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Exact voltage and current distribution in the rectangular geometry
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Image of FIG. 1.
FIG. 1.

The three measurement configurations for a rectangular sample (gray shaded), showing a part of the array of mirror charges and schematic current/electric field lines. The mirror charges also denote the location and sign of the poles of the elliptic functions: (a) configuration A, function ns, (b) configuration B, function cs, and (c) configuration C, function . The coordinate system shows the magnitude of the quarter periods and in relation to the sample dimensions; note the subtle factor-of-2 differences.

Image of FIG. 2.
FIG. 2.

Dependence of on the sample aspect ratio , visualizing the expressions in Table I . The four-terminal resistance is given by .

Image of FIG. 3.
FIG. 3.

Voltage contours in the presence of a magnetic field, with Hall angle . The potential is given by . The current lines are unchanged compared to the field-free configuration.

Image of FIG. 4.
FIG. 4.

Voltage contours and current directions for the anisotropic crystal in configuration A. Note that the direction, along the CuO chains, is the high-conductivity direction, so that the current (represented here as a vector field) is no longer orthogonal to the voltage contours. For representational reasons, the length of the vector is held constant. The slight asymmetry in the plot originates from the small Hall effect.


Generic image for table
Table I.

The complex potential , its visualization through lines of constant and using , and various other parameters of interest for the three configurations A–C as pictured in Fig. 1 . For configuration C, we take the positive voltage contact to be at and the negative one at .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Exact voltage and current distribution in the rectangular geometry