Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux
arXiv:0806.0826 · doi:10.1103/PhysRevB.78.125305
Abstract
We study the persistent current of noninteracting electrons subject to a pointlike magnetic flux in the simply connected chaotic Robnik-Berry quantum billiard, and also in an annular analog thereof. For the simply connected billiard we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than mesoscopic fluctuations in the persistent current in the simply connected billiard, and can ultimately be traced to the response of the angular momentum levels (neglected in semiclassical expansions) on the unit disk to a pointlike flux at its center. The same behavior is observed for the annular billiard when the inner radius is much smaller than the outer one, while the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon.
20 pages, 11 figures; added references for section 1
References in corpus (18)
- Orbital Magnetism in the Ballistic Regime: Geometrical Effects
- Diamagnetic orbital response of mesoscopic silver rings
- Interactions and Interference in Quantum Dots: Kinks in Coulomb Blockade Peak Positions
- Mesoscopic fluctuations of the ground state spin of a small metal particle
- Quantum chaos in a deformable billiard: Applications to quantum dots
- On the relationship between the noise-induced persistent current and dephasing rate
- AC electric and magnetic responses of non-connected Aharonov-Bohm rings
- Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
- Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit
- The magnetic response of disordered metallic rings: the large contribution of the far levels
- Square billiard with a magnetic flux
- A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
- Aharonov-Bohm effect and resonances in the circular quantum billiard with two leads
- Enhancement of persistent currents due to confinement in metallic samples
- Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dots
- Persistent Currents in Quantum Chaotic Systems
- Orbital Magnetism in Disordered Mesoscopic Metals
- Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures