Theory of double-resonant Raman spectra in graphene: Intensity and line shape of defect-induced and two-phonon bands

声子 物理 强度(物理) 谱线 激光线宽 石墨烯 拉曼光谱 激发 原子物理学 密度泛函理论 拉曼散射 分子物理学 材料科学 凝聚态物理 光学 量子力学 激光器 纳米技术
作者
Pedro Venezuela,Michele Lazzeri,Francesco Mauri
出处
期刊:Physical Review B [American Physical Society]
卷期号:84 (3) 被引量:541
标识
DOI:10.1103/physrevb.84.035433
摘要

We calculate the double-resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes (such as in the $D$ line at $\ensuremath{\sim}$1350 cm${}^{\ensuremath{-}1}$, ${D}^{\ensuremath{'}}$ at $\ensuremath{\sim}$1600 cm${}^{\ensuremath{-}1}$, and ${D}^{\ensuremath{'}\ensuremath{'}}$ at $\ensuremath{\sim}$1100 cm${}^{\ensuremath{-}1}$), and two-phonon ones (such as in the $2D$, $2{D}^{\ensuremath{'}}$, or $D+{D}^{\ensuremath{'}\ensuremath{'}}$ lines). Phonon and electronic dispersions reproduce calculations based on density-functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kinds of idealized defects. For an excitation energy of ${\ensuremath{\epsilon}}_{L}=2.4$ eV, the agreement with measurements is very good and calculations reproduce the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the $D$, ${D}^{\ensuremath{'}}$, $2D$, and $2{D}^{\ensuremath{'}}$ lines; the line shapes; the presence of small intensity lines in the 1800--2000-cm${}^{\ensuremath{-}1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects, and on their concentration. According to the present findings, the intensity ratio between the $2{D}^{\ensuremath{'}}$ and $2D$ lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and ${D}^{\ensuremath{'}}$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal. The present analysis reveals that, for both $D$ and $2D$ lines, the dominant DR processes are those in which electrons and holes are both involved in the scattering, because of a destructive quantum interference that kills processes involving only electrons or only holes. The most important phonons belong to the $\mathbf{K}\ensuremath{\rightarrow}\mathbit{\ensuremath{\Gamma}}$ direction ($inner$ phonons) and not to the K $\ensuremath{\rightarrow}$ M one ($outer$ phonons), as usually assumed. The small $2D$ linewidth at ${\ensuremath{\epsilon}}_{L}=2.4$ eV is a consequence of the interplay between the opposite trigonal warpings of the electron and phonon dispersions. At higher excitation, e.g., ${\ensuremath{\epsilon}}_{L}=3.8$ eV, the $2D$ line becomes broader and evolves in an asymmetric double peak structure.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
徐小赞发布了新的文献求助10
刚刚
结实大白完成签到,获得积分10
1秒前
PRIPRO关注了科研通微信公众号
1秒前
魔幻的觅珍完成签到,获得积分10
1秒前
文献达人完成签到,获得积分10
1秒前
1秒前
1秒前
共享精神应助欢喜的心情采纳,获得10
1秒前
冰千蕙发布了新的文献求助10
2秒前
MZ发布了新的文献求助10
3秒前
时尚战斗机应助善良的人采纳,获得10
3秒前
4秒前
领导范儿应助满anna采纳,获得10
4秒前
秦玉蓉发布了新的文献求助10
5秒前
6秒前
必中完成签到,获得积分20
7秒前
英姑应助wang采纳,获得10
8秒前
所所应助ylver采纳,获得50
8秒前
reirei应助sun_lin采纳,获得10
9秒前
眼睛大雨筠应助云ch采纳,获得60
10秒前
热心市民小红花应助Cici采纳,获得10
12秒前
秦玉蓉完成签到,获得积分10
12秒前
传奇3应助微微采纳,获得10
13秒前
13秒前
美丽灵活呜呜豹完成签到,获得积分10
15秒前
香蕉觅云应助CQ采纳,获得10
17秒前
17秒前
Salut完成签到,获得积分10
18秒前
量子星尘发布了新的文献求助10
18秒前
传奇3应助gu采纳,获得10
18秒前
19秒前
19秒前
默默安双完成签到 ,获得积分20
21秒前
ZXCVB发布了新的文献求助10
21秒前
pipi发布了新的文献求助10
22秒前
曹璐瑶发布了新的文献求助10
22秒前
24秒前
里德完成签到 ,获得积分10
24秒前
qq发布了新的文献求助10
24秒前
25秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
Cognitive Neuroscience: The Biology of the Mind 1000
Technical Brochure TB 814: LPIT applications in HV gas insulated switchgear 1000
Toward a Combinatorial Approach for the Prediction of IgG Half-Life and Clearance 500
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 500
Picture Books with Same-sex Parented Families: Unintentional Censorship 500
Nucleophilic substitution in azasydnone-modified dinitroanisoles 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3969940
求助须知:如何正确求助?哪些是违规求助? 3514642
关于积分的说明 11175298
捐赠科研通 3249947
什么是DOI,文献DOI怎么找? 1795178
邀请新用户注册赠送积分活动 875617
科研通“疑难数据库(出版商)”最低求助积分说明 804891