A generalized Langevin equation with quantum baths (QMD) for thermal transport is derived with the help of nonequilibrium Green's function (NEGF) formulation. The exact relationship of the quasi-classical approximation to NEGF is demonstrated using Feynman diagrams of the nonlinear self energies. To leading order, the retarded self energies agree, but QMD and NEGF differ in lesser/greater self energies. An implementation for general systems using Cholesky decomposition of the correlated noises is discussed. Some means of stabilizing the dynamics are given. Thermal conductance results for graphene strips under strain and temperature dependence of carbon nanotubes are presented. The "quantum correction" method is critically examined.
In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal π-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene.
Electron spin resonance (ESR) investigation of graphene nanoribbons (GNRs) prepared through longitudinal unzipping of multiwalled carbon nanotubes (MWCNTs) indicates the presence of C-related dangling bond centers, exhibiting paramagnetic features. ESR signal broadening from pristine or oxidized graphene nanoribbons (OGNRs) is explained in terms of unresolved hyperfine structure, and in the case of reduced GNRs (RGNRs), the broadening of ESR signal can be due to enhancement in conductivity upon reduction. The spin dynamics observed from ESR linewidth-temperature data reflect a variable range h…
We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.
We study transport length scales in carbon nanotubes and graphene ribbons under the influence of Anderson disorder. We present generalized analytical expressions for the density of states, the elastic mean free path and the localization length in arbitrarily structured quantum wires. These allow us to analyze the electrical response over the full energy range, including the regions around van Hove singularies, traditionally difficult to access by alternative approaches. Comparing with the results of numerical simulations, we demonstrate that both the diffusive and the localized regime are well…
Molybdenum disulfide nanoribbons and nanotubes are quasi-1D semiconductors with strong spin-orbit interaction, a nanomaterial highly promising for quantum electronic applications. Here, it is demonstrated that a bismuth semimetal layer between the contact metal and this nanomaterial strongly improves the properties of the contacts. Two-point resistances on the order of 100k$Ω$ are observed at room temperature. At cryogenic temperature, Coulomb blockade is visible. The resulting stability diagrams indicate a marked absence of trap states at the contacts and the corresponding disorder, compared …
We use the robust nearest-neighbour tight-binding approximation to study on the same footing interband dipole transitions in narrow-bandgap carbon nanotubes and graphene nanoribbons. It is demonstrated that curvature effects in metallic single-walled carbon nanotubes and edge effects in gapless graphene nanoribbons not only open up bang gaps, which typically correspond to THz frequencies, but also result in a giant enhancement of the probability of optical transitions across these gaps. Moreover, the matrix element of the velocity operator for these transitions has a universal value (equal to …
This contribution reports on comparative studies on giant magnetoresistance (GMR) in carbon nanotubes (CNTs) and graphene nanoribbons of similar aspect ratios (i.e perimeter/length and width/length ratios, for the former and the latter, respectively). The problem is solved at zero temperature in the ballistic transport regime, by means of the Green's functions technique within the tight-binding model and with the so-called wide band approximation for electrodes. The GMR effect in graphene is comparable to that of CNTs, it depends strongly on the chirality and only slightly on the aspect ratio.…
We perform a comprehensive first-principles study of the electronic properties of phosphorene nanoribbons, phosphorene nanotubes, multilayer phosphorene, and heterobilayers of phosphorene and two-dimensional (2D) transition metal dichalcogenide (TMDC) monolayer. The tensile strain and electric-field effects on electronic properties of low-dimensional phosphorene nanostructures are also investigated. Our calculations show that zigzag phosphorene nanoribbons (z-PNRs) are metals, regardless of the ribbon width while armchair phosphorene nanoribbons (a-PNRs) are semiconductors with indirect bandga…
