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Title
Abstract
Figures
Introduction
Experimental
Results
Discussion
Conclusions
References

Phonon renormalization in doped bilayer graphene

Profile image of Biswanath ChakrabortyBiswanath Chakraborty
https://doi.org/10.1103/PHYSREVB.79.155417
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Abstract

We report phonon renormalization in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping as a result of the nonadiabatic Kohn anomaly at the ⌫ point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This gives a change of slope in the variation of G peak position with doping which allows a direct measurement of the interlayer coupling strength.

Figures (9)
FIG. 1. (Color online) (a) Top view of a bilayer graphene. Red dotted line represents the bottom layer, while the solid blue line the top layer. A; and B, are the sublattices of the bottom layer, and A, and B, those of the top layer. (b) Energy dispersion of a bilayer graphene. y,; is the energy separation between the two subbands. s=+1 for conduction band and s=—1 for valence band. The lattice structure of bilayer graphene is shown in Fig. l(a), where the bottom and top layers are represented by a dashed red line and solid blue line, respectively. The indexes 1 and 2 in Fig. 1(a) label the sublattices of the bottom and top layers, respectively.*-*° As seen from Fig. 1(a), the A,
FIG. 1. (Color online) (a) Top view of a bilayer graphene. Red dotted line represents the bottom layer, while the solid blue line the top layer. A; and B, are the sublattices of the bottom layer, and A, and B, those of the top layer. (b) Energy dispersion of a bilayer graphene. y,; is the energy separation between the two subbands. s=+1 for conduction band and s=—1 for valence band. The lattice structure of bilayer graphene is shown in Fig. l(a), where the bottom and top layers are represented by a dashed red line and solid blue line, respectively. The indexes 1 and 2 in Fig. 1(a) label the sublattices of the bottom and top layers, respectively.*-*° As seen from Fig. 1(a), the A,
In compar sens single layer graphene has linear energy dis- persion €, = 5%. where s is a band index: +1 for conduction band and —1 for valence band. j is the subband index, whose values are | and 2, as shown in Fig. 1(b). This also plots the energy dispersion of a bilayer graphene, where y, (Refs. 12, 13, and 43-46) measures the energy separation between the two subbands. The density of states (DOS) is calculated using Eq. (2) and is given by Il. EXPERIMENTAL
In compar sens single layer graphene has linear energy dis- persion €, = 5%. where s is a band index: +1 for conduction band and —1 for valence band. j is the subband index, whose values are | and 2, as shown in Fig. 1(b). This also plots the energy dispersion of a bilayer graphene, where y, (Refs. 12, 13, and 43-46) measures the energy separation between the two subbands. The density of states (DOS) is calculated using Eq. (2) and is given by Il. EXPERIMENTAL
FIG. 2. (Color online) Experimental setup. The black dotted box on SiO, indicates the polymer electrolyte (PEO+LiC10,). Left in- set shows a scanning electron microscope image of the SLG and BLG. Scale bar: 4 wm. Right inset, comparison of the 2D Raman band for our SLG and BLG.
FIG. 2. (Color online) Experimental setup. The black dotted box on SiO, indicates the polymer electrolyte (PEO+LiC10,). Left in- set shows a scanning electron microscope image of the SLG and BLG. Scale bar: 4 wm. Right inset, comparison of the 2D Raman band for our SLG and BLG.
FIG. 4. (Color online) (a) Geometrical capacitance and quantum capacitance are in series with Vg. (b) Vrg is the voltage applied between the gate and source. ® is the electrostatic potential drop and E; is the Fermi energy shift. dV is the voltage drop between the BLG layers. Similarly, for BLG!3°°>!
FIG. 4. (Color online) (a) Geometrical capacitance and quantum capacitance are in series with Vg. (b) Vrg is the voltage applied between the gate and source. ® is the electrostatic potential drop and E; is the Fermi energy shift. dV is the voltage drop between the BLG layers. Similarly, for BLG!3°°>!
