吳江濱，張昕，韓文鵬，喬曉粉，M.Ij?s，A.C.Ferrari,譚平恒*

(1.中國(guó)科學(xué)院半導(dǎo)體研究所，半導(dǎo)體超晶格國(guó)家重點(diǎn)實(shí)驗(yàn)室，北京　100083;

2.CGC,University of Cambridge,9 JJ Thomson Avenue,Cambridge CB3 0FA,UK)

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轉(zhuǎn)角多層石墨烯層間耦合的共振拉曼光譜研究

吳江濱1，張昕1，韓文鵬1，喬曉粉1，M.Ij?s2，A.C.Ferrari2,譚平恒1*

(1.中國(guó)科學(xué)院半導(dǎo)體研究所，半導(dǎo)體超晶格國(guó)家重點(diǎn)實(shí)驗(yàn)室，北京100083;

2.CGC,University of Cambridge,9 JJ Thomson Avenue,Cambridge CB3 0FA,UK)

摘要:我們通過共振拉曼光譜測(cè)量了轉(zhuǎn)角多層石墨烯的層間振動(dòng)模式：剪切模和呼吸模。根據(jù)改進(jìn)的線性模型，我們發(fā)現(xiàn)在轉(zhuǎn)角多層石墨烯界面處的層間呼吸耦合與正常Bernal堆垛多層石墨烯的強(qiáng)度相當(dāng)。此結(jié)果明顯不同于層間剪切耦合，后者在轉(zhuǎn)角多層石墨烯界面處的層間剪切耦合減弱到了正常Bernal堆垛多層石墨烯的20%。另外，我們首次發(fā)現(xiàn)層間呼吸耦合存在著次近鄰原子層之間的相互作用，其強(qiáng)度為最近鄰的9%。我們發(fā)現(xiàn)當(dāng)采用與界面層間旋轉(zhuǎn)角度相對(duì)應(yīng)的激發(fā)光時(shí)，轉(zhuǎn)角多層石墨烯的拉曼信號(hào)得到極大的增強(qiáng)。為此，我們引入光學(xué)躍遷允許的電子聯(lián)合態(tài)密度的概念，通過理論計(jì)算，我們發(fā)現(xiàn)這種聯(lián)合態(tài)密度的極大值決定了拉曼信號(hào)共振線型的激發(fā)光能量極值。本研究表明，層間振動(dòng)模式是探測(cè)二維層狀異質(zhì)層間耦合的有效手段，為其在器件應(yīng)用方面的研究奠定了基礎(chǔ)。

關(guān)鍵詞：石墨烯;層間剪切模;層間呼吸模;二維異質(zhì)結(jié);拉曼光譜

1引言

以石墨烯為代表的二維材料具有優(yōu)良的電學(xué)性能和光學(xué)性能，因此被期待可用來發(fā)展更薄、導(dǎo)電速度更快的新一代電子元件，晶體管和光電器件[1-3]。將石墨烯堆疊起來可以得到多層石墨烯[4]。除了具有和體石墨相同的Bernal堆垛(即AB堆垛)方式的多層石墨烯之外[5]，還可以在實(shí)驗(yàn)室制備或者合成出不同石墨烯片層取向隨機(jī)的多層石墨烯，即轉(zhuǎn)角多層石墨烯[6-9]。轉(zhuǎn)角多層石墨烯內(nèi)各子系統(tǒng)的層數(shù)不同和各子系統(tǒng)間旋轉(zhuǎn)角度的不同將使得其具有無限多的可能性，這無疑大大豐富了石墨烯材料的研究對(duì)象和研究?jī)?nèi)容：例如單層或多層石墨烯堆垛方式的差異有可能導(dǎo)致石墨烯片層不同的層間耦合，從而影響其電子能帶結(jié)構(gòu)，使得轉(zhuǎn)角多層石墨烯具有與其堆垛方式相應(yīng)的各種各樣的光電性質(zhì)[10-15]。因此，探測(cè)和理解這種層間耦合就變得至關(guān)重要。

