Geometric boundary effects on the electronic properties of finite carbon nanotubes (original) (raw)
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Effects of Finite Length on the Electronic Structure of Carbon Nanotubes
The Journal of Physical Chemistry B, 1999
The electronic structure of finite-length armchair carbon nanotubes has been studied using several ab-initio and semi-empirical quantum computational techniques. The additional confinement of the electrons along the tube axis leads to the opening of a band-gap in short armchair tubes. The value of the band-gap decreases with increasing tube length, however, the decrease is not monotonic but shows a well defined oscillation in short tubes. This oscillation can be explained in terms of periodic changes in the bonding characteristics of the HOMO and LUMO orbitals of the tubes. Finite size graphene sheets are also found to have a finite band-gap, but no clear oscillation is observed. As the length of the tube increases the density of states (DOS) spectrum evolves from that characteristic of a zero-dimensional (0-D) system to that characteristic of a delocalized one-dimensional (1-D)
Quantum-size effects in capped and uncapped carbon nanotubes
Annual Reports Section "C" (Physical Chemistry), 2006
Properties of C 60 -related finite-length nanotubes C 40120n with armchair structures and C 42118n with zigzag structures, in which n is, respectively, the number of cyclic cis-and trans-polyene chains inserted between the fullerene hemispheres at the two edges, are analyzed by quantum chemical calculations at the B3LYP DFT level of theory. To clarify end-cap effects on the C 60 -related nanotubes, the corresponding nanotubes terminated by H atoms, C 20n H 20 and C 18n H 18 are also analyzed. Bond-length alternation patterns in the armchair nanotubes change in an oscillatory manner as n with a periodicity of 3, whereas those in the zigzag nanotubes are independent of the chain width. A similar tendency is seen in computed HOMO-LUMO gaps in the finite-length nanotubes. The sharp contrast in the quantum-size effects between the armchair and zigzag nanotubes is a consequence of interchain interactions in the cylinders, which depend on their edge structures. The interchain interactions in the armchair nanotubes are significant, due to the delocalization of orbital amplitudes within single cis-polyene chains, whereas those in the zigzag nanotubes are weak, due to the nodal properties of the single trans-polyene chains. The geometrical and electronic features in the C 60 -related nanotubes are also well affected by the fullerene hemispheres at the two edges because orbital interactions between the end-caps and the cylindrical segments conserve their orbital symmetries in the frontier orbital regions. DFT calculations illuminate that the structural and electronic properties of the C 60 -related nanotubes are dominated by tube lengths, edge structures, and end caps.
Eigenstates and transmission coefficients of finite-sized carbon nanotubes
The Journal of Chemical Physics, 2003
The tight-binding eigenstates of isolated finite-sized zigzag and armchair nanotubes are obtained analytically using the transfer matrix method. Edge states are encountered for zigzag tubes but not for armchair tubes. Inclusion of curvature leads to a decaying-oscillating behavior of the highest occupied and lowest unoccupied molecular orbital gap in armchair tubes as a function of length. For zigzag tubes the inclusion of curvature induces the conversion of an extended state at nonbonding energy to an edge state. In addition the transmission coefficient of zigzag and armchair tubes with featureless leads is analytically obtained. The existence of a transmission peak at the Fermi level that decays exponentially with nanotube length for zigzag tubes is explained.
Electronic Structure of the Finite-Sized Single-Walled Carbon Nanotubes
International Journal of Nanoscience, 2003
The effects of tubule length and terminal capping on the geometrical and electronic properties of finite-sized zig-zag (9, 0) single-walled carbon nanotubes (SWNT), which length varying from 2 up to 12 unit cells (~50 Å), were investigated using molecular mechanics, semi-empirical methods (AM1 and EHMO) and density functional theory (B3LYP). AM1 method indicates how the nanotube ends are capped affects strongly the tubule geometric parameters. Although these effects seem to decrease exponentially as the tube gets longer, the converging values for C–C bond length in the open- and closed-end structures are slightly different. It was learned that combination of low-level methods like AM1 and EHMO (which tend to overestimate and underestimate the HOMO–LUMO energy gap, respectively) together with high-level method such as DFT is efficient to estimate band gap for finite-sized nanostructures. The HOMO–LUMO energy gaps obtained from semi-empirical and DFT methods decrease as the tubule len...
Radial oscillations of local density of states in carbon nanotubes
Physical Review B, 2001
By performing an analytical study of the electronic structure of metallic carbon nanotubes, we show that the local density of states exhibits well-defined oscillations as a function of the nanotube radius. The periods of such oscillations are obtained from size quantization effects derived from folding up finite graphene sheets into tubular structures. A clear analogy with the de Haas-van Alphen effect in metals is established to explain the origin and features of such oscillations. Results of energy change calculations for impurity-doped carbon nanotubes also show the same type of oscillations.
