ferrari, A. C. & Basko, D. M. Raman spectroscopy as a versatile tool for studying the properties of graphene. Nat. Nanotechnol. 8, 235 (2013).10.1038/nnano.2013.46 ↗
3. Zhang, X. et al. Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. Chem. Soc. Rev. 44, 2757 (2015).10.1039/C4CS00282B ↗
4. Das, A. et al. Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor. Nat. Nanotechnol. 3, 210 (2008).10.1038/nnano.2008.67 ↗
5. Tan, P.-H. et al. The shear mode of multi-layer graphene. Nat. Mater. 294 https://doi.org/10.1038/nmat3245 (2011).10.1038/nmat3245 ↗
6. Zhao, Y. et al. Inter layer breathing and shear modes in few-trilayer MoS2 and WSe2. Nano Lett. 13 (2013).10.1021/nl304169w ↗
7. Rafailov, P., Dworzak, M. & Thomsen, C. Luminescence and raman spectroscopy on mgb2. Solid State Commun. 122, 455–458 (2002).10.1016/S0038-1098(02)00158-8 ↗
8. Yoon, D. et al. Fano resonance in Raman scattering of graphene. Carbon 61, 373–378 (2013).10.1016/j.carbon.2013.05.019 ↗
9. Sohier, T. et al. Enhanced electron-phonon interaction in multivalley materials. Phys. Rev. X 9, 031019 (2019).
10. Sarkar, S. et al. Anharmonicity in Raman-active phonon modes in atomically thin MoS2. Phys. Rev. B 101, 205302 (2020).10.1103/PhysRevB.101.205302 ↗
11. Paul, S., Karak, S., Mathew, A., Ram, A. & Saha, S. Electron-phonon and phonon-phonon anharmonic interactions in 2h–MoX2 (x = S, Te): A comprehensive resonant Raman study. Phys. Rev. B 104, 075418 (2021).10.1103/PhysRevB.104.075418 ↗
12. Berciaud, S. et al. Electron and optical phonon temperatures in electrically biased graphene. Phys. Rev. Lett. 104, 227401 (2010).10.1103/PhysRevLett.104.227401 ↗
13. Ferrante, C. et al. Raman spectroscopy of graphene under ultrafast laser excitation. Nat. Commun. 9, 308 (2018).10.1038/s41467-017-02508-x ↗
14. Howard, C. A., Dean, M. P. M. & Withers, F. Phonons in potassium-doped graphene: The effects of electron-phonon interactions, dimensionality, and adatom ordering. Phys. Rev. B 84, 241404 (2011).10.1103/PhysRevB.84.241404 ↗
15. Maksimov, E. & Shulga, S. Nonadiabatic effects in optical phonon self-energy. Solid State Commun. 97, 553 (1996).10.1016/0038-1098(95)00745-8 ↗
16. Engelsberg, S. & Schrieffer, J. R. Coupled electron-phonon system. Phys. Rev. 131, 993 (1963).10.1103/PhysRev.131.993 ↗
17. Caruso, F. et al. Nonadiabatic Kohn anomaly in heavily boron-doped diamond. Phys. Rev. Lett. 119, 017001 (2017).10.1103/PhysRevLett.119.017001 ↗
18. Cappelluti, E. Electron-phonon effects on the Raman spectrum in Mgb2. Phys. Rev. B 73, 140505 (2006).10.1103/PhysRevB.73.140505 ↗
19. Ponosov, Y. S. & Streltsov, S. V. Raman evidence for nonadiabatic effects in optical phonon self-energies of transition metals. Phys. Rev. B 94, 214302 (2016).10.1103/PhysRevB.94.214302 ↗
