We study theoretically the plasmon scattering at the intersection of two metallic carbon nanotubes. We demonstrate that for a small angle of crossing, $θ\ll 1$, the transmission coefficient is an oscillatory function of $λ/θ$, where $λ$ is the interaction parameter of the Luttinger liquid in an individual nanotube. We calculate the tunnel density of states, $ν(ω,x)$, as a function of energy, $ω$, and distance, $x$, from the intersection. In contrast to a single nanotube, we find that, in the geometry of crossed nanotubes, conventional "rapid" oscillations in $ν(ω,x)$ due to the plasmon scattering acquire an aperiodic "slow-breathing" envelope which has $λ/θ$ nodes.
We develop a general approach to calculations of the electron spectrum of metallic multi-wall carbon nanotubes (MWNT) with arbitrary number of coaxial layers. It is based on the model with singular attractive potential of equidistant conductive cylinders. The knowledge of one-electron spectrum allows to construct the corresponding Green function and then to calculate the entropy and density of states for MWNT. We analyze the tunnelling between the nanotube and normal metal electrode. The possibility of direct determination of one-electron density of states by measurements of the tunnelling con…
Quantum dots defined in carbon nanotubes are a platform for both basic scientific studies and research into new device applications. In particular, they have unique properties that make them attractive for studying the coherent properties of single electron spins. To perform such experiments it is necessary to confine a single electron in a quantum dot with highly tunable barriers, but disorder has until now prevented tunable nanotube-based quantum-dot devices from reaching the single-electron regime. Here, we use local gate voltages applied to an ultra-clean suspended nanotube to confine a si…
We present a two-step procedure to probe hotspots of plasmon-enhanced Raman scattering with carbon nanotubes. Dielectrophoretic deposition places a small carbon nanotube bundle on top of plasmonic Au nanodimer. After 'pre-characterising' both the nanotubes and dimer structure, we subsequently use the tip of an AFM to push the bundle into the plasmonic hotspot located in the 25nm wide dimer gap, characterize its location inside the gap, and observe the onset of plasmon-enhanced Raman scattering. Evidence for the activation of the carbon nanotube's double-resonant D-mode by the near-field of the…
We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter (~1 nm) semiconducting single-walled carbon nanotubes. We show that these interactions can result in strong exciton-surface-plasmon coupling. The exciton absorption lineshapes exhibit the line (Rabi) splitting $~0.1-0.3$ eV as the exciton energy is tuned to the nearest interband surface plasmon resonance of the nanotube. We expect this effect to open a path to new optoelectronic device applications of semiconducting carbon nanotubes.
The possibility of low-energy surface plasmon amplification by optically excited excitons in small-diameter single wall carbon nanotubes is theoretically demonstrated. The nonradiative exciton-plasmon energy transfer causes the buildup of the macroscopic population numbers of coherent localized surface plasmons associated with high-intensity coherent local fields formed at nanoscale throughout the nanotube surface. These strong local fields can be used in a variety of new optoelectronic applications of carbon nanotubes, including near-field nonlinear-optical probing and sensing, optical switch…
We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter (~1 nm) semiconducting single-walled carbon nanotubes. We show that these interactions can result in strong exciton-surface-plasmon coupling. The exciton absorption line shape exhibits Rabi splitting ~0.1 eV as the exciton energy is tuned to the nearest interband surface plasmon resonance of the nanotube. We also show that the quantum confined Stark effect may be used as a tool to control the exciton binding energy and the nanotube band gap in carbon nanotubes in order, e.g., to bri…
A rigorous theory of photon emission accompanied inelastic tunnelling inside the gap of plasmonic nanoantennas has been developed. The disappointingly low efficiency of the electrical excitation of surface plasmon polaritons in these structures can be increased by orders of magnitude when a resonant tunnelling structure is incorporated inside the gap. Resonant tunnelling assisted surface plasmon emitter may become a key element in future electrically-driven nanoplasmonic circuits.
