Berry Phase Contribution Research Articles

Fractional statistics of Laughlin quasiparticles in quantum antidots

In two dimensions, fractionally charged particles must possess fractional exchange statistics. In experiments on quantum antidots in the quantum Hall regime the charge of the tunneling particles can be determined directly as a measure of the gate voltage needed to attract one particle. In the same experiments, when the magnetic field is varied, it is observed that the fundamental Aharonov-Bohm period is $h∕e$ even for fractionally charged Laughlin quasiparticles. In this paper we analyze these experiments, explicitly taking into account the fractional statistical Berry's phase contribution.

Berry-phase contribution to the anomalous Hall effect in gadolinium

When conduction electrons are forced to follow the local spin texture, the resulting Berry phase can induce an anomalous Hall effect (AHE). In gadolinium, as in double-exchange magnets, the exchange interaction is mediated by the conduction electrons and the AHE may therefore resemble that of chromium dioxide and other metallic double-exchange ferromagnets. The Hall resistivity, magnetoresistance, and magnetization of single crystal gadolinium were measured in fields up to 30 T. Measurements between 2 K and 400 K are consistent with previously reported data. A scaling analysis for the Hall resistivity as a function of the magnetization suggests the presence of a Berry's-phase contribution to the anomalous Hall effect.

Weak-field thermal hall conductivity in the mixed state of d-wave superconductors.

Thermal transport in the mixed state of a d-wave superconductor is considered within the weak-field regime. We express the thermal conductivity, kappa(xx), and the thermal Hall conductivity, kappa(xy), in terms of the cross section for quasiparticle scattering from a single vortex. Solving for the cross section (neglecting the Berry phase contribution and the anisotropy of the gap nodes), we obtain kappa(xx)(H,T) and kappa(xy)(H,T) in surprisingly good agreement with the qualitative features of the experimental results for YBa2Cu3O6.99. In particular, we show that the simple, yet previously unexpected, weak-field behavior, kappa(xy)(H,T) approximately T squareroot [H], is that of thermally excited nodal quasiparticles, scattering primarily from impurities, with a small skew component provided by vortex scattering.

Skyrmion strings and the anomalous Hall effect in CrO2.

Topological (or singularity point) defects are thought to play a crucial role in the phase transitions of 3D spin systems, as they do in such 2D systems as the XY model. In double-exchange ferromagnets the conduction electrons are strongly coupled with core spins through Hund's rule, and, in the presence of a nontrivial spin texture, acquire a Berry phase contribution to the anomalous Hall effect. We combine Hall effect and magnetization data on CrO2 with a thermodynamical scaling hypothesis to confirm that the critical behavior of the topological-spin-defect density is consistent with that of the heat capacity. This analysis is the first experimental confirmation of the topological character of critical fluctuations.

Quantum effects in the Hall resistivity of CMR oxides

This forum paper reviews recent work by the author and colleagues on an unforeseen consequence of the constraint that charge carriers follow the local spin texture. As a result of the double-exchange mechanism in the presence of strong Hund's-rule coupling, the constraint produces a universal Berry-phase contribution to the anomalous Hall effect in the vicinity of the ferromagnetic transition. Such effects are apparent in both 3D and layered manganites and are expected in other double-exchange systems.

Dynamic interplay of Berry’s phase and spectral flow in the current-voltage characteristics of a restricted class of large SNS annular Josephson junctions

It has been argued that a competition arises between the Berry phase and spectral flow effects in a restricted class of large SNS annular Josephson junctions. A crossover is expected to occur in the junction response at the temperature ${T}_{*}$ where the superconducting dynamics enters the hydrodynamic limit. For $Tg{T}_{*},$ spectral flow occurs in the weak link and masks the Berry phase effects; while for $T\ensuremath{\ll}{T}_{*},$ spectral flow does not occur allowing Berry phase effects to freely influence junction dynamics. In this paper we focus on temperatures $T\ensuremath{\lesssim}{T}_{*}$ where spectral flow masking of Berry phase effects begins to switch off. In the case where a single vortex is present in the weak link, we numerically calculate the I--V curves for a restricted class of annular Josephson junctions in which nonvanishing Berry phase effects are expected to occur. We find that as Berry phase effects strengthen, distinctive shifts appear in the I--V curves which are the signature of the crossover, and provide clear targets for an experimental test of the underlying theory. We estimate ${T}_{*}$ for a clean junction, summarize the restrictions defining the class of annular junctions in which nonvanishing Berry phase effects are expected to occur, and show how the I--V curve shifts can be understood as a consequence of: (1) a Berry phase contribution to the tunneling current density; (2) the magnetic structure of the vortex core; and (3) Bernoulli's theorem.

Berry Phase Theory of the Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites

We show that the anomalous Hall effect (AHE) observed in colossal magnetoresistance manganites is a manifestation of Berry phase effects caused by carrier hopping in a nontrivial spin background. We determine the magnitude and temperature dependence of the Berry phase contribution to the AHE, finding that it increases rapidly in magnitude as the temperature is raised from zero through the magnetic transition temperature ${T}_{c}$, peaks at a temperature ${T}_{\mathrm{max}}>{T}_{c}$, and decays as a power of $T$, in agreement with experimental data. We suggest that our theory may be relevant to the anomalous Hall effect in conventional ferromagnets as well.

Berry phase contribution to the vacuum persistence amplitude; effective action approach

We compute the Berry geometric phase contribution to the vacuum decay amplitude for the parametric harmonic oscillator. Path integral methods are employed to set up an effective action whose (almost) adiabatic approximation will enable us to derive an expression for the probability that the ground state remains in the ground state.