The conductance of a point contact between two hopping insulators is expected to be dominated by the individual localized states in its vicinity. Here we study the additional effects due to an external magnetic field. Combined with the measured conductance, the measured magnetoresistance provides detailed information on these states (e.g. their localization length, the energy difference and the hopping distance between them). We also calculate the statistics of this magnetoresistance, which can be collected by changing the gate voltage in a single device. Since the conductance is dominated by the quantum interference of particular mesoscopic structures near the point contact, it is predicted to exhibit Aharonov-Bohm oscillations, which yield information on the geometry of these structures. These oscillations also depend on local spin accumulation and correlations, which can be modified by the external field. Finally, we also estimate the mesoscopic Hall voltage due to these structures.
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