Probing LO phonons of graphene under tension via the 2D′ Raman mode

We use ab initio simulations and perturbation theory to study the 2D′ Raman mode of graphene subject to biaxial and uniaxial strains up to 2%. We demonstrate that 2D′ Raman measurements, as a function of polarization and laser energy EL, can probe the LO phonons of graphene with arbitrary radial and angular extent around Γ. The 2D′ profile is highly sensitive to uniaxial strain and depends on both polarization and strain orientation. The Grüneisen parameter γ2D′≈1.71 has a mild dependency on the laser energy EL, and is found to be in good agreement with experiments and comparable in value to γG. The shear deformation potential β2D′ depends strongly on the polarization and strain orientation, becoming negative when the polarizer and analyzer are perpendicular to each other. Finally, we describe a robust method to determine the uniaxial strain by relying solely on polarized measurements of the 2D′ mode

Double resonance Raman spectra of graphene : a full 2D calculation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2007.Includes bibliographical references (leaves 85-87).Visible range Raman spectra of graphene are generated based on the double resonant process employing a full two-dimensional numerical calculation applying second-order perturbation theory. Tight binding expressions for both the TO phonon dispersion and the [pi] - [pi]* electronic bands are used, which are then fit to experimental or ab-initio results. We are able to reproduce the single-peak D mode of graphene at ~ 1380 cm-1 that is identical to experiment. A near linear shift in the D mode peak with changing incoming laser energy of 33 cm-1/eV is calculated. Our shift marginally underestimates the experimental shifts as most of the literature features specimens that contain a few or more layers of graphene through to graphite that ought to subtly alter their electronic and phonon dispersions. However, our approach is readily applicable to such homologous forms of graphene once we have available their electronic band structure and phonon dispersions.by Rohit Narula.S.M

A primer on Twistronics: Massless Dirac Fermion's journey to Moir\'e patterns and Flat bands in Twisted Bilayer Graphene

The recent discovery of the strongly correlated phases in magic angle twisted bilayer graphene heralded a new area of investigation into the strongly-correlation physics in graphene. This is remarkably different from the initial period of graphene research which was dominated by interest in one body physics of massless Dirac fermions. This pedagogical review article provides a self-contained theoretical perspective of the journey of the wonder material graphene from its single-particle physics dominated regime to the flat band regime of strong-correlation physics. Starting from the origin of Dirac points in condensed matter systems, along this road, this review discusses the effect of superlattice on the Fermi velocity and Van Hove singularities in the dispersion relation of the graphene, and how it naturally leads to investigation into Moir\'e pattern in Van der Wall's heterostructure such as graphene-hexagonal boron-nitride and twisted bilayer graphene. Subsequently It discusses in detail the origin of flat bands in twisted bilayer graphene at the magic angles. by analysing in detail a number of prominent theoretical works in this direction. The theoretical description is intercepted at appropriate places by connecting it with the relevant experimental works. In a final section we also provide a list of the topics in the field of twisted bilayer graphene that are not covered in this review, but can be approached with the help of this primer.Comment: Invited Topical Review (Submitted for Publication

Polarized Plasmonic Enhancement by Au Nanostructures Probed through Raman Scattering of Suspended Graphene

We characterize plasmonic enhancement in a hotspot between two Au nanodisks using Raman scattering of graphene. Single layer graphene is suspended across the dimer cavity and provides an ideal two-dimensional test material for the local near-field distribution. We detect a Raman enhancement of the order of 103 originating from the cavity. Spatially resolved Raman measurements reveal a near-field localization one order of magnitude smaller than the wavelength of the excitation, which can be turned off by rotating the polarization of the excitation. The suspended graphene is under tensile strain. The resulting phonon mode softening allows for a clear identification of the enhanced signal compared to unperturbed graphene

