M. Szopa

Flux qubit on a mesoscopic nonsuperconducting ring

The possibility of making a flux qubit on a nonsuperconducting mesoscopic ballistic quasi-one-dimensional ring is discussed. We showed that such a 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 superconducting quantum interference device magnetometer. Two or more qubits can be coupled by the flux the circulating currents generate. The problem of decoherence is also discussed.

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.

Coherence of currents in mesoscopic cylinders

The persistent currents driven by the pure Aharonov-Bohm type magnetic field in mesoscopic normal metal or semiconducting cylinders are studied. A two-dimensional (2D) Fermi surfaces are characterized by four parameters. Several conditions for the coherence and enhancement of currents are discussed. These results are then generalized to a three-dimensional (3D) thin-walled cylinder to show that under certain geometric conditions on the Fermi surface, a novel effect - the appearance of spontaneous currents is predicted.

Symmetry extensions of Euler's polyhedral theorem and the band theory of solids

Irreducible symmetry representations characterize topological invariants of point group molecules. In the present paper this result is extended to periodic structures in two and three dimensions, using plane and space symmetry groups. Applications include a symmetry analysis of the band structure for the graphite sheet and related nanotubes of the leapfrog type.

SPONTANEOUS FLUX AND FLUX TRAPPED IN MESOSCOPIC CYLINDERS

Persistent currents in mesoscopic cylinders made of a very clean metal and with nearly flat Fermi surface are studied. It is shown that the inclusion of the orbital magnetic interaction between electrons can lead to spontaneous currents (spontaneous fluxes) and to flux trapping if the number of interacting electrons is large enough. The free energy of the cylinder is discussed and the self-consistent formulas for the quantized flux in the cylinder is derived. It is argued that the properties of such mesoscopic cylinders are to some extent similar to the properties of superconducting samples.

Orbital magnetic moments in pure and doped carbon nanotubes

The unusual band structure of carbon nanotubes CNs results in their remarkable magnetic properties. The application of magnetic field B parallel to the tube axis can change the conducting properties of the CN from metallic to semiconducting and vice versa. Apart from that, B induces via the Bohm-Aharonov effect orbital magnetic moments orb in the nanotube. These moments are studied both in pure and hole- or electron-doped CNs, isolated or in a circuit. Remarkably, orb in pure CNs depend uniquely on their original conducting properties, length, and temperature but do not depend on the nanotube radius or the particular chirality. In doped nanotubes the magnetic moments can be strongly altered and depend on the radius and chirality. Temperature can even change their character from diamagnetic at low T to paramagnetic at high T. A general electron-hole asymmetry increasing with the doping is found.

The canonical form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two‐level system to a single quantized boson mode, is studied in the Bargmann–Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff‐transformed equations give rise to a two‐dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.

SPONTANEOUS CURRENTS IN MESOSCOPIC RINGS

In a system of mesoscopic rings the influence of orbital magnetic interaction between the electrons is investigated. At a critical temperature Tc the system undergoes a phase transition into a current carrying state. Tc depends strongly on geometry of the system and/or its Fermi-surface, and on the quantum size gap at the Fermi level. Elastic scattering reduces Tc and eventually suppresses the transition.

Coherent quantum dynamics of mesoscopic metallic ring with a barrier

In this paper we consider a mesoscopic 1D, ballistic, metallic ring with a potential barrier. We show that the coherent coupling between two distinct quantum states with different winding numbers can lead to a formation of a qubit. We discuss the possible realizations of such a ring, the adjustment of a potential barrier parameters and the possible decoherence sources.

Geometry and Topology Induced Electronic Properties of Graphene Derived Quantum Systems

Three different topological structures built on the basis of a graphene lattice are investigated. Clusters of the (3,6) type homeomorphic with the sphere, toroidal, and cylindrical carbon nanotubes are shown to have the same dispersion relation, inherited from the planar graphene lattice. The persistent currents in axially symmetric structures, their dependence on the size and geometry of the molecule, are also discussed.