Here, we assume equal charge density in both layers. Thus, the total electrostatic voltage drop in BLG is ®2'G=@816 + dV. dV would move the relative position of the conduction and valence band in BLG.'’ In our experimental geometry (Fig. 2) once the equilibrium is reached, both SLG and BLG will have the same chemical potential. Therefore, eV7¢ =e DG 4 ENG— eB S4 EPS, where E}VS and EBS are the Fermi energy shifts in SLG and BLG, respectively. In our calculation we neglect the term 6V, since, for a given charge density, the value of dV is always smaller compared to ERG and CpBLG 16,17,49 Thus
Here, we assume equal charge density in both layers. Thus, the total electrostatic voltage drop in BLG is ®2'G=@816 + dV. dV would move the relative position of the conduction and valence band in BLG.'’ In our experimental geometry (Fig. 2) once the equilibrium is reached, both SLG and BLG will have the same chemical potential. Therefore, eV7¢ =e DG 4 ENG— eB S4 EPS, where E}VS and EBS are the Fermi energy shifts in SLG and BLG, respectively. In our calculation we neglect the term 6V, since, for a given charge density, the value of dV is always smaller compared to ERG and CpBLG 16,17,49 Thus
FIG. 5. Fermi energy shift as a function of Vyg. Dashed line: SLG; solid line: BLG. The dotted lines in Fig. 6 are the experimental Pos(G), FWHM(G) as a function of E;. In SLG, Pos(G) does not increase up to Ep~0.1 eV (~hwy/2), where wp is the fre- quency of the £,, phonon in the undoped case [hawo/(2mhc)=Pos(Go), with c the speed of light], and then IV. RESULTS
FIG. 5. Fermi energy shift as a function of Vyg. Dashed line: SLG; solid line: BLG. The dotted lines in Fig. 6 are the experimental Pos(G), FWHM(G) as a function of E;. In SLG, Pos(G) does not increase up to Ep~0.1 eV (~hwy/2), where wp is the fre- quency of the £,, phonon in the undoped case [hawo/(2mhc)=Pos(Go), with c the speed of light], and then IV. RESULTS
increases with E,. Figures 6(b) and 6(d) indicate that in SLG and BLG, FWHM(G) decreases for both electron and hole doping, as expected”! since phonons decay into real electron- hole pairs when E-<fiw,/2. Figure 6(c) plots Pos(G) of BLG. We find that (i) Pos(G) does not increase until E; ~0.1 eV (~hawp/2). (ii) Between 0.1 and 0.4 eV the BLG slope R os is smaller than the SLG one. (iii) A kink is observed in Fig. 6(c) at E-~0.4 eV. (iv) For E,>0.4 eV the slope is larger than in SLG. (v) The kink position does not significantly depend on y, used to convert V7g in Ep (e.g., ~66% change in y, modifies Ep by ~6%).
increases with E,. Figures 6(b) and 6(d) indicate that in SLG and BLG, FWHM(G) decreases for both electron and hole doping, as expected”! since phonons decay into real electron- hole pairs when E-<fiw,/2. Figure 6(c) plots Pos(G) of BLG. We find that (i) Pos(G) does not increase until E; ~0.1 eV (~hawp/2). (ii) Between 0.1 and 0.4 eV the BLG slope R os is smaller than the SLG one. (iii) A kink is observed in Fig. 6(c) at E-~0.4 eV. (iv) For E,>0.4 eV the slope is larger than in SLG. (v) The kink position does not significantly depend on y, used to convert V7g in Ep (e.g., ~66% change in y, modifies Ep by ~6%).
FIG. 7. (Color online) Phonon renormalization for BLG: (i) Er<hao, (Il) hag<Ep<y,, (I) Er>y,. Blue (dark gray) and red (light gray) arrows correspond, respectively, to positive and negative contributions to IT. Solid and dashed arrows correspond to interband and intraband processes, respectively.
FIG. 7. (Color online) Phonon renormalization for BLG: (i) Er<hao, (Il) hag<Ep<y,, (I) Er>y,. Blue (dark gray) and red (light gray) arrows correspond, respectively, to positive and negative contributions to IT. Solid and dashed arrows correspond to interband and intraband processes, respectively.
FIG. 8. (a) Ratio of 2D and G peaks intensities for SLG (solid circles) and BLG (open circles) as a function of electron concentra- tion. (b) Position of 2D for SLG (solid circles) and 2D main com- ponents for BLG (open circles) as a function of electron concentration.
FIG. 8. (a) Ratio of 2D and G peaks intensities for SLG (solid circles) and BLG (open circles) as a function of electron concentra- tion. (b) Position of 2D for SLG (solid circles) and 2D main com- ponents for BLG (open circles) as a function of electron concentration.

