104 research outputs found
Midgap spectrum of the fermion-vortex system
I study the midgap spectrum of the fermion-vortex system in two spatial
dimensions. The existence of bound states, in addition to the zero modes found
by Jackiw and Rossi, is established. For a singly quantized vortex, I present
complete analytical solutions in terms of generalized Laguerre polynomials in
the opposite limits of vanishing and large vortex core size. There is an
infinite number of such bound states, with a spectrum that is, when squared,
given by, respectively, the Coulomb potential and the isotropic harmonic
oscillator. Possible experimental signatures of this spectrum in
condensed-matter realizations of the system are pointed out.Comment: 10 pages, no figure
A new class of models for surface relaxation with exact mean-field solutions
We introduce a class of discrete models for surface relaxation. By exactly
solving the master equation which governs the microscopic dynamics of the
surface, we determine the steady state of the surface and calculate its
roughness. We will also map our model to a diffusive system of particles on a
ring and reinterpret our results in this new setting.Comment: 12 pages, 3 figures,references adde
Fractionalization in a square-lattice model with time-reversal symmetry
We propose a two-dimensional time-reversal invariant system of essentially
non-interacting electrons on a square lattice that exhibits configurations with
fractional charges e/2. These are vortex-like topological defects in the
dimerization order parameter describing spatial modulation in the electron
hopping amplitudes. Charge fractionalization is established by a simple
counting argument, analytical calculation within the effective low-energy
theory, and by an exact numerical diagonalization of the lattice Hamiltonian.
We comment on the exchange statistics of fractional charges and possible
realizations of the system.Comment: 4 pages, 3 figures, RevTex 4. (v2) improved discussion of lattice
effects and confinement; clearer figure
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