二維層狀材料的層間剪切模(C模)和層間呼吸模(LBM)直接反映了層間耦合的性質(zhì)[16-17]。對(duì)于一個(gè)N層的層狀二維材料，存在N-1個(gè)的C模和LBM模，我們將其記為CNN-i和LBMNN-i(i=1,2,…,N-1)，其中CN1和LBMN1表示頻率最高的模式[8-9,18]。多層石墨烯的C模已經(jīng)被成功地觀測(cè)到，并且可以用來探測(cè)狄拉克點(diǎn)(Dirac point)附近能量為幾個(gè)meV的電子激發(fā)[19]。到目前為止，因?yàn)閷?duì)稱性和相對(duì)弱的電聲子耦合等原因，多層石墨烯的LBM在常溫下還未能被觀察到[20]。

在這里，我們將層數(shù)為n的AB堆垛的石墨烯(nLG，n≥1)和層數(shù)為m的AB堆垛的石墨烯(mLG，m≥1)以一定的角度θ堆垛到一起，形成m+n層的轉(zhuǎn)角多層石墨烯(t(m+n)LG)。通過選擇與旋轉(zhuǎn)角度相對(duì)應(yīng)的激發(fā)光，系統(tǒng)地探測(cè)了t(m+n)LG的C模和LBM。我們發(fā)現(xiàn)在t(m+n)LG中探測(cè)到了來自nLG和mLG的C模和來自t(m+n)LG的LBM。通過改進(jìn)的線性原子鏈模型[21](LCM)擬合發(fā)現(xiàn)轉(zhuǎn)角界面處的剪切耦合為AB堆垛界面處的20%，而呼吸耦合并沒有明顯的變化。此外，我們發(fā)現(xiàn)存在著次近鄰原子層的呼吸耦合，其強(qiáng)度為最近鄰原子層耦合的9%。最后，我們提出了“光學(xué)躍遷允許的聯(lián)合態(tài)密度(JDOSOAT)”的概念，很好地解釋了在t(m+n)LG中拉曼信號(hào)的共振增強(qiáng)現(xiàn)象。

2實(shí)驗(yàn)裝置

本文所用的t(m+n)LG是通過機(jī)械剝離法或者轉(zhuǎn)移法制備的。同時(shí)利用光學(xué)襯度方法[22-24](optical contrast)和原子力顯微鏡(atomic force microscopy)確定了樣品層數(shù)。所涉及到的拉曼光譜測(cè)試是采用法國(guó)Horiba Jobin Yvon公司的LabRam HR800共焦顯微拉曼光譜儀。所使用的能量為1.58和1.71 eV的激光是來自鈦寶石激光器，能量為1.96，2.03，2.09和2.28 eV的激光是來自He-Ne激光器，能量為1.83，1.92，2.18，2.34和2.41 eV的激光是來自Kr+激光器，以及能量為2.54和2.67 eV的激光是來自Ar+激光器。為防止出現(xiàn)樣品的加熱效應(yīng)，測(cè)試?yán)庾V所用的激光功率低于0.5mW。為了探測(cè)超低頻率的拉曼信號(hào)，我們采用了四塊光密度(optical density)為3，光譜帶寬(spectral bandwidth)為5~10 cm-1的體布拉格光柵(BragGrate notch filters)去除瑞利線(Rayleigh line)。當(dāng)激發(fā)光能量為2.41 eV時(shí)光譜分辨率為0.54 cm-1。轉(zhuǎn)角多層石墨烯的能帶結(jié)構(gòu)是由DFTB+軟件包[25-27]計(jì)算的。另外，我們采用緊束縛方法計(jì)算了光學(xué)躍遷矩陣元[28-29]。

3結(jié)果與討論

圖1a為t(1+1)LG和t(1+3)LG的光學(xué)圖像，圖1b展示了它們的光學(xué)襯度譜。與(m+n)LG相，比t(m+n)LG的光學(xué)襯度譜多出了一個(gè)吸收峰。這個(gè)吸收峰來自于界面層間旋轉(zhuǎn)導(dǎo)致的能帶結(jié)構(gòu)變化，這點(diǎn)將在后文進(jìn)行詳細(xì)地討論。圖1c畫出了t(1+3)LG的拉曼光譜。在G模兩側(cè)存在著兩個(gè)相對(duì)較弱的模式，通常稱其為R(1510 cm-1)和R’(1618 cm-1)模。這兩個(gè)模式是來自于上下兩層石墨烯旋轉(zhuǎn)之后產(chǎn)生的超晶格[30]。根據(jù)這兩個(gè)模式的頻率我們可以定出這個(gè)t(1+3)LG界面處層間旋轉(zhuǎn)角θ為10.6°。在37和22 cm-1處，我們觀察到了兩個(gè)C模，根據(jù)它們的頻率，我們將其分別指認(rèn)為C31和C32。同時(shí)在93和116 cm-1處，我們也觀察到了兩個(gè)相對(duì)較寬的模式。根據(jù)第一性原理計(jì)算的結(jié)果[31]，這個(gè)兩個(gè)模式可以被指認(rèn)為L(zhǎng)BM42和LBM41。另外，通過對(duì)稱性分析發(fā)現(xiàn)，t(m+n)LG (m≠n)具有C3對(duì)稱性，其對(duì)應(yīng)的C模和LBM的拉曼張量如下[32]：

