Amplification of Hypersound in Graphene with degenerate energy dispersion

Hypersound amplification/absorption of acoustic phonons in Graphene with degenerate energy dispersion $\varepsilon(p)$ near the Fermi level was theoretically studied. For $k_{\beta}T > 1$, the dependence of the absorption coefficient $\Gamma/\Gamma_0$ on ${V_D\over V_s}$ was studied where the results satisfied the Cerenkov effect. That is when ${V_D\over V_s} > 1$, an amplification was obtained but for ${V_D\over V_s} < 1$, an absorption was obtained which could lead to Acoustoelectric Effect (AE) in Graphene. A linear dependence of the $\Gamma/\Gamma_0$ on $\omega_q$ was observed where the result obtianed qualitatively agreed with an experimentally observed acoustoelectric current in Graphene via the Weinrich relation. It is interesting to note from this study that, frequencies above $10THz$ can be attained for $V_D = 1.1ms^{-1}$. This study permit the use of Graphene as hypersound phonon laser (SASER).Comment: 13 pages, 6 figure

Acoustoelectric Effect in Graphene with degenerate Energy dispersion

The acoustoelectric effect $AE$ in Graphene with degenerate energy dispersion is theoretically studied for hypersound in the regime $ql >> 1$. At low temperatures ($k_{\beta}T <<1$), the non-linear dependence of Acoustoelectric current $j/j_0$ on the frequency $\omega_q$ and temperature $T$ are numerically analysed. The obtained graph for $j/j_0$ against $\omega_q$ qualitatively agreed with an experimentally obtained results. For $j/j_0$ versus $T$, the dependence of Acoustoelectric current in Graphene was found to manifest at low temperatures.Comment: three figur

Acoustoelectric Effect in degenerate Carbon Nanotube

Acoustoelectric Effect $AE$ in degenerate Carbon Nanotube ($CNT$) was theoretically studied for hypersound in the regime $ql >> 1$. The dependence of acoustoelectric current $j^{ac}$ on the acoustic wave number $\vec{q}$ and frequency $\omega_q$ at $T = 10K$ and scattering angle ($\theta > 0$) was evaluated at various harmonics $n =\pm 1, 2, ...$ (where $n$ is an integer). In the first harmonics ($n = \pm 1$), the non-linear dependence of $j^{ac}$ on $\omega_q$ and $\vec{q}$ were obtained. For $n = \pm 2$, the numerically evaluated $j^{ac}$ qualitatively agreed with an experimentally obtained result.Comment: 6 figure

On the amplification of acoustic phonons in carbon nanotube

We present a theoretical study of acoustic phonons amplification in Carbon Nanotubes (CNT). The phenomenon is via Cerenkov emission (CE) of acoustic phonons using intraband transitions proposed by Mensah et. al.,~\cite{1} in Semiconductor Superlattices (SSL) and confirmed in ~\cite{2}. From this, an asymmetric graph of $\Gamma^{CNT}$ on $\frac{V_d}{V_s}$ and $\Omega\tau$ were obtained where amplification ($\Gamma_{amp}^{CNT}$) $>>$ absorption ($\Gamma_{abs}^{CNT}$). The ratio, $\frac{\vert \Gamma_{amp}^{CNT}\vert}{\vert\Gamma_{abs}^{CNT}\vert}\approx 3.5$, at $V_d = 1.02V_s$, $\omega_q = 3.0\ \mathrm{THz}$ and $T = 85\ K$ for scattering angle $\theta > 0$ . A threshold field at which $\Gamma_{abs}^{CNT}$ switches over to $\Gamma_{amp}^{CNT}$ was calculated to be $E_{z}^{dc} = 6.2\times 10^3\ \mathrm{V/m}. This field is far less than that deduced using Bloch-Type Oscillation (BTO)~\cite{3} which is E_{BTO}^{dc} = 3.0\times 10^5\ \mathrm{V/m}$. The obtained$\Gamma_{amp}^{CNT}$ would enable the use of CNT for the production of SASER.Comment: 12 pages, 2 figure

Laser Stimulated Thermal Conductivity in chiral carbon nanotube

An investigation of laser stimulated thermal conductivity in chiral CNT is presented. The thermal conductivity of a chiral CNT is calculated using a tractable analytical approach. This is done by solving the Boltzmann transport equation with energy dispersion relation obtained in the tight binding approximation. The electron thermal conductivity along the circumferential \chi_c and axial \chi_z are obtained. The results obtained are numerically analyzed and both \chi_c and \chi_z are found to oscillate in the presence of laser radiations. We have also noted that the laser source caused a drastic reduction in the both \chi_c and \chi_z values.Comment: 15 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1104.191