Graphene/carbon-nanotube (CNT) hybrid material can be useful in energy storage and nanoelectronic technologies. Here we address the CNT-oscillator encapsulated in a graphene-nanoribbon (GNR) trench as a novel design, and investigate its properties via classical molecular dynamics simulations. Since the energy barrier was very low while the CNT was encapsulated in the GNR trench, the CNT absorbed on the GNR surface could easily be encapsulated in the GNR trench. MD simulations showed that the CNT oscillator encapsulated in a GNR trench is compatible with simple CNT oscillators, so we anticipate…
We study Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction in carbon nanotubes (CNTs) and graphene nanoribbons in the presence of spin orbit interactions and magnetic fields. For this we evaluate the static spin susceptibility tensor in real space in various regimes at zero temperature. In metallic CNTs the RKKY interaction depends strongly on the sublattice and, at the Dirac point, is purely ferromagnetic (antiferromagnetic) for the localized spins on the same (different) sublattice, whereas in semiconducting CNTs the spin susceptibility depends only weakly on the sublattice and is dominantly…
Properties of bulk and boundaries of materials can, in general, be quite different, both for topological and non-topological reasons. One of the simplest boundary problems to pose is the tight-binding problem of noninteracting electrons on a finite honeycomb lattice. Despite its simplicity, the problem is quite rich and directly related to the physics of graphene. We revisit this long-studied problem and present an analytical derivation of the electron spectrum and wave functions for graphene rectangular derivatives. We provide an exact analytical description of extended and localized states, …
Nanoribbons (nanographite ribbons) are carbon systems analogous to carbon nanotubes. We characterize a wide class of nanoribbons by a set of two integers $<p,q>$, and then define the width $w$ in terms of $p$ and $q$. Electronic properties are explored for this class of nanoribbons. Zigzag (armchair) nanoribbons have similar electronic properties to armchair (zigzag) nanotubes. The band gap structure of nanoribbons exhibits a valley structure with stream-like sequences of metallic or almost metallic nanoribbons. These sequences correspond to equi-width curves indexed by $w$. We reveal a peculi…
Three typical one-dimensional (1D)/quasi-1D nanocarbons, linear carbon chains, carbon nanotubes, and graphene nanoribbons have been proven to grow inside single-wall carbon nanotubes. This gives rise to three types of hybrid materials whose behaviour and properties compared among each other are far from understood. After proving successful the synthesis of these nanostructured materials in recently published work, we have now been able to study their oxidation stability systematically by using resonance Raman spectroscopy. Surprisingly, the linear carbon chains, which have been theoretically p…
Floating gate transistor is the basic building block of non-volatile flash memory, which is one of the most widely used memory gadgets in modern micro and nano electronic applications. Recently there has been a surge of interest to introduce a new generation of memory devices using graphene nanotechnology. In this paper we present a new floating gate transistor (FGT) design based on multilayer graphene nanoribbon (MLGNR) and carbon nanotube (CNT). In the proposed FGT a multilayer structure of graphene nanoribbon (GNR) would be used as the channel of the field effect transistor (FET) and a laye…
We report on the fabrication and characterization of synthesized multiwall MoS2 nanotube (NT) and nanoribbon (NR) field-effect transistors (FETs). The MoS2 NTs and NRs were grown by chemical transport, using iodine as a transport agent. Raman spectroscopy confirms the material as unambiguously MoS2 in NT, NR, and flake forms. Transmission electron microscopy was used to observe cross sections of the devices after electrical measurements and these were used in the interpretation of the electrical measurements allowing estimation of the current density. The NT and NR FETs demonstrate n-type beha…