We use the macroscopic quantum electrodynamics approach suitable for absorbing and dispersing media to study the properties and role of collective surface excitations --- excitons and plasmons --- in single-wall and double-wall carbon nanotubes. We show that the interactions of excitonic states with surface electromagnetic modes in individual small-diameter (<~1 nm) single-walled carbon nanotubes can result in strong exciton-surface-plasmon coupling. Optical response of individual nanotubes exhibits Rabi splitting ~0.1 eV, both in the linear excitation regime and in the non-linear excitation r…
Quantum electrodynamics theory of the resonance Raman scattering is developed for an atom in a close proximity to a carbon nanotube. The theory predicts a dramatic enhancement of the Raman intensity in the strong atomic coupling regime to nanotube plasmon near-fields. This resonance scattering is a manifestation of the general electromagnetic surface enhanced Raman scattering effect, and can be used in designing efficient nanotube based optical sensing substrates for single atom detection, precision spontaneous emission control, and manipulation.
We calculate the plasma excitations in a bundle as well as a two-dimensional (2D) periodic array of aligned parallel multishell nanotubes on a substrate. The carbon nanotubes are oriented perpendicular to the substrate. The model we use for the system is an electron gas confined to the surface of an infinitely long cylinder embedded in a background dielectric medium. Electron tunneling between individual tubules is neglected. We include the Coulomb interaction between electrons on the same tubule and on different tubules for the same nanotube and neighboring nanotubes. We present a self-consis…
Plasmon resonance is expected to occur in metallic and doped semiconducting carbon nanotubes in the terahertz frequency range, but its convincing identification has so far been elusive. The origin of the terahertz conductivity peak commonly observed for carbon nanotube ensembles remains controversial. Here we present results of optical, terahertz, and DC transport measurements on highly enriched metallic and semiconducting nanotube films. A broad and strong terahertz conductivity peak appears in both types of films, whose behaviors are consistent with the plasmon resonance explanation, firmly …
We investigated, both experimentally and theoretically, the reflection phase shift (RPS) of one-dimensional plasmon polaritons. We launched 1D plasmon polaritons in carbon nanotube and probed the plasmon interference pattern using scanning near-field optical microscopy (SNOM) technique, through which a non-zero phase shift was observed. We further developed a theory to understand the nonzero phase shift of 1D polaritons, and found that the RPS can be understood by considering the evanescent field beyond the nanotube end. Interesting, our theory shows a strong dependence of RPS on polaritons wa…
We demonstrate the realization of an electrically-driven integrated source of surface plasmon polaritons. Light-emitting individual single-walled carbon nanotube field effect transistors were fabricated in a plasmonic-ready platform. The devices were operated at ambient condition to act as an electroluminescence source localized near the contacting gold electrodes. We show that photon emission from the semiconducting channel can couple to propagating surface plasmons developing in the electrical terminals. Momentum-space spectroscopy suggests that excited plasmon modes are bound to the metal-g…
A low energy theory of suspended carbon nanotube quantum dots in weak tunnelling coupling with metallic leads is presented. The focus is put on the dependence of the spectrum and the Franck-Condon factors on the geometry of the junction including several vibronic modes. The relative size and the relative position of the dot and its associated vibrons strongly influence the electromechanical properties of the system. A detailed analysis of the complete parameters space reveals different regimes: in the short vibron regime the tunnelling of an electron into the nanotube generates a plasmon-vibro…
