MAGNETOCONDUCTANCE OF AHARONOV-BOHM RINGS WITH HALF-BOUND STATES

The effects of half-bound states or zero-energy resonances on the elec tronic magnetotransport in Aharonov-Bohm rings are investigated. These states can be obtained by adding attractive impurity potentials withi n the ring. In the most symmetric case of attractive impurities locate d on the two crossings with the leads connecting the ring to the exter nal reservoirs, the zero-energy resonance condition can be reduced to a simple analytical expression containing the magnetic field and the i mpurity parameters. If the resonance occurs at zero magnetic field, it is pushed into the discrete spectrum for finite fields, and the two b ound states become degenerate for magnetic flux Phi=h/2e for arbitrary ring size. This system provides an ideal experimental setup for study ing the particular properties of half-bound states, which correspond t o the exceptional solutions of Levinson's theorem. It is also shown th at the presence of a zero-energy resonance has dramatic consequences i n the magnetic-field dependence of the conductance.