Nonlinear Conductivity in Graphene

We consider the tight-binding approximation for the description of energy bands of graphene, together with the standard Boltzmann's transport equation and constant relaxation time, an expression for the conductivity was obtained. We predicted strong nonlinear effects in graphene which may be useful for high frequency generation

Generation of Terahertz Radiation by Wave Mixing in Armchair Carbon Nanotubes

Using semiclassical Boltzmann equation we have studied theoretically an effect of a direct current (DC) generation in undoped armchair carbon nanotube (CN) by mixing two coherent electromagnetic waves with commensurate frequencies i.e omega and 2 omega . We compared the results of the armchair with that of the zigzag carbon nanotubes for the same conditions (i.e. when the normalized current is plotted against the amplitude). Quantitatively they agree with each other except that the absolute value of the peaks of the current for zigzag is about 1.1 times that of the armchair. We noticed that the current is negative similar to that observed in zigzag CNs describing the same effect. However it is interesting to note that graph of normalized current against omega tau showed that the armchair is greater than that of the zigzag for about 1.1 times which is opposite. We also observed that when the phase shift theta lies between pi divided by 2 and 3 pi divided by 2 there is an inversion and the current becomes positive. We suggest the use of this approach for the generation of terahertz radiation and also for the determination of the relaxation time of electrons in carbon nanotubes.Comment: 6pages,5figure

Generation of Terahertz Radiation by Wave Mixing in Zigzag Carbon Nanotubes

With the use of the semiclassical Boltzmann equation we have calculated a direct current (d.c) in undoped zigzag carbon nanotube (CN) by mixing two coherent electromagnetic waves with commensurate frequencies i.e and . This effect is attributed to the nonparabolicity of the electron energy band which is very strong in carbon nanotubes. We observed that the current is negative similar to that observed in superlattice. However if the phase shift lies between and there is an inversion and the current becomes positive. It is interesting to note that exhibit negative differential conductivity as expected for d.c through carbon nanotubes. This method can be used to generate terahertz radiation in carbon nanotubes. It can also be used in determining the relaxation time of electrons in carbon nanotubesComment: 12pages,5figure

Stark-cyclotron Resonance in an Array of Carbon Nanotubes

Using the kinetic approach based on the semiclassical Boltzmann transport equation with constant relaxation time, we theoretically studied the Stark-cyclotron resonance in an array of Carbon Nanotubes (CNs). Exact expression for the current density was obtained. We noted that Stark-cyclotron resonance occurs when the Larmor frequency coincides with the Stark frequency. A coincidence of these frequencies produce resonance.Comment: 1 figur

Acoustomagnetoelectric Effect in Graphene Nanoribbon in the Presence of External Electric and Magnetic Field

The Acoustomagnetoelectric Effect (AME) in Graphene Nanoribbon (GNR) was theoretically studied using the Boltzmann kinetic equation. On open circuit, the general formular for Surface Acoustomagnetoelectric field ($\vec{E}_{SAME}$) in GNR with energy dispersion $\varepsilon(p)$ near the Fermi point was calculated. The $E_{SAME}$ was found to depend on the magnetic strength ($\eta$), $\alpha$ = ${\hbar \omega_q}/{E_g}$ and the energy gap ($E_g$). The expression for $\vec{E}_{SAME}$ was analyzed numerically for varying width of GNR, magnetic strength ($\eta$) and $\alpha$ at different sub-bands indices ($p_i$). It was noted that the dependence of $\vec{E}_{SAME}$ on the width of GNR increased to a saturation point of approximately $15$Vcm$^{-1}$ and remained constant. For $E_{SAME}$ versus $\eta$, the $E_{SAME}$ increases rapidly to a maximum point and then decayed to a constant minimum value. The graph was modulated either by varying the width of GNR or the sub-band index $p_i$ with an inversion occurring at $p_i = 6$. The dependence of $E_{SAME}$ versus $\alpha$ was analyzed. The $E_{SAME}$ was constant up to a point and sharply increased asymptotically at approximately $\alpha = 1$. A $3$D graph of $\vec{E}_{SAME}$ with $\eta$ and width is also presented. This study is relevant for investigating the properties of GNR