We present a quantization of the hydrodynamic model to describe the excitation of plasmons in a single-walled carbon nanotube by a fast point charge moving near its surface at an arbitrary angle of incidence. Using a two-dimensional electron gas represented by two interacting fluids, which takes into account the different nature of the sigma and pi electrons, we obtain plasmon energies in near-quantitative agreement with experiment. Further, the implemented quantization procedure allows us to study the probability of exciting various plasmon modes, as well as the stopping force and energy loss…
A single-wall carbon nanotube possesses two different types of plasmons specified by the wavenumbers in the azimuthal and axial directions. The azimuthal plasmon that is caused by interband transitions has been studied, while the effect of charge doping is unknown. In this paper, we show that when nanotubes are heavily doped, intraband transitions cause the azimuthal plasmons to appear as a plasmon resonance in the near-infrared region of the absorption spectra, which is absent for light doping due to the screening effect. The axial plasmons that are inherent in the cylindrical waveguide struc…
We show that a single quantum emitter can efficiently couple to the tunable plasmons of a highly doped single-wall carbon nanotube (SWCNT). Plasmons in these quasi-one-dimensional carbon structures exhibit deep subwavelength confinement that pushes the coupling efficiency close to 100% over a very broad spectral range. This phenomenon takes place for distances and tube diameters comprising the nanometer and micrometer scales. In particular, we find a beta factor ~1 for QEs placed 1-100 nm away from SWCNTs that are just a few nanometers in diameter, while the corresponding Purcell factor exceed…
We study theoretically the in-plane electromagnetic response and the exciton-plasmon interactions for an experimentally feasible carbon nanotube (CN) film systems composed of parallel aligned periodic semiconducting CN arrays embedded in an ultrathin finite-thickness dielectric. For homogeneous single-CN films, the intertube coupling and thermal broadening bring the exciton and interband plasmon resonances closer together. They can even overlap due to the inhomogeneous broadening for films composed of array mixtures with a slight CN diameter distribution. In such systems the real part of the r…
Carbon nanotubes provide a rare access point into the plasmon physics of one-dimensional electronic systems. By assembling purified nanotubes into uniformly sized arrays, we show that they support coherent plasmon resonances, that these plasmons enhance and hybridize with phonons, and that the phonon-plasmon resonances have quality factors as high as 10. Because coherent nanotube plasmonics can strengthen light-matter interactions, it provides a compelling platform for surface-enhanced infrared spectroscopy and tunable, high-performance optical devices at the nanometer scale.
We theoretically investigate intersubband plasmon excitations in doped single wall carbon nanotubes (SWNTs) by examining the dependence of plasmon frequency on the nanotube diameter, chirality, and Fermi energy. The intersubband plasmons can be excited by light with polarization perpendicular to the nanotube axis and thus the plasmon excitations corresponds to optical transitions between the two different subbands, which are sensitive to the Fermi energy. In every SWNT, this mechanism leads to the emergence of the optical absorption peak at the plasmon frequency for a given Fermi energy, $E_F$…
Generating and detecting radiation in the technologically relevant range of the so-called terahertz gap ($0.1 - 10$ THz) is challenging because of a lack of efficient sources and detectors. Quantum dots in carbon nanotubes have shown great potential to build sensitive terahertz detectors usually based on photon-assisted tunnelling. A recently reported mechanism combining resonant quantum dot transitions and tunnelling barriers asymmetries results in a narrow linewidth photocurrent response with a large signal-to-noise ratio under weak THz radiation. That device was sensitive to one frequency, …
The non homogeneity of the charge distribution in a carbon nanotube leads to the formation of an excitonic resonance, in a similar way to the one observed in X-ray absorption in metals. As a result, a positive anomaly at low bias appears in the tunnelling density of states. This effect depends on the screening of the electron--electron interactions by metallic gates, and it modifies the coupling of the nanotube to normal and superconducting electrodes.
We consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube (CNT) networks forming the device channel with asymmetric electrodes. One electrode is the Ohmic contact to the CNT network and the another contact is the Schottky contact. These structures can serve as detectors of the terahertz (THz) radiation. We develop the device model for response of the lateral CNT networks which comprise a mixture of randomly oriented semiconductor CNTs (s-CNTs) and quasi-metal CNTs (m-CNTs). The proposed model includes the concept of the two-dimensional plasmons in relatively dens…
We develop an electron transport theory for the hybrid system of a semiconducting carbon nanotube that encapsulates a one-atom-thick metallic wire. The theory predicts Fano resonances in electron transport through the system, whereby the interaction of electrons on the wire with nanotube plasmon generated near-fields blocks some of the wire transmission channels to open up the new coherent plasmon-mediated channel in the nanotube forbidden gap outside the wire transmission band. Such a channel makes the entire hybrid system transparent in the energy domain where neither wire, nor nanotube is i…
Elementary electronic excitations, which are due to the Coulomb-field scatterings, present the diverse phenomena in 3D, 2D, 1D-nanotube electron gases, graphene and carbon nanotubes. The critical mechanisms cover the dimension-dependent bare Coulomb potentials, energy dispersions, and free/valence carrier density. They are responsible for the main features, the available excitation channels (the electron-hole regions), the joint van Hove singularities, the undamped/damped collective excitations at small/sufficiently high transferred momenta, the momentum dependences of plasmon frequencies (aco…
We simulate the localized surface plasmon resonances of an Au nanoparticle within tunneling proximity of a Au substrate and demonstrate that the modes may be identified with those responsible for light emission from a scanning tunneling microscope. Relative to the modes of an isolated nanoparticle these modes show significant red-shifting, extending further into the infrared with increasing radius, primarily due to a proximity-induced lowering of the effective bulk plasmon frequency. Spatial mapping of the field enhancement factor shows an oscillatory variation of the field, absent in the case…
We study theoretically the impact of Zener tunneling on the charge-transport properties of quasi-metallic (Qm) carbon nanotubes (characterized by forbidden band gaps of few tens of meV). We also analyze the interplay between Zener tunneling and elastic scattering on defects. To this purpose we use a model based on the master equation for the density matrix, that takes into account the inter-band Zener transitions induced by the electric field (a quantum mechanical effect), the electron-defect scattering and the electron-phonon scattering. In presence of Zener tunnelling the Qm tubes support an…
In cavity quantum electrodynamics, optical emitters that are strongly coupled to cavities give rise to polaritons with characteristics of both the emitters and the cavity excitations. We show that carbon nanotubes can be crystallized into chip-scale, two-dimensionally ordered films and that this new material enables intrinsically ultrastrong emitter-cavity interactions: rather than interacting with external cavities, nanotube excitons couple to the near-infrared plasmon resonances of the nanotubes themselves. Our polycrystalline nanotube films have a hexagonal crystal structure, ~25 nm domains…
We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this paper, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the ra…
We evaluate the rate of energy loss of a plasmon in a disorder-free carbon nanotube. The plasmon decays into neutral bosonic excitations of the electron liquid. The process is mediated either by phonon-assisted backscattering of a single electron, or Umklapp backscattering of two electrons. To lowest order in the backscattering interactions the partial decay rates are additive. At zero doping the corresponding decay rates scale as power-laws of the temperature with positive and negative exponents for the two mechanisms, respectively. The precise values of the exponents depend on the Luttinger …
The determination of the optical spectrum of single-wall carbon nanotubes (SWCNTs) is essential for the development of opto-electronic components and sensors with application in many fields. Real SWCNTs are finite, but almost all the studies performed so far use infinite SWCNTs. However, the spectra of finite and infinite systems are different. In this work the optical spectrum of finite (3,3) and (5,5) SWCNTs is calculated as a function of nanotube length. For the (3,3) SWCNTs, the calculated absorption spectra for light polarised both parallel and perpendicularly to the nanotube axis are in …
We investigate the two-plasmon spontaneous decay of a quantum emitter near single-walled carbon nanotubes (SWCNT) and graphene-coated wires (GCWs). We demonstrate efficient, enhanced generation of two-plasmon entangled states in SWCNTs due to the strong coupling between tunable guided plasmons and the quantum emitter. We predict two-plasmon emission rates more than twelve orders of magnitude higher than in free-space, with average lifetimes of a few dozens of nanoseconds. Given their low dimensionality, these systems could be more efficient for generating and detecting entangled plasmons in co…
