The ability to control the conductance of single molecules will have a major impact in nanoscale electronics. Azobenzene, a molecule that changes conformation as a result of a trans/cis transition when exposed to radiation, could form the basis of a light-driven molecular switch. It is therefore crucial to clarify the electrical transport characteristics of this molecule. Here, we investigate, theoretically, charge transport in a system in which a single azobenzene molecule is attached to two carbon nanotubes. In clear contrast to gold electrodes, the nanotubes can act as true nanoscale electrodes and we show that the low-energy conduction properties of the junction may be dramatically modified by changing the topology of the contacts between the nanotubes and the molecules, and/or the chirality of the nanotubes (that is, zigzag or armchair). We propose experiments to demonstrate controlled electrical switching with nanotube electrodes.

The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed that crucially depend on the tube's chirality: (i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states. This phenomenon occurs due to the magnetic-field-dependent open boundary conditions obeyed by the carbon nanotube's wave functions. The transport is fully suppressed above threshold values of the magnetic field, which depend on the nanotube chirality, length, and on the spin-orbit coupling. (ii) Reversible spin-polarized currents can be obtained upon tuning the magnetic field, exploiting the curvature-induced spin-orbit splitting.

We investigate Fabry-Perot interference in an ultraclean carbon nanotube resonator. The conductance shows a clear superstructure superimposed onto conventional Fabry-Perot oscillations. A sliding average over the fast oscillations reveals a characteristic slow modulation of the conductance as a function of the gate voltage. We identify the origin of this secondary interference in intervalley and intravalley backscattering processes which involve wave vectors of different magnitude, reflecting the trigonal warping of the Dirac cones. As a consequence, the analysis of the secondary interference pattern allows us to estimate the chiral angle of the carbon nanotube. DOI: 10.1103/PhysRevLett.117.166804 Clean carbon nanotubes (CNTs) are an excellent material system to observe Fabry-Perot interference when highly transparent contacts suppress charging effects [1]. This is often the case in the hole regime of transport in CNTs [2,3]. So far, experiments mostly concentrated on the effects of the linear, Dirac-like part of the CNT dispersion relation, resulting in simple Fabry-Perot (FP) interference [1,[4][5][6]. Its hallmark is an oscillatory behavior of the differential conductance GðV g ; V b Þ as a function of both gate voltage V g and bias voltage V b , with frequency proportional to the CNT length [1]. On top of this regular oscillation, slower modulations are sometimes observed in experiments [1,5,7]. Such secondary interference has been attributed to disorder [7,8] or to channel mixing at the CNT-contact interface [9]. It has been suggested that a slow modulation can also originate from intrinsic interference effects in chiral CNTs [10]. In general, being related to a difference of accumulated phases, secondary interference probes the nonlinearity of the CNT dispersion relation due to the trigonal warping and, in turn, the chiral angle [9,10].In this Letter, we report on the investigation of a peculiar secondary interference pattern in the hole regime of an ultraclean CNT. Upon averaging over the fast primary FP oscillations, the resulting average linear conductancē GðV g Þ shows a quasiperiodic slow modulation deep in the hole regime. We combine detailed tight-binding calculations and fundamental symmetry arguments to identify the origin of the slow modulation. Our analysis of the gate voltage dependence ofḠðV g Þ allows us to estimate the CNT's chiral angle θ.We measure the differential conductance of a suspended CNT attached to 50-nm-thick Pt=Ti leads, separated by a 1.2-μm-wide trench, at T ¼ 15 mK [11]. The fabrication process is optimized to produce defect-free devices [12]. . A striking feature of our data is the slow modulation of the conductance pattern as a function of V g , visible as a series of darker and brighter intervals in Fig. 1(a) alternating on a scale of approximately 2 V.In Fig. 1(b), we show the differential conductance trace GðV g Þ for V b ¼ 0. Primarily, we observe a fast oscillation of the conductance at a frequency f 1 ¼ 12.8 V −1. This fundamental frequency is directly related to t...

The electronic spectra of long carbon nanotubes (CNTs) can, to a very good approximation, be obtained using the dispersion relation of graphene with both angular and axial periodic boundary conditions. In short CNTs one must account for the presence of open ends, which may give rise to states localized at the edges. When a magnetic field is applied parallel to the tube axis, it modifies both momentum quantization conditions, causing hitherto extended states to localize near the ends. We study analytically and numerically the appearance and evolution of this peculiar localization phenomenon in CNTs of any nonarmchair chirality, including the electron spin. Conductance calculations show different evolution of spin up and down states in increasing magnetic field. The existence of geometry-induced localized states at the zigzag edge of graphene nanoribbons has been predicted some years ago, 1,2 recently seen experimentally and shown to influence the transport in graphene quantum dots.3 Similar states at the ends of single-wall nanotubes have been observed 4 and studied. [5][6][7][8] In zigzag-armchair nanotube junctions, the interface states calculated to appear at the junction were identified with the end states of the zigzag nanotube fragment. 9,10 In this work we study another type of edge states, namely those which arise when initially extended states become localized in a parallel magnetic field.11,12 We present a detailed analytical and numerical study of this effect in CNTs of arbitrary nonarmchair chirality, including the spin-orbit coupling and the Zeeman effect. We find that this phenomenon occurs also in those chiral CNTs which have no localized end states when the magnetic field is absent. Numerical calculations of the conductance of finite CNT devices in a continuously varying magnetic field suggest the possibility of spin-selective transport.The model. Our starting point is the tight-binding Hamiltonian for a honeycomb lattice with one p z orbital per atom and with the interatomic potentialV . If we calibrate our energy scale so that the on-site energies vanish, the Hamiltonian is given byĤwhere i and j are the lattice site indices, |z j is a p z orbital at site j , and t ij = z j |V |z i is the hopping integral between the sites. This Hamiltonian nicely captures the properties of flat graphene and CNTs. In order to properly describe finite size nanotubes in the magnetic field it is necessary to include the Peierls phase and curvature effects in the hopping elements t ij . We follow here the approach of Ando. 13 For the sake of clarity we shall initially neglect the spin-orbit coupling and the Zeeman effect, as they do not change our main conclusion. The spin-dependent effects will be addressed later.The graphene coordinate system and the relevant real space vectors are shown in Fig. 1(a), while the graphene Brillouin zone with K and K points is shown in Fig. 1(b). In order to find the appropriate boundary conditions and eigenstates of CNTs we use an approach based on the Dirac equation treatment. 2,14...