20. Ponosov, Y. S., Bolotin, G. A., Thomsen, C. & Cardona, M. Raman scattering in os: Nonadiabatic renormalization of the optical phonon self-energies. Phys. Status Solidi (b) 208, 257 (1998).10.1002/(SICI)1521-3951(199807)208:1<257::AID-PSSB257>3.0.CO;2-F ↗
21. Novko, D. Nonadiabatic coupling effects in MgB2 reexamined. Phys. Rev. B 98, 041112 (2018).10.1103/PhysRevB.98.041112 ↗
22. Novko, D. Broken adiabaticity induced by Lifshitz transition in MoS2 and WS2 single layers. Commun. Phys. 3, 1 (2020).10.1038/s42005-020-0299-1 ↗
23. Garcia-Goiricelaya, P., Lafuente-Bartolome, J., Gurtubay, I. G. & Eiguren, A. Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2. Phys. Rev. B 101, 054304 (2020).10.1103/PhysRevB.101.054304 ↗
24. Girotto, N. & Novko, D. Dynamical renormalization of electron-phonon coupling in conventional superconductors. Phys. Rev. B 107, 064310 (2023).10.1103/PhysRevB.107.064310 ↗
25. Novko, D., Caruso, F., Draxl, C. & Cappelluti, E. Ultrafast hot phonon dynamics in MgB2 driven by anisotropic electron-phonon coupling. Phys. Rev. Lett. 124, 077001 (2020).10.1103/PhysRevLett.124.077001 ↗
26. Pisana, S. et al. Breakdown of the adiabatic Born–Oppenheimer approximation in graphene. Nat. Mater. 6, 198 (2007).10.1038/nmat1846 ↗
27. Lazzeri, M. & Mauri, F. Nonadiabatic Kohn anomaly in a doped graphene monolayer. Phys. Rev. Lett. 97, 266407 (2006).10.1103/PhysRevLett.97.266407 ↗
28. Saitta, A. M., Lazzeri, M., Calandra, M. & Mauri, F. Giant nonadiabatic effects in layer metals: Raman spectra of intercalated graphite explained. Phys. Rev. Lett. 100, 226401 (2008).10.1103/PhysRevLett.100.226401 ↗
29. Piscanec, S., Lazzeri, M., Robertson, J., Ferrari, A. C. & Mauri, F. Optical phonons in carbon nanotubes: Kohn anomalies, Peierls distortions, and dynamic effects. Phys. Rev. B 75, 035427 (2007).10.1103/PhysRevB.75.035427 ↗
30. Hu, S.-Q. et al. Nonadiabatic electron-phonon coupling and its effects on superconductivity. Phys. Rev. B 105, 224311 (2022).10.1103/PhysRevB.105.224311 ↗
31. Hu, S.-Q., Chen, D.-Q., Zhang, S.-J., Liu, X.-B. & Meng, S. Probing precise interatomic potentials by nonadiabatic nonlinear phonons. Mater. Today Phys. 27, 100790 (2022).10.1016/j.mtphys.2022.100790 ↗
32. Bonini, N., Lazzeri, M., Marzari, N. & Mauri, F. Phonon anharmonicities in graphite and graphene. Phys. Rev. Lett. 99, 176802 (2007).10.1103/PhysRevLett.99.176802 ↗
33. Linas, S. et al. Interplay between Raman shift and thermal expansion in graphene: Temperature-dependent measurements and analysis of substrate corrections. Phys. Rev. B 91, 075426 (2015).10.1103/PhysRevB.91.075426 ↗
34. Calizo, I., Balandin, A. A., Bao, W., Miao, F. & Lau, C. N. Temperature dependence of the Raman spectra of graphene and graphene multilayers. Nano Lett. 7, 2645–9 (2007).10.1021/nl071033g ↗
35. Shaina, P. R., George, L., Yadav, V. & Jaiswal, M. Estimating the thermal expansion coefficient of graphene: the role of graphene-substrate interactions. J. Phys.: Condens. Matter 28, 085301 (2016).