Resonant Raman scattering in graphene

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, February 2011.Cataloged from PDF version of thesis.Includes bibliographical references (pages 131-144).In this thesis we encounter the formulation of a rigorous theory of resonant Raman scattering in graphene, the calculation of the so-obtained Raman matrix element K2f,1o for the 2D Raman mode with the full inclusion of the matrix elements and a physically appealing bridge between theory and experiment by eschewing the problematic ascription of graphene with a finite thickness. Finally, we elucidate an experimental study of the Raman D and G modes of graphene and highly-defected pencil graphite over the visible range of laser radiation. Marking a departure from the usual practice for light scattering in semiconductors of including only the dynamics of the electrons and holes separately, we show via fourth-order quantum mechanical perturbation theory using a Fock state basis that for resonant Raman scattering in graphene the processes to leading order are those that involve the simultaneous action of the electrons and holes. Such processes are indeed an order of magnitude stronger than those prevalent in the literature under the double resonance [1, 2, 3] moniker. We translate our perturbation theoretic analysis into simple rules for constructing Feynman diagrams for processes to leading order and we thereby enumerate the 2D and D modes. Using expressions for the terms to leading order obtained from our theoretical treatment we proceed to evaluate the Raman matrix element [4] for the Raman 2D mode by using state-of-the-art electronic [5] and iTO phonon dispersions [6] fit to ab initio GW calculations. For the first time in the literature we include the variation of the light-matter and electron-phonon interaction matrix elements calculated via an ab initio density functional theory (DFT) calculation under the local density approximation (LDA) for the electronic wavefunctions. Our results for the peak structure, position and intensity dependence are in excellent agreement with experiments [7, 8, 9, 10]. Strikingly, our results show that depending on the combination of the input (polarizer) and output (analyzer) polarization of the laser radiation, very different regions of the phonon dispersion are accessed. This has a direct impact on the dominant electronic transitions according to the pseudo-momentum conservation condition satisfied by the scattering of an electron by a phonon ki = kf + q. Using sample substitution [11] we deconvolve the highly wavelength dependent response of the spectrometer from the Raman spectra of graphene suspended on an SiO2 - Si substrate and graphite for the D and G modes in the visible range. We derive a model that considers graphene suspended on an arbitrary stratified medium while sidestepping its problematic ascription as an object of finite thickness and calculate the absolute Raman response of graphene (and graphite) via its explicitly frequency independent Raman matrix element [K'2f10]2 vs. laser frequency. For both graphene and graphite the [K'2f10]2 per graphene layer vs. laser frequency rises rapidly for the G mode and less so for the D mode over the visible range. We find a dispersion of the D mode position with laser frequency for both graphene and graphite of 41 cm-YeV and 35 cm-YeV respectively, in good agreement with Narula and Reich 131 assuming constant matrix elements, the observed intensity follows the joint density states of the electronic bands of graphene. Finally, we show the sensitivity of our calculation to the variation in thickness of the underlying SiO2 layer for graphene.by Rohit Narula.Ph. D

Absolute Raman matrix elements of graphene and graphite

Using sample substitution [Grimsditch et al., J. Raman Spectrosc. 10, 77 (1981)] we deconvolve the highly wavelength-dependent response of the spectrometer from the Raman spectra of graphene suspended on an SiO[subscript 2]-Si substrate and graphite for the D and G modes in the visible range. We derive a model that considers graphene suspended on an arbitrary stratified medium while sidestepping its problematic ascription as an object of finite thickness and calculate the absolute Raman response of graphene (and graphite) via its explicitly frequency-independent Raman matrix element [Falicov and Martin, Light Scattering in Solids I: Introductory Concepts (Springer-Verlag, Berlin, 1983), p. 1083] |K2f,10′|[superscript 2] vs laser frequency. For both graphene and graphite the |K2f,10′|[superscript 2] per graphene layer vs laser frequency rises rapidly for the G mode and less so for the D mode over the visible range. Although we find a dispersion of the D mode position with laser frequency for both graphene and graphite of 41 cm[superscript −1]/eV and 35 cm[superscript −1]/eV, respectively, in good agreement with Narula and Reich [Phys. Rev. B 78, 165422 (2008)] assuming constant matrix elements, the observed intensity dependence is in disagreement. Finally, we show the sensitivity of our calculation to the variation in thickness of the underlying SiO[subscript 2] layer for graphene. Our findings shall serve as an experimental verification of the behavior of the relevant matrix elements in graphene and its allotropes that may be calculated theoretically in the future.European Research Council (Grant No. 210642-OptNano

Loeffler's Syndrome

Nidhi Narula, Rajiv Mahajan and Manojkumar Rohithttp://link.springer.com/article/10.1007%2Fs00246-010-9732-7?LI=tru

Sudden death of a young child due to cardiac rhabdomyoma

This report describes a 1½-year-old boy who succumbed to acute obstruction of the left ventricular outflow tract by a cardiac rhabdomyoma. He was admitted to have a transient loss of consciousness episode evaluated. A mobile intracardiac mass obstructing the left ventricular outflow tract and protruding into the aortic root during systole was detected by transthoracic echocardiography. At autopsy, it was confirmed to be a rhabdomyoma.Anju Gupta, Nidhi Narula, Rajiv Mahajan and Manojkumar Rohi

Dominant Phonon Wavevectors and Strain-induced Splitting of the 2D Graphene Raman Mode

The dominant phonon wavevectors $q^{*}$ probed by the 2D Raman mode of graphene are highly anisotropic and rotate with the orientation of the polarizer:analyzer direction relative to the lattice. The corresponding electronic transitions connect the electronic equibandgap contours where the product of the ingoing and outgoing optical matrix elements is strongest, showing a finite component along $\bm{K}-\bm{\Gamma}$ that sensitively determines $q^{*}$. We revoke the notion of 'inner' and 'outer' processes. Our findings explain the splitting of the 2D mode of graphene under uniaxial tensile strain. The splitting originates from a strain-induced distortion of the phonon dispersion; changes in the electronic band structure and resonance conditions are negligeable for the 2D Raman spectrum.Comment: 4 pages, 6 figure