We numerically investigate the electronic transport properties of graphene nanoribbons and carbon nanotubes with inter-valley coupling, e.g., in \sqrt{3}N \times \sqrt{3}N and 3N \times 3N superlattices. By taking the \sqrt{3} \times \sqrt{3} graphene superlattice as an example, we show that tailoring the bulk graphene superlattice results in rich structural configurations of nanoribbons and nanotubes. After studying the electronic characteristics of the corresponding armchair and zigzag nanoribbon geometries, we find that the linear bands of carbon nanotubes can lead to the Klein tunnelling-l…
We derive the generalized magneto-absorption spectra for curved graphene nanorib- bons and carbon nanotubes by using the Peierls tight-binding model. The main spectral characteristics and the optical selection rules result from the cooperative or competitive relationships between the geometric structure and a magnetic field. In curved ribbons, the dominant selection rule remains unchanged during the variation of the curvature. When the arc angle increases, the prominent peaks are split, with some even vanishing as the angle exceeds a critical value. In carbon nanotubes, the angular-momentum co…
We report on the transport properties of novel carbon nanostructures made of partially unzipped carbon nanotubes, which can be regarded as a seamless junction of a tube and a nanoribbon. We find that graphene nanoribbons act at certain energy ranges as a perfect valley filters for carbon nanotubes, with the maximum possible conductance. Our results show that a partially unzipped carbon nanotube is a magnetoresistive device, with a very large value of the magnetoresistance. We explore the properties of several structures combining nanotubes and graphene nanoribbons, demonstrating that they beha…
We investigated the atomic structures, Raman spectroscopic and electrical transport properties of individual graphene nanoribbons (GNRs, widths ~10-30 nm) derived from sonochemical unzipping of multi-walled carbon nanotubes (MWNTs). Aberration-corrected transmission electron microscopy (TEM) revealed a high percentage of two-layer (2L) GNRs and some single layer ribbons. The layer-layer stacking angles ranged from 0o to 30o including average chiral angles near 30o (armchair orientation) or 0o (zigzag orientation). A large fraction of GNRs with bent and smooth edges was observed, while the rest…
We report on the fabrication and characterization of all-carbon hybrid quantum devices based on graphene and single-walled carbon nanotubes. We discuss both, carbon nanotube quantum dot devices with graphene charge detectors and nanotube quantum dots with graphene leads. The devices are fabricated by chemical vapor deposition growth of carbon nanotubes and subsequent structuring of mechanically exfoliated graphene. We study the detection of individual charging events in the carbon nanotube quantum dot by a nearby graphene nanoribbon and show that they lead to changes of up to 20% of the conduc…
The honeycomb carbon structure of graphene and nanotubes has a dynamics which can give rise to a spectrum. This can be excited via the interaction with an external electromagnetic field. In this work, non-linear waves on graphene and nanotubes associated with the carbon structure are investigated using a gauge model. Typical energies are estimated and there scaling with the nanoribbon width investigated. Furthermore, the soliton-photon interaction depends on the incident photon polarization. In particular, we find that the nanoribbon is transparent when the polarization is along the largest le…
An elegant formula for coordinates of carbon atoms in a unit cell of a single-walled nanotube (SWNT) is presented and a new molecular motor of double-walled carbon nanotube whose inner tube is a long (8,4) SWNT and outer tube a short (14,8) SWNT is constructed. The interaction between inner an outer tubes is analytically derived by summing the Lennard-Jones potentials between atoms in inner and outer tubes. It is proved that the molecular motor in a thermal bath exhibits a directional motion with the temperature variation of the bath.
