Shyamalendu M. Bose

Theory of the tangential G-band feature in the Raman spectra of metallic carbon nanotubes

The tangential G-band in the Raman spectra of a metallic single-wall carbon nanotube shows two peaks: a higher frequency component having the Lorentzian shape and a lower-frequency component of lower intensity with a Breit-Wigner-Fano (BWF)-type lineshape. This interesting feature has been analyzed on the basis of phonon-plasmon coupling in a nanotube. It is shown that while the gapless semi-acoustic plasmon cannot account for the observed spectra as claimed by other investigators, the low-lying optical plasmon corresponding to the tangential motion of the electrons on the nanotube surface can explain the observed features. In particular, this theory can explain occurrence of both the Lorentzian and BWF lineshapes in the G-band Raman spectra of metallic single-wall carbon nanotubes. Furthermore, the theory shows that the BWF peak moves to higher frequency, has a lower intensity and a lower half width at higher diameters of the nanotube. All these features are in agreement with experimental observations.

Raman spectra of unfilled and filled carbon nanotubes : Theory

The Raman spectra of two G-bands and a radial breathing mode (RBM) of unfilled and filled single-wall semiconducting and metallic carbon nanotubes have been investigated theoretically, in the presence of electron-phonon and phonon-phonon interactions. Excitation of low frequency optical plasmons in the metallic nanotube is responsible for the peak known as the Breit-Wigner-Fano (BWF) line shape in the G-band Raman spectra. In a filled nanotube there is an additional peak due to excitation of the phonon of the filling atom or molecule. Positions, shapes and relative strengths of these Raman peaks depend on the phonon frequencies of the nanotube and that of the filling atoms, and strengths and forms of the plasmon-phonon and phonon-phonon interactions. For example, filling atoms with phonon frequency close to the RBM frequency of the nanotube may broaden and lower the RBM Raman peak to such an extent that it may become barely visible. Hybridization between the G-bands and the filling atom phonon is also strong when these two frequencies are close to each other and it has important effects on the G-band and the BWF line shapes. When the phonon frequency of the filling atom is far from the RBM and G-band frequencies, it gives rise to a separate peak with modest effects on the RBM and G-band spectra. Raman spectra of semiconducting unfilled and filled nanotubes have similar behavior as those of metallic nanotubes except that normally they have Lorentzian line shapes and do not show a BWF line shape. However, if a semiconducting nanotube is filled with donor atoms, it is predicted that the BWF type line shape may be observed near the RBM, or the G-band or the filling atom Raman peak.

Low Energy Intraband Plasmons and Electron Energy Loss Spectra of Single and Multilayered Graphene

We present a theory for the calculation of the low energy intraband plasmon frequencies and the electron energy loss (EEL) spectra of single layer and multilayer graphene sheets. Our calculation shows that the number of plasmons that can be excited is equal to the number of graphene layers in the sample. One of these is the dominant in-phase plasmon having a square root dependence on the wave number at low wave vectors, whereas the others are out-of-phase plasmons having near linear dependences on the wave number. The EEL spectra of a single layer graphene shows a single peak at the plasmon frequency, which has been observed experimentally. The EEL spectra of all multilayer graphenes have two peaks, one corresponding to the dominant in-phase plasmon and the other due to the out of phase plasmons. We predict that careful measurement of the EEL of multilayer graphene will show both peaks due to the low energy intraband plasmons.

Electronic properties of ordered and disordered linear clusters of atoms and molecules

Abstract The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig–Penney model with the potential offered by each ion being approximated by an attractive δ-function. The energy eigenvalues, the eigenstates and the density of states are calculated exactly for a linear cluster of N atoms or molecules. The dependence of these quantities on the various parameters of the problem show interesting behavior. Effects of random distribution of the positions of the atoms and random distribution of the strengths of the potential have also been studied. The results obtained in this paper can have direct applications for linear chains of atoms produced on metal surfaces or for artificially created chains of atoms using scanning tunneling microscope or in studying molecular conduction of electrons across one-dimensional barriers.

Thermoelectric figure of merit of a material with caged structure and rattler atoms

A model is proposed to calculate the thermoelectric figure of merit of a framework crystal containing rattler atoms in cages. Such systems are expected to behave like a Phonon Glass and Electron Crystal (PGEC). The model resembles an effective Anderson model for a correlated system. The dispersion of the electronic energies and of the phonon frequencies in the system is calculated exactly. These results are used to evaluate the electronic and the thermal transport coefficients, which in turn give the temperature dependence of the thermoelectric figure of merit. Explicit calculation of the thermoelectric figure of merit for a one-dimensional case shows that the lattice thermal conductivity plays an important role in providing a peak structure to its temperature dependence. The results are presented for three different electronic dispersions and it is found that the room temperature figure of merit attains the highest value for the tight binding case. The calculation provides guidelines for designing a better thermoelectric material for use as a refrigerator.

Magnetovoltaic effect in a quantum dot undergoing Jahn-Teller transition

A model is proposed to study the electrical transport properties of a quantum dot capable of undergoing a structural phase transition driven by the Jahn-Teller mechanism. The dot attached to two metallic leads is described by the single impurity Anderson model Hamiltonian to which a term describing the Jahn-Teller distortion and another term to include the possibility of the presence of a magnetic field are added. Calculation of the electrical conductance and Jahn-Teller order parameter reveals several interesting features the most striking of which is the new phenomenon of “magnetovoltaic effect.”

Electronic density of states of a one-dimensional superlattice

The electronic density of states in a long-period superlattice is investigated. Using the transfer matrix formalism, exact solutions are obtained for a one-dimensional model consisting of two square well potentials of finite depth and width. New energy bands and minigaps are found to develop not only in the bound state region but also in the ionisation region.

Electrical transport in a quantum dot undergoing Jahn-Teller transition

A model is proposed to study the electrical conductance of a quantum dot capable of undergoing structural phase transition . The energy levels of the dot are assumed doubly degenerate so that it can undergo an electrically driven structural transition due to the Jahn-Teller mechanism. The model also allows for the presence of a magnetic field. The dot is described by the well known single impurity Anderson model (SIAM) along with two added terms describing the Jahn-Teller distortion and the magnetic field Calculation of the electrical transport properties of such a quantum dot reveals several interesting new features.

Theory of Raman Spectra of Unfilled and Filled Carbon Nanotube

The Raman spectra of two G‐bands and a radial breathing mode (RBM) of unfilled and filled single‐wall semiconducting and metallic carbon nanotubes have been investigated in the presence of electron‐phonon and phonon‐phonon interactions. Excitation of low frequency optical plasmons in the metallic nanotube is shown to be responsible for the asymmetric band known as the Breit‐Wigner‐Fano (BWF) line shape in the G‐band Raman spectra. In a filled nanotube there is an additional peak due to excitation of the phonon of the filling atom or molecule. Positions, shapes and relative strengths of these Raman peaks depend on the phonon frequencies of the nanotube and that of the filling atoms, and strengths and forms of the electron‐phonon and phonon‐phonon interactions. Raman spectra of semiconducting unfilled and filled nanotubes have similar behavior as those of metallic nanotubes except that normally they have Lorentzian line shapes and do not show a BWF line shape. However, if a semiconducting nanotube is filled...

An alternative formulation of the theory of superconductivity

The cluster variation method of the cooperative phenomena has been applied to the study of the theory of superconductivity. The results obtained in this formulation are equivalent to the BCS results and follow in a straight forward and natural way both at zero and finite temperatures.