36. Yoon, D., Son, Y.-W. & Cheong, H. Negative thermal expansion coefficient of graphene measured by Raman spectroscopy. Nano Lett. 11, 3227–31 (2011).10.1021/nl201488g ↗
37. Tian, S. et al. Temperature-dependent Raman investigation on suspended graphene: Contribution from thermal expansion coefficient mismatch between graphene and substrate. Carbon 104, 27–32 (2016).10.1016/j.carbon.2016.03.046 ↗
38. Lee, Y.-R., Huang, J., Lin, J.-C. & Lee, J.-R. Study of the substrate-induced strain of the as-grown graphene on cu(100) using temperature-dependent Raman spectroscopy: Estimating the mode-gruneisen parameter with temperature. J. Phys. Chem. C. 121, 27427 (2017).10.1021/acs.jpcc.7b08170 ↗
39. Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).10.1103/PhysRevLett.97.187401 ↗
40. Tuinstra, F. & Koenig, J. L. Raman spectrum of graphite. J. Chem. Phys. 53, 1126–1130 (1970).10.1063/1.1674108 ↗
41. Everall, N., Lumsdon, J. & Christopher, D. The effect of laser-induced heating upon the vibrational Raman spectra of graphites and carbon fibres. Carbon 29, 133–137 (1991).10.1016/0008-6223(91)90064-P ↗
42. Tan, P., Deng, Y., Zhao, Q. & Cheng, W. The intrinsic temperature effect of the Raman spectra of graphite. Appl. Phys. Lett. 74, 1818–1820 (1999).10.1063/1.123096 ↗
43. Sonntag, J., Watanabe, K., Taniguchi, T., Beschoten, B. & Stampfer, C. Charge carrier density dependent Raman spectra of graphene encapsulated in hexagonal boron nitride. Phys. Rev. B 107, 075420 (2023).10.1103/PhysRevB.107.075420 ↗
44. Liu, H.-N., Cong, X., Lin, M.-L. & Tan, P.-H. The intrinsic temperature-dependent Raman spectra of graphite in the temperature range from 4 k to 1000 k. Carbon 152, 451–458 (2019).10.1016/j.carbon.2019.05.016 ↗
45. Hlinka, J. et al. Lattice dynamics of Cac6 by Raman spectroscopy. Phys. Rev. B 76, 144512 (2007).10.1103/PhysRevB.76.144512 ↗
46. Chacón-Torres, J. C., Ganin, A. Y., Rosseinsky, M. J. & Pichler, T. Raman response of stage-1 graphite intercalation compounds revisited. Phys. Rev. B 86, 075406 (2012).10.1103/PhysRevB.86.075406 ↗
47. Casiraghi, C. Probing disorder and charged impurities in graphene by Raman spectroscopy. Phys. Status Solidi (RRL) - Rapid Res. Lett. 3, 175 – 177 (2009).
48. Lin, J. et al. Anharmonic phonon effects in Raman spectra of unsupported vertical graphene sheets. Phys. Rev. B 83, 125430 (2011).10.1103/PhysRevB.83.125430 ↗
49. Han, Z. et al. Raman linewidth contributions from four-phonon and electron-phonon interactions in graphene. Phys. Rev. Lett. 128, 045901 (2022).10.1103/PhysRevLett.128.045901 ↗
50. Chae, D.-H., Krauss, B., Klitzing, K. & Smet, J. Hot phonons in an electrically biased graphene constriction. Nano Lett. 10, 466–71 (2010).10.1021/nl903167f ↗
51. Tiberj, A. et al. Reversible optical doping of graphene. Sci. Rep. 3, 2355 (2013).10.1038/srep02355 ↗
52. Coulter, J. et al. Uncovering electron-phonon scattering and phonon dynamics in type-I Weyl semimetals. Phys. Rev. B 100, 220301 (2019).10.1103/PhysRevB.100.220301 ↗
53. Montagnac, G., Caracas, R., Bobocioiu, E., Vittoz, F. & Reynard, B. Anharmonicity of graphite from UV Raman spectroscopy to 2700 k. Carbon 54, 68–75 (2013).10.1016/j.carbon.2012.11.004 ↗
54. Chen, X. et al. Intrinsic phonon anharmonicity in heavily doped graphene probed by Raman spectroscopy. Carbon 185, 282–288 (2021).10.1016/j.carbon.2021.09.017 ↗
55. Giura, P. et al. Temperature evolution of infrared- and Raman-active phonons in graphite. Phys. Rev. B 86, 121404 (2012).10.1103/PhysRevB.86.121404 ↗
56. Ando, T. Anomaly of optical phonon in monolayer graphene. J. Phys. Soc. Jpn. 75, 124701 (2006).10.1143/JPSJ.75.124701 ↗
57. Chen, X. et al. Control of Raman scattering quantum interference pathways in graphene. ACS Nano 17, 5956 (2023).10.1021/acsnano.3c00180 ↗
