Ahmad R. T. Nugraha

Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus

Orthorhombic black phosphorus (BP) and other layered materials, such as gallium telluride (GaTe) and tin selenide (SnSe), stand out among two-dimensional (2D) materials owing to their anisotropic in-plane structure. This anisotropy adds a new dimension to the properties of 2D materials and stimulates the development of angle-resolved photonics and electronics. However, understanding the effect of anisotropy has remained unsatisfactory to date, as shown by a number of inconsistencies in the recent literature. We use angle-resolved absorption and Raman spectroscopies to investigate the role of anisotropy on the electron-photon and electron-phonon interactions in BP. We highlight, both experimentally and theoretically, a nontrivial dependence between anisotropy and flake thickness and photon and phonon energies. We show that once understood, the anisotropic optical absorption appears to be a reliable and simple way to identify the crystalline orientation of BP, which cannot be determined from Raman spectroscopy without the explicit consideration of excitation wavelength and flake thickness, as commonly used previously.

Dielectric constant model for environmental effects on the exciton energies of single wall carbon nanotubes

The excitonic optical transition energies Eii of single wall carbon nanotubes, that are modified by surrounding materials around the tubes (known as the environmental effect), can be reproduced by defining a dielectric constant κ which depends on the subband index, nanotube diameter, and exciton size. The environmental effects on excitons can be recognized on a plot of the functional form of κ simply by the different linear slopes obtained for different samples. This treatment should be very useful for calculating Eii for any type of nanotube environment, hence providing an accurate assignment of many nanotube (n,m) chiralities.

Luminescence Properties of Individual Empty and Water-Filled Single-Walled Carbon Nanotubes

The influence of water filling on the photoluminescence (PL) properties of SWCNTs is studied by ensemble and single-molecule PL spectroscopy. Red-shifted PL and PL excitation spectra are observed upon water filling for 16 chiralities and can be used to unambiguously distinguish empty SWCNTs from filled ones. The effect of water filling on the optical transitions is well-reproduced by a continuum dielectric constant model previously developed to describe the influence of the nanotube outer environment. Empty nanotubes display narrower luminescence lines and lower inhomogeneous broadening, signatures of reduced extrinsic perturbations. The radial breathing mode phonon sideband is clearly observed in the PL spectrum of small diameter empty tubes, and a strong exciton-phonon coupling is measured for this vibration. Biexponential PL decays are observed for empty and water-filled tubes, and only the short-living component is influenced by the water filling. This may be attributed to a shortening of the radiative lifetime of the bright state by the inner dielectric environment.

Theory of coherent phonons in carbon nanotubes and graphene nanoribbons

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.

Diameter dependence of thermoelectric power of semiconducting carbon nanotubes

We calculate the thermoelectric power (or thermopower) of many semiconducting single wall carbon nanotubes (s-SWNTs) within a diameter range 0.5–1.5 nm by using the Boltzmann transport formalism combined with an extended tight-binding model. We find that the thermopower of s-SWNTs increases as the tube diameter decreases. For some s-SWNTs with diameters less than 0.6 nm, the thermopower can reach a value larger than 2000 μV/K at room temperature, which is about 6 to 10 times larger than that found in commonly used thermoelectric materials. The large thermopower values may be attributed to the one dimensionality of the nanotubes and to the presence of large band gaps of the small-diameter s-SWNTs. We derive an analytical formula to reproduce the numerical calculation of the thermopower and we find that the thermopower of a given s-SWNT is directly related with its band gap. The formula also explains the shape of the thermopower as a function of tube diameter, which looks similar to the shape of the so-called Kataura plot of the band gap dependence on tube diameter.

Ultrafast Generation of Fundamental and Multiple-Order Phonon Excitations in Highly Enriched (6,5) Single-Wall Carbon Nanotubes

Using a macroscopic ensemble of highly enriched (6,5) single-wall carbon nanotubes, combined with high signal-to-noise ratio and time-dependent differential transmission spectroscopy, we have generated vibrational modes in an ultrawide spectral range (10-3000 cm(-1)). A total of 14 modes were clearly resolved and identified, including fundamental modes of A, E1, and E2 symmetries and their combinational modes involving two and three phonons. Through comparison with continuous wave Raman spectra as well as calculations based on an extended tight-binding model, we were able to identify all the observed peaks and determine the frequencies of the individual and combined modes. We provide a full summary of phonon frequencies for (6,5) nanotubes that can serve as a basic reference with which to refine our understanding of nanotube phonon spectra as well as a testbed for new theoretical models.

Quantum Effects in the Thermoelectric Power Factor of Low-Dimensional Semiconductors

We theoretically investigate the interplay between the confinement length L and the thermal de Broglie wavelength Λ to optimize the thermoelectric power factor of semiconducting materials. An analytical formula for the power factor is derived based on the one-band model assuming nondegenerate semiconductors to describe quantum effects on the power factor of the low-dimensional semiconductors. The power factor is enhanced for one- and two-dimensional semiconductors when L is smaller than Λ of the semiconductors. In this case, the low-dimensional semiconductors having L smaller than their Λ will give a better thermoelectric performance compared to their bulk counterpart. On the other hand, when L is larger than Λ, bulk semiconductors may give a higher power factor compared to the lower dimensional ones.

Coherent radial-breathing-like phonons in graphene nanoribbons

We have developed a microscopic theory for the generation and detection of coherent phonons in armchair and zigzag carbon nanoribbons using an extended tight-binding model for the electronic states and a valence force field model for the phonons. The coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We examine the coherent phonon radial breathing like mode amplitudes as a function of excitation energies and nanoribbon types. For photoexcitation near the optical absorption edge the coherent phonon driving term for the radial breathing like mode is much larger for zigzag nanoribbons where transitions between localized edge states provide the dominant contribution to the coherent phonon driving term. Using an effective mass theory, we explain how the armchair nanoribbon width changes in response to laser excitation.

Breit-Wigner-Fano line shapes in Raman spectra of graphene

Excitation of electron-hole pairs in the vicinity of the Dirac cone by the Coulomb interaction gives rise to an asymmetric Breit-Wigner-Fano lineshape in the phonon Raman spectra in graphene. This asymmetric lineshape appears due to the interference effect between the phonon spectra and the electron-hole pair excitation spectra. The calculated Breit-Wigner-Fano asymmetric factor 1/qBWF as a function of the Fermi energy shows a V-shaped curve with a minimum value at the charge neutrality point and gives good agreement with the experimental result.

Fermi energy-dependence of electromagnetic wave absorption in graphene

Undoped graphene is known to absorb 2.3% of visible light at a normal angle of incidence. In this paper, we theoretically demonstrate that the absorption of 10–100 GHz of an electromagnetic wave can be tuned from nearly 0 to 100% by varying the Fermi energy of graphene when the angle of incidence of the electromagnetic wave is kept within total internal reflection geometry. We calculate the absorption probability of the electromagnetic wave as a function of the Fermi energy of graphene and the angle of incidence of the wave. These results open up possibilities for the development of simple electromagnetic wave-switching devices operated by gate voltage.