Hall effect and magnetoresistance in four-probe tight-binding mesoscopic rings
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The Hall effect and magnetoresistance of a mesoscopic system having a four-probe ring geometry are calculated in a tight-binding model, either ordered or disordered, as function of magnetic flux and Fermi energy. The changes induced in the spectrum by the magnetic field affect differently the Aharonov-Bohm (AB) oscillating pattern of the two resistances: 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 number and geometry of the probes.
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