INFLUENCE OF FRINGE FIELDS ON ELECTROSTATIC AHARONOV-BOHM EFFECTS IN MESOSCOPIC RING

A new method is invented to treat electron transport in the Aharonov-B ohm (AB)-type ring geometry where transport in each branch of the ring can be treated separately in terms of transfer matrix theory. The inf luence of fringe field due to the potential edge on the AB effect in a mesoscopic ring is thereby formulated. In the case of potential with an abrupt step, it is found by numerical calculations that the standar d treatment of AB effects is approximately permissible at a low enough electrostatic potential of practical interest. The phase of quantum o scillation, however, shifts towards low electrostatic potential, and t he amplitudes slowly decay as a function of electrostatic potential as it becomes high. In the case of realistic potential with gradual step s, the transfer matrix can be written in an ordered product of infinit esimal matrices causing AB phase shift and electric-field-dependent am plitude modulation. It is shown that the validity of the usual AB trea tment can be assessed in terms of the concept of adiabatic condition.