Hall conductivity is the transverse part of the electrical response in which an applied electric field drives a perpendicular current density. In two dimensions, one convention writes and .
The sign depends on the magnetic-field orientation and chosen axes. In a quantum Hall effect plateau, the longitudinal response is strongly suppressed and the Hall response takes quantized values. Electrical conductivity and electrical resistivity are inverse tensors; taking the reciprocal of a single component is generally incorrect when longitudinal and transverse responses coexist.
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