根據(jù)上述的拉曼張量，LBM在XX偏振配置下可以被觀察到，而在XY偏振下看不到，但是C模在兩種偏振下都可以被看到，而且強(qiáng)度相同。我們?cè)趫D1c中畫出了t(1+3)LG的偏振拉曼實(shí)驗(yàn)結(jié)果，與對(duì)稱性分析的結(jié)論吻合，進(jìn)一步證實(shí)了我們的指認(rèn)。

Fig.1(a) Optical image of a flake comprising a t(1+1)LG and a t(1+3)LG.(b) Optical contrast of t(1+1)LG and t(1+3)LG.For comparison,the contrast of 2LG and 4LG is also plotted.(c) Stokes/anti-Stokes Raman spectra in the C and LB spectral range,and Stokes Raman spectra in the G peak region for 1.96 and 2.33 eV excitation.Polarized Raman spectra are also shown

圖2給出了t(1+2)LG,t(1+1+1)LG,t(1+3)LG,t(2+2)LG,t(2+3)LG和t(5+5)LG的拉曼光譜。它們的旋轉(zhuǎn)角度與對(duì)應(yīng)的激發(fā)光能量都被標(biāo)注出來。我們?cè)趖(1+2)LG中觀察到了C21(31 cm-1)模和LBM31(109 cm-1)，而在t(2+2)LG中觀察到C21(31 cm-1)模和LBM41(109 cm-1)，在其他的t(m+n)LG中也觀察到了類似的情況。也就是，我們?cè)趖(m+n)LG中觀察了分別來自于nLG和mLG的C模和來自(m+n)LG的LBM。在t(m+n)LG中，轉(zhuǎn)角的界面阻隔了層間的剪切耦合，使得C模局域在AB堆垛的子系統(tǒng)內(nèi)。而這種阻隔對(duì)呼吸耦合并不起作用，因此LBM模仍為(m+n)LG的模式。

一般地，多層石墨烯等二維層狀材料的C模和LBM的頻率以及原子位移方式可以通過求解如下的線性齊次方程組得到[8]：

Fig.2Stokes/anti-Stokes Raman spectra in the C and LB peak region and Stokes spectra in the G spectral region for six tMLGs.Eexis also indicated.The spectra are scaled and offset for clarity.The scaling factors of the individual spectra are shown.Vertical lines are guides to the eye

Fig.3(a) Linear chain model (LCM),LCM with the twisted interface (tLCM) and LCM with second-nearest interlayer coupling (2LCM).(b) Experimental (Exp.,open crosses) and theoretical (tLCM,open circles,and 2LCM,open diamonds) data of C and LB modes in tNLG

在圖1c中，我們發(fā)現(xiàn)當(dāng)激發(fā)光為1.96 eV時(shí)，t(1+3)LG的拉曼信號(hào)得到極大增強(qiáng)，是激發(fā)光為2.33 eV時(shí)的拉曼強(qiáng)度的30倍左右。由此可見，在t(m+n)LG中，存在著拉曼信號(hào)增強(qiáng)現(xiàn)象。共振拉曼信號(hào)的增強(qiáng)現(xiàn)象可以用二階微擾理論來解釋。因?yàn)橹挥泄鈱W(xué)躍遷允許的能帶才能在拉曼過程中有貢獻(xiàn)，在這里我們引入光學(xué)躍遷允許的聯(lián)合態(tài)密度[8]：