Energy gap of alternant carbon nanotubes
Macromolecular Theory and Simulations, 1995
The energy spectra of two types of non-helical carbon nanotubes are investigated theoretically. It is shown that either the topological or the correlational contributions determine the width of the band gap. In some cases (for nanotubes with diameter < 1 nm) the electron correlation changes qualitatively the results for the width of the energy gap ΔE: if in the one-electron approximation the band width ΔE = 0, the contribution of the electron correlation becomes dominant and increases the band gap ΔE > 0. At small diameter of the nanotubes (D > 1 nm) the ground state of the tubes corresponds to semiconductors with moderate or narrow energy gap, while at D > 1 nm ΔE decreases monotonously. The energy spectra of the planar ribbon polymers are compared with those of the iso-electronic nanotubes.
Physical Review B, 2010
Optical properties of three kinds of zigzag ͑5,0͒, ͑13,0͒, and ͑9,0͒ single-walled carbon nanotubes ͑SWCNTs͒ are studied using an approximate quantum mechanical method named complete neglect of differential overlap, which distinguishes basis atomic orbitals with different azimuthal l quantum numbers ͑CNDOL͒. This method models the electron energy transitions and excited state charge distributions through a configuration interaction of singly ͑CIS͒ excited determinants allowing the direct understanding of properties related with the total electronic wave function of nanoscopic systems, projecting a reliable quantum mechanical understanding to real life objects. The finite SWCNT's structures were obtained by replicating the unit cells of periodic SWCNTs and saturating the edge dangling bonds with hydrogens. The unit cell was previously relaxed using standard density functional theory methods. The behavior of these SWCNTs were interpreted in the framework of the CNDOL scheme by increasing the lengths of the tubes above 3 nm. As the nanotubes grow in length, the position of excited states for each SWCNT evolve differently: in contrast with ͑9,0͒ SWCNT, which exhibits favorable conditions for photoexcitation, the ͑13,0͒ and ͑5,0͒ SWCNTs do not show a lowering of the lowest excited states. This behavior is discussed by taking into account electron-electron interactions as considered in the framework of the CIS procedure. Furthermore, the ͑13,0͒ and ͑5,0͒ SWCNTs present forbidden transitions for the lowest excitations and its first dipole-allowed transitions are at 0.9-1.0 and 1.4-1.6 eV, respectively. In contrast, ͑9,0͒ SWCNT allows excitations by photon at less than 0.4 eV as the length of the nanotube tends to infinite. Excitons appear more bounded, energetically and spatially, in the ͑13,0͒ than in the ͑9,0͒ and ͑5,0͒ SWCNTs.
Physica B: Condensed Matter, 2011
We have used a non-equilibrium surface Green's function matching formalism combined with a tightbinding Hamiltonian to consider the effect of different arrangements of pentagon rings on localization of density of states at the tip regions of semi-infinite capped carbon nanotubes. The transfer matrixes are obtained by an iterative procedure. The results demonstrate that the positions of the peaks near Fermi energy are remarkably affected by the relative locations of pentagons. It is observed that in thin nanotubes, carbon atoms belonging two neighboring pentagon rings have significant contribution in the localized states near fermi energy. From our calculations, it turns out that the metallic or semiconducting behavior of capped nanotubes in the tip regions depends on the metallic or semiconducting nature of their nanotube stems.
Local electronic properties of carbon nanotube heterojunctions
Physical Review B, 2000
Local electronic properties of metallic-semiconducting carbon nanotube heterostructures are investigated by studying the behavior of the one-electron local density of states ͑LDOS͒ along the tubes. We determine how these properties change from the metallic to the semiconducting side of a nanotube junction. We show that Friedel oscillations may not always be evident on the metallic side, and we found clear exponential decay of the LDOS on the semiconducting side. The exponential rates of decay as well as the absence of the oscillations are explained in terms of a simple picture that relates the LDOS to the bulk electronic structure of the constituent parts of the heterostructures.
The two classes of low-energy spectra in finite carbon nanotubes
Physical Review B, 2015
Electrons in carbon nanotubes (CNTs) possess spin and orbital degrees of freedom. The latter is inherited from the bipartite graphene lattice with two inequivalent Dirac points. The electronic spectra obtained in several transport experiments on CNT quantum dots in parallel magnetic field often show an anticrossing of spectral lines assigned to the opposite Dirac valleys. So far this valley mixing has been attributed to the disorder, with impurity induced scattering. We show that this effect can arise also in ultraclean CNTs of the armchair class and it can be caused solely by the presence of the boundaries. In contrast, in CNTs of the zigzag class it does not occur. These two fundamentally different classes of spectra arise because of different rotational symmetries of the low energy eigenstates in the two types of CNTs. The magnitude of the level splitting depends in a non-monotonous way on the distance of the involved energy levels from the charge neutrality point.