Observing the Berry phase in diffusive conductors: Necessary conditions for adiabaticity

In a recent preprint (cond-mat/9803170), van~Langen, Knops, Paasschens and Beenakker attempt to re-analyze the proposal of Loss, Schoeller and Goldbart (LSG) [Phys. Rev. B~48, 15218 (1993)] concerning Berry phase effects in the magnetoconductance of diffusive systems. Van Langen et al. claim that the adiabatic approximation for the Cooperon previously derived by LSG is not valid in the adiabatic regime identified by LSG. It is shown that the claim of van~Langen et al. is not correct, and that, on the contrary, the magnetoconductance does exhibit the Berry phase effect within the LSG regime of adiabaticity. The conclusion reached by van~Langen et al. is based on a misinterpretation of field-induced dephasing effects, which can mask the Berry phase (and any other phase coherent phenomena) for certain parameter values.Comment: 25 pages, 9 figure

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.Comment: LaTex, 22 page

Self-adjointness of Dirac operators via Hardy-Dirac inequalities

Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.Comment: PACS 03.65.P, 03.3

Uniform Density Theorem for the Hubbard Model

A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix \uprho (x,y) in the ground state and in the canonical and grand canonical ensembles is shown to be constant on the diagonal $x=y$, and to vanish if $x \not=y$ and if $x$ and $y$ are on the same sublattice. For free electron hopping models, it is shown in addition that there are no correlations between sites of the same sublattice in any higher order density matrix. Physical implications are discussed.Comment: 15 pages, plaintex, EHLMLRJM-22/Feb/9

Hybridization and spin decoherence in heavy-hole quantum dots

We theoretically investigate the spin dynamics of a heavy hole confined to an unstrained III-V semiconductor quantum dot and interacting with a narrowed nuclear-spin bath. We show that band hybridization leads to an exponential decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips, and that the accordant single-hole-spin decoherence time T2 can be tuned over many orders of magnitude by changing external parameters. In particular, we show that, under experimentally accessible conditions, it is possible to suppress hyperfine-mediated nuclear-pair-flip processes so strongly that hole-spin quantum dots may be operated beyond the `ultimate limitation' set by the hyperfine interaction which is present in other spin-qubit candidate systems.Comment: 7 pages, 3 figure

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.