58. Ponosov, Y. S., Loa, I., Mogilenskikh, V. E. & Syassen, K. Raman scattering in osmium under pressure. Phys. Rev. B 71, 220301 (2005).10.1103/PhysRevB.71.220301 ↗
59. Bohnen, K.-P., Heid, R. & Renker, B. Phonon dispersion and electron-phonon coupling in mgb2 and alb2. Phys. Rev. Lett. 86, 5771–5774 (2001).10.1103/PhysRevLett.86.5771 ↗
60. Kortus, J., Mazin, I. I., Belashchenko, K. D., Antropov, V. P. & Boyer, L. L. Superconductivity of metallic boron in mgb2. Phys. Rev. Lett. 86, 4656–4659 (2001).10.1103/PhysRevLett.86.4656 ↗
61. Liu, A. Y., Mazin, I. I. & Kortus, J. Beyond eliashberg superconductivity in MgB2: Anharmonicity, two-phonon scattering, and multiple gaps. Phys. Rev. Lett. 87, 087005 (2001).10.1103/PhysRevLett.87.087005 ↗
62. Choi, H. J., Roundy, D., Sun, H., Cohen, M. L. & Louie, S. G. The origin of the anomalous superconducting properties of MgB2. Nature 418, 758 (2002).10.1038/nature00898 ↗
63. Eiguren, A. & Ambrosch-Draxl, C. Wannier interpolation scheme for phonon-induced potentials: Application to bulk MgB2, w, and the (1×1) h-covered w(110) surface. Phys. Rev. B 78, 045124 (2008).10.1103/PhysRevB.78.045124 ↗
64. Calandra, M., Profeta, G. & Mauri, F. Adiabatic and nonadiabatic phonon dispersion in a Wannier function approach. Phys. Rev. B 82, 165111 (2010).10.1103/PhysRevB.82.165111 ↗
65. Margine, E. R. & Giustino, F. Anisotropic Migdal-Eliashberg theory using Wannier functions. Phys. Rev. B 87, 024505 (2013).10.1103/PhysRevB.87.024505 ↗
66. Yildirim, T. et al. Giant anharmonicity and nonlinear electron-phonon coupling in MgB2: A combined first-principles calculation and neutron scattering study. Phys. Rev. Lett. 87, 037001 https://doi.org/10.1103/PhysRevLett.87.037001. (2001).10.1103/PhysRevLett.87.037001 ↗
67. Ponosov, Y. S. & Streltsov, S. V. Raman-active E2g phonon in mgb2: Electron-phonon interaction and anharmonicity. Phys. Rev. B 96, 214503 (2017).10.1103/PhysRevB.96.214503 ↗
68. Novko, D., Alducin, M., Blanco-Rey, M. & Juaristi, J. I. Effects of electronic relaxation processes on vibrational linewidths of adsorbates on surfaces: The case of co/cu(100). Phys. Rev. B 94, 224306 (2016).10.1103/PhysRevB.94.224306 ↗
69. Novko, D., Alducin, M. & Juaristi, J. I. Electron-mediated phonon-phonon coupling drives the vibrational relaxation of co on cu(100). Phys. Rev. Lett. 120, 156804 (2018).10.1103/PhysRevLett.120.156804 ↗
70. Marsiglio, F. & Carbotte, J. P. Electron-Phonon Superconductivity, 73 https://doi.org/10.1007/978-3-540-73253-2_3 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008).10.1007/978-3-540-73253-2_3 ↗
71. Kupčić, I. & Barišić, S. Optical properties of the q1d multiband models – the transverse equation of motion approach. Fiz. A 14, 47 (2005).
72. Kupčić, I. Intraband memory function and memory-function conductivity formula in doped graphene. Phys. Rev. B 95, 035403 (2017).10.1103/PhysRevB.95.035403 ↗
73. Novko, D. Dopant-induced plasmon decay in graphene. Nano Lett. 17, 6991 (2017).10.1021/acs.nanolett.7b03553 ↗
74. Kupčić, I. General theory of intraband relaxation processes in heavily doped graphene. Phys. Rev. B 91, 205428 (2015).10.1103/PhysRevB.91.205428 ↗
75. Allen, P. B. Electron self-energy and generalized Drude formula for infrared conductivity of metals. Phys. Rev. B 92, 054305 (2015).10.1103/PhysRevB.92.054305 ↗
76. Sharapov, S. G. & Carbotte, J. P. Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state. Phys. Rev. B 72, 134506 (2005).10.1103/PhysRevB.72.134506 ↗
77. Chakraborty, B. & Allen, P. B. Solids with thermal or static disorder. ii. optical properties. Phys. Rev. B 18, 5225–5235 (1978).10.1103/PhysRevB.18.5225 ↗
78. Kupčić, I. Raman spectroscopy of collective modes in charge-density-wave systems: The mean-field microscopic theory. J. Raman Spectrosc. 40, 442 – 452 (2008).