We present a technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz frequencies. By modeling the nanotube as a nano-transmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex, frequency dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nano-transmission line is equivalent to directly exciting the yet-to-be observed one dimensional plasmons, the low energy excitation of a Luttinger liquid. Our technique has already been applie…
Carbon Nanotubes (CNs) are made of tubular graphite layers. These macromolecules have interesting features which are generally introduced in the first chapter of the thesis. In the rest of the thesis, the light conduction in metallic CNs is investigated. In chapter 2, by modeling metallic single-wall CNs as 2D free electron gas layers, we find the density of electrons on a 2D electron gas and solve the Maxwell's equations for these cylindrical waveguides. We assume the same time-dependency or frequency for the electrons oscillations on the 2D gas layers and the propagating electromagnetic wave…
Recently, it was suggested that the polarization dependence of light absorption to a single-walled carbon nanotube is altered by carrier doping. We specify theoretically the doping level at which the polarization anisotropy is reversed by plasmon excitation. The plasmon energy is mainly determined by the diameter of a nanotube, because pseudospin makes the energy independent of the details of the band structure. We find that the effect of doping on the Coulomb interaction appears through the screened exchange energy, which can be observed as changes in the absorption peak positions. Our result…
The zero-bias anomaly in the dependence of the tunneling density of states $ν(ε)$ on the energy $ε$ of the tunneling particle for two- and one-dimensional multilayered structures is studied. We show that for a ballistic two-dimensional (2D) system the first order interaction correction to DOS due to the plasmon excitations studied by Khveshchenko and Reizer is partly compensated by the contribution of electron-hole pairs which is twice as small and has the opposite sign. For multilayered systems the total correction to the density of states near the Fermi energy has the form $δν/ν_0 = {max} (|…
We investigate transport through a tunnelling junction between an uncorrelated metallic lead and a Luttinger liquid when the latter is subjected to a time dependent perturbation. The tunnelling current as well as the electron energy distribution function are found to be strongly affected by the perturbation due to generation of harmonics in the density oscillations. Using a semiconducting lead instead of a metallic one results in electrons being injected into the lead even without applied voltage. Some applications to carbon nanotubes are discussed.
The random phase approximation (RPA) theory is used to derive the Luttinger parameter g for metallic carbon nanotubes. The results are consistent with the Tomonaga-Luttinger models. All metallic carbon nanotubes, regardless if they are armchair tubes, zigzag tubes, or chiral tubes, should have the same Luttinger parameter g. However, a (10,10) carbon peapod should have a smaller g value than a (10,10) carbon nanotube. Changing the Fermi level by applying a gate voltage has only a second order effect on the g value. RPA theory is a valid approach to calculate plasmon energy in carbon nanotube s…
We develop theoretical arguments that demonstrate the possibility of metallic field-effect transistors (METFET's) in one-dimensional systems and particularly in armchair carbon nanotubes. A very inhomogeneous electric field, such as the field of a tunnelling tip, can penetrate the relatively weakly screened nanotubes and open an energy gap. As a consequence, an energy barrier forms that impedes electron flow and thus permits transistor action. This type of metallic field effect is advantageous because of the high conductance of the metallic tubes in the ON--state.
Tunneling density of states of both the massless and massive (gapped) particles in metallic carbon nanotubes is known to have anomalous energy dependence. This is the result of coupling to multiple low-energy bosonic excitation (plasmons). For both kinds of particles the ensuing effect is the suppression of the density of states by electron-electron interactions. We demonstrate that the optical absorption between gapless and gapped states is affected by the many-body effects in the opposite way. The absorption probability is enhanced compared with the non-interacting value and develops a power…
For single-walled carbon nanotubes (SWCNTs) with a length of 1-50 nm, the surface plasmon-polariton (SPP) resonance is within the terahertz frequency range; therefore, SWCNT lattices can be used to design frequency-selective surface (FSS). The numerical model of electromagnetic wave diffraction on a two-dimensional periodic SWCNT lattice can be described by an integro-differential equation of the second-order with respect to the surface current along SWCNT. The equation can be solved by the Bubnov-Galerkin method. Frequency dependence of reflecting and transmitting electromagnetic waves for FS…
