HALL-EFFECT AND MAGNETORESISTANCE IN 4-PROBE TIGHT-BINDING MESOSCOPICRINGS

The Hall effect and magnetoresistance of a mesoscopic system having a four-probe ring geometry are calculated in a tight-binding model, eith er ordered or disordered, as function of magnetic flux and Fermi energ y. The changes induced in the spectrum by the magnetic field affect di fferently the Aharonov-Bohm (AB) oscillating pattern of the two resist ances: after the gap reaches the Fermi energy, the Hall effect remains bounded while the magnetoresistance increases exponentially with the sample size. The results are shown to depend significantly on the numb er and geometry of the probes.