79. Antonius, G. & Louie, S. G. Theory of exciton-phonon coupling. Phys. Rev. B 105, 085111 (2022).10.1103/PhysRevB.105.085111 ↗
80. Holstein, T. Theory of transport phenomena in an electron-phonon gas. Ann. Phys. 29, 410–535 (1964).10.1016/0003-4916(64)90008-9 ↗
81. Profeta, G., Calandra, M. & Mauri, F. Phonon-mediated superconductivity in graphene by lithium deposition. Nat. Phys. 8, 131 (2012).10.1038/nphys2181 ↗
82. Ludbrook, B. M. et al. Evidence for superconductivity in Li-decorated monolayer graphene. Proc. Natl Acad. Sci. 112, 11795 (2015).10.1073/pnas.1510435112 ↗
83. Ichinokura, S., Sugawara, K., Takayama, A., Takahashi, T. & Hasegawa, S. Superconducting calcium-intercalated bilayer graphene. ACS Nano 10, 2761 (2016).10.1021/acsnano.5b07848 ↗
84. Weller, T. E., Ellerby, M., Saxena, S. S., Smith, R. P. & Skipper, N. T. Superconductivity in the intercalated graphite compounds c6yb and c6ca. Nat. Phys. 1, 39 (2005).10.1038/nphys0010 ↗
85. Calandra, M. & Mauri, F. Theoretical explanation of superconductivity in c6Ca. Phys. Rev. Lett. 95, 237002 (2005).10.1103/PhysRevLett.95.237002 ↗
86. Varma, C. M. & Simons, A. L. Strong-coupling theory of charge-density-wave transitions. Phys. Rev. Lett. 51, 138 (1983).10.1103/PhysRevLett.51.138 ↗
87. Yoshiyama, H., Takaoka, Y., Suzuki, N. & Motizuki, K. Effects on lattice fluctuations on the charge-density-wave transition in transition-metal dichalcogenides. J. Phys. C: Solid State Phys. 19, 5591 (1986).10.1088/0022-3719/19/28/011 ↗
88. Flicker, F. & van Wezel, J. Charge order from orbital-dependent coupling evidenced by NbSe2. Nat. Commun. 6, 7034 (2015).10.1038/ncomms8034 ↗
89. Yan, H. et al. Time-resolved Raman spectroscopy of optical phonons in graphite: Phonon anharmonic coupling and anomalous stiffening. Phys. Rev. B 80, 121403 (2009).10.1103/PhysRevB.80.121403 ↗
90. Ishioka, K. et al. Ultrafast electron-phonon decoupling in graphite. Phys. Rev. B 77, 121402 (2008).10.1103/PhysRevB.77.121402 ↗
91. Hu, S.-Q. et al. Tracking photocarrier-enhanced electron-phonon coupling in nonequilibrium. npj Quantum Mater. 7, 14 (2022).10.1038/s41535-021-00421-7 ↗
92. Girotto, N. & Novko, D. Dynamical phonons following electron relaxation stages in photoexcited graphene. J. Phys. Chem. Lett. 14, 8709 (2023).10.1021/acs.jpclett.3c01905 ↗
93. Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515 (2001).10.1103/RevModPhys.73.515 ↗
94. Ponosov, Y., Thomsen, C. & Cardona, M. Electronic Raman scattering and phonon self-energy effects in osmium. Phys. C: Supercond. 235-240, 1153–1154 (1994).10.1016/0921-4534(94)91801-5 ↗
95. Cerdeira, F. & Cardona, M. Effect of carrier concentration on the raman frequencies of Si and Ge. Phys. Rev. B 5, 1440 (1972).10.1103/PhysRevB.5.1440 ↗
96. Knigavko, A. N., Carbotte, J. P. & Marsiglio, F. Observation of phonon structure in electron density of states of a normal metal. Europhys. Lett. 71, 776 (2005).10.1209/epl/i2005-10156-5 ↗
97. Bianco, R. & Errea, I. Non-perturbative theory of the electron-phonon coupling and its first-principles implementation. arxiv 2303.02621 https://arxiv.org/abs/2303.02621. (2023).
98. Marsiglio, F., Akis, R. & Carbotte, J. P. Phonon self-energy effects due to superconductivity: A real-axis formulation. Phys. Rev. B 45, 9865–9871 (1992).10.1103/PhysRevB.45.9865 ↗
99. Puchkov, A. V., Basov, D. N. & Timusk, T. The pseudogap state in high- superconductors: an infrared study. J. Phys.: Condens. Matter 8, 10049 (1996).
100. Carbotte, J., Schachinger, E. & Basov, D. Coupling strength of charge carriers to spin fluctuations in high-temperature superconductors. Nature 401, 354–6 (1999).10.1038/43843 ↗