Fig.4(a) Band structure of 10.6° t(1+1)LG.The optically allowed transitions are marked by dashed arrows.The transitions with energy ~1.15 eV between parallel bands along K-M are forbidden,as indicated by solid arrows with crosses.(b) Squared optical matrix elements of the corresponding band pairs in (a).(c) Band structure of 10.6° t(1+3)LG.Some typical transitions are indicated by vertical dashed lines.(d) A(G) of t(1+1)LG,(e) A(G) and A(G+) of t(1+3)LG,and (f) A(C31),A(C32),A(LBM42) and A(LBM41) as a function of laser excitation energy.The filled circles,open diamonds,open triangles and open squares are the experimental data,while the lines show the simulations.The dash-dotted lines in (e) are the electronic joint density of states (JDOSs) of all the optically allowed transitions (JDOSOAT) in t(1+3)LG along G-K-M-G.The VHSs of JDOSOATare indicated with arrows

4結(jié)論

在本文中，我們通過機(jī)械剝離和轉(zhuǎn)移方法制備了不同層數(shù)的t(m+n)LG。利用共振拉曼手段，系統(tǒng)地探測(cè)了t(m+n)LG的C模和LBM。在t(m+n)LG中，我們發(fā)現(xiàn)C模是局域在nLG和mLG子系統(tǒng)內(nèi)的，而LBM是全局的。通過改進(jìn)的線性原子鏈模型(LCM)擬合實(shí)驗(yàn)結(jié)果，我們發(fā)現(xiàn)轉(zhuǎn)角界面處的剪切耦合為AB堆垛界面處的20%，而呼吸耦合并沒有明顯的變化。此外，我們還發(fā)現(xiàn)多層石墨烯存在著次近鄰呼吸耦合，其強(qiáng)度為最近鄰呼吸耦合的9%。最后，我們利用“光學(xué)躍遷允許的聯(lián)合態(tài)密度(JDOSOAT)”的概念，很好地解釋了在t(m+n)LG中拉曼信號(hào)的共振增強(qiáng)現(xiàn)象。本文的研究表明，層間振動(dòng)模式是探測(cè)二維層狀異質(zhì)層間耦合的有效手段，為其在器件應(yīng)用方面的研究奠定了基礎(chǔ)。

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Interface Coupling in Twisted Multilayer Graphene by Resonant Raman Spectroscopy

WU Jiang-bin1,ZHANG Xin1,HAN Wen-peng1,QIAO Xiao-fen1,M.Ij?s2,A.C.Ferrari2,TAN Ping-heng1*

(1.StateKeyLaboratoryofSuperlatticesandMicrostructures,InstituteofSemiconductors,ChineseAcademyofSciences,Beijing,100083,P.R.China;2.CGC,UniversityofCambridge,9JJThomsonAvenue,CambridgeCB3 0FA,UK)

Abstract:The C and LB modes of t(m+n)LG are studied systematically by Raman spectroscopy.In the t(m+n)LG,the C modes of nLG and mLG and LBMs of (m+n)LG are observed.We fit the positions of C and LB modes by an improved linear chain model.We find the interlayer shear coupling at the twisted interface is ~20% of that at Bernal stacked interfaces,but the layer breathing coupling at the twisted interface is closed to that of Bernal interface.Moreover,the next-nearest interlayer interaction,which is 9% of the nearest interlayer interaction,must be considered for LBMs.The Raman intensity of the C,LB and G modes is significantly enhanced in t(m+n)LGs for specific excitation energies.This behavior is assigned to the resonance between van Hove singularities in the joint density of states of all optically allowed transitions in twisted multilayer samples and the laser excitation energy,during the optical absorption and emission steps of the Raman process.Beyond tMLGs,the interlayer interaction of other heterostructures can also be measured by Raman spectroscopy.

Key words:graphene;shear mode;layer breathing mode;2D heterostructure;Raman spectroscopy

通訊作者：譚平恒，E-mail：phtan@semi.ac.cn

中圖分類號(hào)：O433.4

文獻(xiàn)標(biāo)志碼：A

doi:10.13883/j.issn1004-5929.201601005

作者簡(jiǎn)介：吳江濱(1990-)，男，福建泉州，博士研究生，研究方向?yàn)槎S層狀材料光學(xué)性質(zhì)，E-mail：jbwu@semi.ac.cn

基金項(xiàng)目：國(guó)家自然科學(xué)基金(11225421，11474277，11434010)

收稿日期：2015-07-11; 修改稿日期:2015-09-20

文章編號(hào)：1004-5929(2016)01-0016-07