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Daniela Lopes Mafra

Scientific Reports, 2012

In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS 2 , WSe 2 , oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications. I n spite of its outstanding properties, for many practical purposes, that, for example, require a band gap, single layer graphene (1LG) cannot be readily applied without the use of complex engineering procedures 1-5. One possible and interesting solution that responds constructively to several drawbacks of 1LG is to look at its multilayer graphene (MLG) counterparts 1-5. MLG systems involve weak interlayer (IL) interactions mediated by Van-der-Waals (VdW) forces. These IL interactions are sensitive to the number of layers and stacking order and are important for technological applications of these systems because they are important for the low-energy electronic and vibrational properties and, therefore, will be important for phenomena such as transport, infrared optics and telecommunication bands in the infrared (IR) range 6-8. In bilayer graphene (2LG), although the effects of the IL interactions on the electronic properties are well understood 9,10 , the present understanding of IL-related vibrational properties, electron-electron (e-e), phonon-phonon (ph-ph), and electron-phonon (e-ph) interactions is still under development 11-15. As regards the IL vibrational properties in 2LG, C. H. Lui et al. 8 studied the out-of-plane optical (ZO9) phonon mode (with frequency v ZO9 5 90 cm 21 predicted at the C-point, as shown in Fig. 1b). The ZO9 mode is also known as the IL breathing mode-LBM, and its combination mode LOZO9 with the longitudinal optical (LO) phonon (with frequency v LO 5 1575 cm 21 predicted at the C-point, as shown in Fig. 1b) occurs in the range for v LOZO9 from 1600 to 1800 cm 21 , for MLG with up to 6 layers, thereby explaining their frequency dependence on both the number of layers and their stacking orders 8. The other related LOZA combination mode (ZA is the IL out-of-plane acoustic mode whose frequency v ZA is zero at the C-point, as shown in Fig. 1b, and the 2ZO overtone (ZO is the out-of-plane tangential optical mode with frequency v ZO 5 885 cm 21 predicted at the Cpoint, as shown in Fig. 1b) demand a more detailed analysis, which is still elusive. All these features involve q ? 0 (throughout the text, q is the phonon wave-vector) intravalley (AV) processes, therefore occurring around the Cpoint in the Brillouin zone. However, only the 2ZO overtone presents two possible forward (q < 0) and backward (q < 2k) scattering mechanisms 11. Note that both the ZA and ZO modes are not Raman active at the C-point, where q 5 0. In spite of recent advances in the study of these interlayer modes, their phonon self-energies and eph interactions for these IL-dependent modes have hardly been discussed. It is worth saying that, these modes ranging from 1600 to 1800 cm 21 are spectroscopic signatures for MLG and by understanding them in detail, we can understand the VdW-related phonon-dependent phenomena associated with these systems. Such knowledge

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Using inelastic scattering of light to understand the nature of electron-phonon interactions and phonon self-energy renormalizations in graphene materials
Daniela Lopes Mafra
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2D Raman band splitting in graphene: Charge screening and lifting of the K-point Kohn anomaly OPEN
Xuanye Wang, Jason Christopher

Pristine graphene encapsulated in hexagonal boron nitride has transport properties rivalling suspended graphene, while being protected from contamination and mechanical damage. For high quality devices, it is important to avoid and monitor accidental doping and charge fluctuations. The 2D Raman double peak in intrinsic graphene can be used to optically determine charge density, with decreasing peak split corresponding to increasing charge density. We find strong correlations between the 2D 1 and 2D 2 split vs 2D line widths, intensities, and peak positions. Charge density fluctuations can be measured with orders of magnitude higher precision than previously accomplished using the G-band shift with charge. The two 2D intrinsic peaks can be associated with the " inner " and " outer " Raman scattering processes, with the counterintuitive assignment of the phonon closer to the K point in the KM direction (outer process) as the higher energy peak. Even low charge screening lifts the phonon Kohn anomaly near the K point for graphene encapsulated in hBN, and shifts the dominant intensity from the lower to the higher energy peak. Raman spectroscopy is a versatile experimental technique for exploring fundamental properties of graphene and characterizing properties such as layer thickness, defect density, charge and strain 1. The 2D Raman mode is of particular interest, as it involves two D band phonons with opposite, non-zero momenta. Despite the higher order process and non-zero momentum phonons, the 2D mode is the strongest Raman mode in single layer graphene. The double resonance (DR) mechanism 2 explains why this higher order phonon mode is so strong; resonant virtual electron and hole scattering picks phonon q vectors that satisfy momentum and energy conservation. The DR process together with the strong K-point Kohn anomaly is why the 2D line provides so much information about the electronic and phonon dispersions around the K and K' points. The phonon Kohn anomaly near K softens the D band phonon energies conically near K, resulting in a discontinuity of the derivative of the dispersion at K 3. The slope of the phonon dispersion is a direct measure of the electron-phonon coupling (EPC) strength 3. The DR and phonon dispersion are responsible for the shift in the 2D band energy with changing laser excitation energy 4. Similarly, the strong dependence of the 2D mode on dielectric screening is readily observable by the shift in the 2D position for different environments, e.g., suspended graphene, graphene on SiO 2 , graphene on top of hexagonal boron nitride (hBN) or encapsulated in hBN, etc 5. Larger dielectric screening 6 will reduce the Fermi velocity, v F , so that the DR conditions will select larger phonon energy. The screening affects v F since electron energies are much higher than expected from a single particle picture, with a significant self-energy correction in a 2D material, in particular for free standing graphene near the charge neutrality point (CNP) 7–9. The self-energy is decreasing as ε −1 , where ε is the effective dielectric constant of the environment 6. Charging the graphene layer will also renormalize and reduce the self-energy and therefore v F. For example, a study of gated graphene on hexagonal boron nitride (hBN) examined with scanning tunnelling spectroscopy demonstrated a change of v F from 1.3 to 1.05 × 10 6 m/s as the doping increased one order of magnitude from 2 × 10 11 cm −2 to 2 × 10 12 cm −2 9. Ultraclean suspended graphene with mobility reaching 10 6 cm 2 /Vs have shown v F reaching 3 × 10 6 m/s, measured by Shubnikov-de Haas oscillations 7. Screening will also have an effect on the phonon dispersion , as it may decrease the strength of the EPC, and thereby weakening the Kohn anomaly at K, resulting in higher phonon energies with increased screening 5,10,11. The reduced v F and reduced Kohn anomaly with screening

