Condensed Matter Theory

Abstract:

A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles. © 2000 The American Physical Society.

Abstract:

The quasiparticle spectrum of a two-dimensional d-wave superconductor in the mixed state, (Formula presented) is studied both analytically and numerically using the linearized Bogoliubov-de Gennes equation. We consider various values of the “anisotropy ratio” (Formula presented) for the quasiparticle velocities at the Dirac points, and we examine the implications of symmetry. For a Bravais lattice of vortices, we find there is always an isolated energy zero (Dirac point) at the center of the Brillouin zone, but for a non-Bravais lattice with two vortices per unit cell there is generally an energy gap. In both of these cases, the density of states should vanish at zero energy, in contrast with the semiclassical prediction of a constant density of states, though the latter may hold down to very low energies for large anisotropy ratios. This result is closely related to the particle-hole symmetry of the band structures in lattices with two vortices per unit cell. More complicated non-Bravais vortex lattice configurations with at least four vortices per unit cell can break the particle-hole symmetry of the linearized energy spectrum, and lead to a finite density of states at zero energy. © 2000 The American Physical Society.

Abstract:

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is nonzero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time dependence of the mean-square displacement, approximately t(2/d) in dimension d>2, associated with the imaginary parts of eigenvalues.