= Hall conductivity
{title2=$\sigma_{xy}$}
<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 $j_x=\sigma_{xx}E_x+\sigma_{xy}E_y$ and $j_y=-\sigma_{xy}E_x+\sigma_{xx}E_y$.
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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