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Observation of the Kohn anomaly near the K point of bilayer graphene
Daniela Mafra

2010

Graphene systems exhibit a strong electron-phonon coupling at special points in the Brillouin zone, that softens the phonon energy and gives rise to kinks in the phonon dispersion which are called Kohn anomaly. The electron-phonon coupling is expected to be strong at the K point, but Raman experiments in graphene systems performed with visible light cannot probe phonons near the K point. This work presents a resonance Raman investigation of AB-stacked bilayer graphene using laser lines in the near infrared and visible range. The Kohn anomaly for both symmetric and anti-symmetric phonons was evidenced, and our results show the importance of considering higher renormalization terms such as electron-electron interactions to correctly describe the phonon dispersion near the K point, confirming the theoretical predictions by Lazzeri et al. [1]. [1] M. Lazzeri et al., Phys. Rev. B. 78, 081406(R) (2008).

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Nonadiabatic Kohn Anomaly in a Doped Graphene Monolayer
Michele Lazzeri

Physical Review Letters, 2006

We compute, from first-principles, the frequency of the E2g, Gamma phonon (Raman G-band) of graphene, as a function of the charge doping. Calculations are done using i) the adiabatic Born-Oppenheimer approximation and ii) time-dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. While, the adiabatic phonon frequency weakly depends on the doping, the dynamic one rapidly varies because of a Kohn anomaly. The adiabatic approximation is considered valid in most materials. Here, we show that doped graphene is a spectacular example where this approximation miserably fails.

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Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation
Tariq Mohiuddin

Physical Review B, 2009

Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. Since its experimental discovery, graphene continues to attract enormous interest, in particular as a new kind of matter, in which electron transport is governed by a Dirac-like wave equation, and as a model system for studying electronic and phonon properties of other, more complex, graphitic materials[1-4]. Here, we uncover the constitutive relation of graphene and probe new physics of its optical phonons, by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly degenerate E2g optical mode splits in two components, one polarized along the strain and the other perpendicular to it. This leads to the splitting of the G peak into two bands, which we call G+ and G-, by analogy with the effect of curvature on the nanotube G peak[5-7]. Both peaks red shift with increasing strain, and their splitting increases, in excellent agreement with first-principles calculations. Their relative intensities are found to depend on light polarization, which provides a useful tool to probe the graphene crystallographic orientation with respect to the strain. The singly degenerate 2D and 2D' bands also red shift, but do not split for small strains. We study the Gruneisen parameters for the phonons responsible for the G, D and D' peaks. These can be used to measure the amount of uniaxial or biaxial strain, providing a fundamental tool for nanoelectronics, where strain monitoring is of paramount importance[8, 9]

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Properties of graphene: a theoretical perspective
K. Ziegler

Advances in Physics, 2010

The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices such as single molecule gas sensors, ballistic transistors, and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest.

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Theory and synthesis of bilayer graphene intercalated with ICl and IBr for low power device applications
Hema C P Movva

Journal of Applied Physics, 2013

Graphene intercalation materials are potentially promising for the implementation of the ultra-low power, excitonic-condensate-based Bilayer pseudoSpin Field-Effect Transistor (BiS-FETs) concept, as well as other novel device concepts requiring a graphene interlayer dielectric. Using density functional theory (DFT) we study the structural and electronic properties of bilayer graphene intercalated with iodine monochloride (ICl) and iodine monobromide (IBr).

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Free-standing graphene monolayers in carbon-based composite obtained from SiC: Raman diagnostics
Volodymyr Dzhagan

physica status solidi (a), 2014

A carbon-based composite was obtained by an optimized method of high-temperature sublimation of polycrystalline SiC. Scanning electron microscopy of the composite detected flakes with lateral sizes of up to tens of microns and some finedispersed carbon material. From a thorough analysis of G and 2D bands in the Raman spectra measured within the flakes we conclude that the flakes consist of free-standing graphene monolayers of high quality, while the fine-dispersed material is mainly graphite. The proposed method of producing the graphene-containing composite is supposed to be very promising due to its relative simplicity and high mass output.

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Reversible optical doping of graphene
Antoine Tiberj

Scientific Reports, 2013

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