We simulate quantum transport between a graphene nanoribbon (GNR) and a single-walled carbon nanotube (CNT) where electrons traverse vacuum gap between them. The GNR covers CNT over a nanoscale region while their relative rotation is 90 degrees, thereby forming a four-terminal crossbar where the bias voltage is applied between CNT and GNR terminals. The CNT and GNR are chosen as either semiconducting (s) or metallic (m) based on whether their two-terminal conductance exhibits a gap as a function of the Fermi energy or not, respectively. We find nonlinear current-voltage (I-V) characteristics i…
We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory der…
We report the first study on the thermal behaviour of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope $-(173\pm 65)$ ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative descriptio…
The k.p method is a semi-empirical approach which allows to extrapolate the band structure of materials from the knowledge of a restricted set of parameters evaluated in correspondence of a single point of the reciprocal space. In the first part of this review article we give a general description of this method, both in the case of homogeneous crystals (where we consider a formulation based on the standard perturbation theory, and Kane's approach) and in the case of non-periodic systems (where, following Luttinger and Kohn, we describe the single-band and multi-band envelope function method a…
The practical realization of nano-scale electronics faces two major challenges: the precise engineering of the building blocks and their assembly into functional circuits. In spite of the exceptional electronic properties of carbon nanotubes only basic demonstration-devices have been realized by time-consuming processes. This is mainly due to the lack of selective growth and reliable assembly processes for nanotubes. However, graphene offers an attractive alternative. Here we report the patterning of graphene nanoribbons (GNRs) and bent junctions with nanometer precision, well-defined widths a…
We show that the energy differences between the lowest optical singlet exciton and the lowest triplet exciton in semiconducting single-walled carbon nanotubes with diameter $\sim 1$ nm and graphene nanoribbons with widths $\sim 2$ nm are an order of magnitude smaller than in the $π$-conjugated polymer poly(para-phenylenevinylene). Our calculated energy gaps between the singlet and triplet excitons are in excellent agreement with the measured values in three different nanotubes with diameters close to 1 nm. The spatial extent of the triplet exciton is nearly the same as that of the singlet exci…
Imposing additional confinement in two-dimensional (2D) materials can yield further control over the associated electronic, optical, and topological properties. However, synthesis of ultra-narrow nanoribbons (NRs) remains a challenge, particularly for the transition metal dichalcogenides (TMDs), and synthesizing TMD NRs narrower than 50 nm has remained elusive. Here, we report the vapor-phase synthesis of ultra-narrow TaS2 NRs. The NRs are grown within the hollow cavity of carbon nanotubes, thereby limiting their lateral dimensions and layer number, while simultaneously stabilizing them agains…
We characterize radio frequency detection in a high-quality metallic single-walled carbon nanotube. At a bath temperature of 77 K, only bolometric (thermal) detection is seen. At a bath temperature of 4.2 K and low bias current, the response is due instead to the electrical nonlinearity of the non-ohmic contacts. At higher bias currents, the contacts recover ohmic behavior and the observed response agrees well with the calculated bolometric responsivity. The bolometric response is expected to operate at terahertz frequencies, and we discuss some of the practical issues associated with developi…
Capacitance-voltage (C-V) characteristics are important for understanding fundamental electronic structures and device applications of nanomaterials. The C-V characteristics of graphene nanoribbons (GNRs) are examined using self-consistent atomistic simulations. The results indicate strong dependence of the GNR C-V characteristics on the edge shape. For zigzag edge GNRs, highly non-uniform charge distribution in the transverse direction due to edge states lowers the gate capacitance considerably, and the self-consistent electrostatic potential significantly alters the band structure and carrie…
Graphene nanoribbons with perfect edges are predicted to exhibit interesting electronic and spintronic properties, notably quantum-confined bandgaps and magnetic edge states. However, graphene nanoribbons produced by lithography have, to date, exhibited rough edges and low-temperature transport characteristics dominated by defects, mainly variable range hopping between localized states in a transport gap near the Dirac point. Here, we report that one- and two-layer nanoribbons quantum dots made by unzipping carbon nanotubes10 exhibit well-defined quantum transport phenomena, including Coulomb …
Carbon Nanotubes (CNTs) are one of the most important materials in nanotechnology. In some of their technological applications (electromechanical oscillators and mechanical actuators for artificial muscles, for instance), it is necessary to subject them to large deformations. Although this frequently happens in air, there are only few studies about the interaction of deformed CNTs with the atmosphere and the dynamics of these processes has not yet been addressed. In this work, we have investigated, through fully atomistic reactive molecular dynamics simulations, the process of hydrogenation of…
