Theory of coherent phonons in carbon nanotubes and graphene nanoribbons

Abstract

We survey our recent theoretical studies on the generation and detection of coherent radial breathing mode (RBM) phonons in single-walled carbon nanotubes and coherent radial breathing like mode (RBLM) phonons in graphene nanoribbons. We present a microscopic theory for the electronic states, phonon modes, optical matrix elements and electron-phonon interaction matrix elements that allows us to calculate the coherent phonon spectrum. An extended tight-binding (ETB) model has been used for the electronic structure and a valence force field (VFF) model has been used for the phonon modes. The coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on the photoexcited carrier density. We discuss the dependence of the coherent phonon spectrum on the nanotube chirality and type, and also on the graphene nanoribbon mod number and class (armchair versus zigzag). We compare these results with a simpler effective mass theory where reasonable agreement with the main features of the coherent phonon spectrum is found. In particular, the effective mass theory helps us to understand the initial phase of the coherent phonon oscillations for a given nanotube chirality and type. We compare these results to two different experiments for nanotubes: (i) micelle suspended tubes and (ii) aligned nanotube films. In the case of graphene nanoribbons, there are no experimental observations to date. We also discuss, based on the evaluation of the electron-phonon interaction matrix elements, the initial phase of the coherent phonon amplitude and its dependence on the chirality and type. Finally, we discuss previously unpublished results for coherent phonon amplitudes in zigzag nanoribbons obtained using an effective mass theory.

Optical selection rules of zigzag graphene nanoribbons

“…The edge states in zigzag ribbons have been predicted to be important in transport [24,25,30], electromagnetic [31], and optical properties [9,13,32]. Although considerable attention has been given to zigzag ribbons' optical properties [9,13,22,26,[32][33][34][35][36][37][38][39], including many-body effects [36,40,41], the effect of external fields [13,36], curvature [26], wave function overlapping * v.saroka@exeter.ac.uk integrals [37,38], the finite length effect [42], and the role of unit cell symmetry [43], a number of problems have not been covered yet. In particular, it is known that the optical matrix element of graphene is anisotropic at the Dirac point [44,45] due to the topological singularity inherited from the wave functions [46,47].…”

On‐Surface Synthesis and Characterization of Acene‐Based Nanoribbons Incorporating Four‐Membered Rings

“…The 1.1 nm periodicity of the dots agreeswith the expected one for the cyclobutadiene moi- To furtherc haracterize the so-formed nanoribbons and to explore their stability under ambient conditions, we have performed ex situ Raman spectroscopy,awidely used experimental technique for the characterizationo fg raphene-related nanomaterials (Figure 4a nd Figure S8 in the Supporting Information). [27] Thisv ibrational mode is highly sensitivet ov ariationso fj ust one single unit in the width of GNRs, thus allowing to accurately determine their width.F igure 4d isplays in black the Raman spectrum for 2. [27] Thisv ibrational mode is highly sensitivet ov ariationso fj ust one single unit in the width of GNRs, thus allowing to accurately determine their width.F igure 4d isplays in black the Raman spectrum for 2.…”

“…[25,26] Specifically,t he presence of ac haracteristicv ibrational mode in graphene nanoribbons (GNRs), knowna sr adial breathing-like mode (RBLM), is utilized as af ingerprint for the determination of their width and quality. [27] Thisv ibrational mode is highly sensitivet ov ariationso fj ust one single unit in the width of GNRs, thus allowing to accurately determine their width.F igure 4d isplays in black the Raman spectrum for 2. Five highly intenseR amanb ands located at7 47, 1185,1 431, 1608, and 1689 cm À1 are observed.…”

Adjustable thermal resistor by reversibly folding a graphene sheet

“…5, the power spectra of atoms in the plane are similar to graphene, where the in-plane/out-of-plane mode phonons are mainly distributed in high-frequency/low-frequency range33,34 . As is illustrated inFig.…”