Conductance fluctuations in diffusive rings: Berry phase effects and criteria for adiabaticity

We study Berry phase effects on conductance properties of diffusive mesoscopic conductors, which are caused by an electron spin moving through an orientationally inhomogeneous magnetic field. Extending previous work, we start with an exact, i.e. not assuming adiabaticity, calculation of the universal conductance fluctuations in a diffusive ring within the weak localization regime, based on a differential equation which we derive for the diffuson in the presence of Zeeman coupling to a magnetic field texture. We calculate the field strength required for adiabaticity and show that this strength is reduced by the diffusive motion. We demonstrate that not only the phases but also the amplitudes of the h/2e Aharonov-Bohm oscillations are strongly affected by the Berry phase. In particular, we show that these amplitudes are completely suppressed at certain magic tilt angles of the external fields, and thereby provide a useful criterion for experimental searches. We also discuss Berry phase-like effects resulting from spin-orbit interaction in diffusive conductors and derive exact formulas for both magnetoconductance and conductance fluctuations. We discuss the power spectra of the magnetoconductance and the conductance fluctuations for inhomogeneous magnetic fields and for spin-orbit interaction.Comment: 18 pages, 13 figures; minor revisions. To appear in Phys. Rev.

The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.Comment: 9 page

Hyperfine-induced decoherence in triangular spin-cluster qubits

We investigate hyperfine-induced decoherence in a triangular spin-cluster for different qubit encodings. Electrically controllable eigenstates of spin chirality (C_z) show decoherence times that approach milliseconds, two orders of magnitude longer than those estimated for the eigenstates of the total spin projection (S_z) and of the partial spin sum (S_{12}). The robustness of chirality is due to its decoupling from both the total- and individual-spin components in the cluster. This results in a suppression of the effective interaction between C_z and the nuclear spin bath

Quantum Computation and Spin Electronics

In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five criteria for the realization of a quantum computer and consider the implications that these criteria have for quantum computation using the spin states of single-electron quantum dots. Finally, we consider the transport of quantum information via the motion of individual electrons in mesoscopic structures; specific transport and noise measurements in coupled quantum dot geometries for detecting and characterizing electron-state entanglement are analyzed.Comment: 28 pages RevTeX, 4 figures. To be published in "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics," eds. I. O. Kulik and R. Ellialtioglu (NATO Advanced Study Institute, Turkey, June 13-25, 1999

Berry phase and persistent current in disordered mesoscopic rings

A novel quantum interference effect in disordered quasi-one-dimensional rings in the inhomogeneous magnetic field is reported. We calculate the canonical disorder averaged persistent current using the diagrammatic perturbation theory. It is shown that within the adiabatic regime the average current oscillates as a function of the geometric flux which is related to the Berry phase and the period becomes half the value of the case of a single one-dimensional ring. We also discuss the magnetic dephasing effect on the averaged current.Comment: 6 pages, RevTeX, 2 figures. To appear in Phys. Rev. B Rapid Communications Vol.60 No.12 (1999