Isospectral But Physically Distinct: Modular Symmetries and their Implications for Carbon Nanotori

Recently there has been considerable interest in the properties of carbon nanotori. Such nanotori can be parametrized according to their radii, their chiralities, and the twists that occur upon joining opposite ends of the nanotubes from which they are derived. In this paper, however, we demonstrate that many physically distinct nanotori with wildly different parameters nevertheless share identical band structures, energy spectra, and electrical conductivities. This occurs as a result of certain geometric symmetries known as modular symmetries which are direct consequences of the properties of the compactified graphene sheet. Using these symmetries, we show that there is a dramatic reduction in the number of spectrally distinct carbon nanotori compared with the number of physically distinct carbon nanotori. The existence of these modular symmetries also allows us to demonstrate that many statements in the literature concerning the electronic properties of nanotori are incomplete because they fail to respect the spectral equivalences that follow from these symmetries. We also find that as a result of these modular symmetries, the fraction of spectrally distinct nanotori which are metallic is approximately three times greater than would naively be expected on the basis of standard results in the literature. Finally, we demonstrate that these modular symmetries also extend to cases in which our carbon nanotori enclose non-zero magnetic fluxes.Comment: 12 pages, ReVTeX, 6 figures, 1 table. Replaced to match published versio

Flux qubit on mesoscopic nonsuperconducting ring

The possibility of making a flux qubit on nonsuperconducting mesoscopic ballistic quasi 1D ring is discussed. We showed that such ring can be effectively reduced to a two-state system with two external control parameters. The two states carry opposite persistent currents and are coupled by tunneling which leads to a quantum superposition of states. The qubit states can be manipulated by resonant microwave pulses. The flux state of the sample can be measured by a SQUID magnetometer. Two or more qubits can be coupled by the flux the circulating currents generate. The problem of decoherence is also discussed.Comment: Phys. Rev. B. (accepted

Persistent currents in carbon nanotubes

Persistent currents driven by a static magnetic flux parallel to the carbon nanotube axis are investigated. Owing to the hexagonal symmetry of graphene the Fermi contour expected for a 2D-lattice reduces to two points. However the electron or hole doping shifts the Fermi energy upwards or downwards and as a result, the shape of the Fermi surface changes. Such a hole doping leading to the Fermi level shift of (more or less) 1eV has been recently observed experimentally. In this paper we show that the shift of the Fermi energy changes dramatically the persistent currents and discuss the electronic structure and possible currents for zigzag as well as armchair nanotubes.Comment: 8 text pages, 6 figures, to appear in Physics Letters