For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogues of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the end spins: for $S=1/2$ end spins their interaction is antiferromagnetic, while for $S…
The model of thermal rectifier based on the asymmetry of interaction of the molecular chain ends with thermostats is proposed in this work. The rectification mechanism is not related to the chain asymmetry, but to the asymmetry of the interaction of chain ends with thermostats, for instance, due to different lengths of the end thermostats. The chain can be homogeneous, it is only important that the thermal conductivity of the chain should depend on temperature strict monotonically. The effect is maximal when convergence of the thermal conductivity with increasing length just begins to manifest…
Bottom-up synthesized graphene nanoribbons (GNRs) are quantum materials that can be structured with atomic precision, providing unprecedented control over their physical properties. Accessing the intrinsic functionality of GNRs for quantum technology applications requires the manipulation of single charges, spins, or photons at the level of an individual GNR. However, experimentally, contacting individual GNRs remains challenging due to their nanometer-sized width and length as well as their high density on the metallic growth substrate. Here, we demonstrate the contacting and electrical chara…
Carbon nanoribbons (CNRs) are graphene (planar) structures with large aspect ratio. Carbon nanobelts (CNBs) are small graphene nanoribbons rolled up into spiral-like structures, i. e., carbon nanoscrolls (CNSs) with large aspect ratio. In this work we investigated the energetics and dynamical aspects of CNBs formed from rolling up CNRs. We have carried out molecular dynamics simulations using reactive empirical bond-order potentials. Our results show that similarly to CNSs, CNBs formation is dominated by two major energy contribution, the increase in the elastic energy due to the bending of th…
We present a detailed description of semi-quantum molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the effects of phonon quantum statistics are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of thermal properties and heat transport in different…
Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination are investigated via density functional theory (DFT) in Kohn-Sham formulation. "Selection rules" will be formulated, that allow to extract (approximately) the electronic structure of the AGNR bands starting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, a threefold periodicity of the excitation gap with the ribbon width (N, number of carbon atoms per carbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicity would be obs…
We report the observation of two fundamental sub-gap transport processes through a quantum dot (QD) with a superconducting contact. The device consists of a carbon nanotube contacted by a Nb superconducting and a normal metal contact. First, we find a single resonance with position, shape and amplitude consistent with the theoretically predicted resonant Andreev tunneling (AT) through a single QD level. Second, we observe a series of discrete replicas of resonant AT at a separation of $\sim145\,μ$eV, with a gate, bias and temperature dependence characteristic for boson-assisted, inelastic AT, …
We demonstrate that electron-phonon interaction in quantum dots embedded in one-dimensional systems leads to pronounced, non-Markovian decoherence of optical transitions. The experiments we present focus on the lineshape of photoluminescence from low-temperature axially localized carbon nanotube excitons. The independent boson model that we use to model the phonon interactions reproduces with very high accuracy the broad and asymmetric emission lines and the weak red-detuned radial breathing mode replicas observed in the experiments. The intrinsic phonon-induced pure-dephasing of the zero-phon…
We propose carbon nanotubes (CNTs) with magnetic impurities as a versatile platform to achieve unconventional Kondo physics, where the CNT bath is gapped by the spin-orbit interaction and surface curvature. While the strong-coupling phase is inaccessible for the special case of half-filled impurities in neutral armchair CNTs, the system in general can undergo quantum phase transitions to the Kondo ground state. The resultant position-specific phase diagrams are investigated upon variation of the CNT radius, chirality, and carrier doping, revealing several striking features, e.g., the existence…
Topological signatures in the quench dynamics of periodically driven quantum systems
Indian Institute of Science Education and Research Tirupati（印度科学教育与研究学院蒂鲁帕提分校）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Indian Institute of Science, Bengaluru（班加罗尔印度科学学院）
Motivated by a recent experiment on nonlinear tunneling in a suspended Carbon nanotube connected to two normal electrodes [S. Sapmaz, {\it et al}., Phys. Rev. Lett. {\bf 96}, 26801 (2006)], we investigate nonequilibrium vibration-mediated sequential tunneling through a molecular quantum dot with two electronic orbitals asymmetrically coupled to two electrodes and strongly interacting with an internal vibrational mode, which is itself weakly coupled to a dissipative phonon bath. For this purpose, we establish rate equations using a generic quantum Langevin equation approach. Based on these equa…
