Reverse-field reciprocity for conducting specimens in magnetic fields

Abstract

A new static-electromagnetic reciprocity principle is presented, extending ordinary resistive reciprocity to the case of nonzero magnetic fields by requiring the magnetic field to be reversed when the reciprocal measurement is made. The principle is supported by measurements on various types of specimens, including those which exhibit the quantum-Hall effect. A derivation using elementary electromagnetic theory shows that the principle will hold provided only that the specimen is electrically linear (Ohmic), and that the Onsager form for the conductivity tensor applies throughout. The principle has important implications for electrical measurements on semiconductors in applied-magnetic fields.

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

“…The geometry of the device is such that no pair of contacts allows a perfectly isolated determination of R xx or R xy , and measurements must be performed in a van der Pauw method. Magnetic field and geometric symmetrization techniques were thus used to separate these values with quantitative precision [44].…”

“…By exchanging the voltage contacts with the current contacts we can measure the transpose of the resistance tensor, and can therefore symmetrize by using the following formulas, which remain valid for all systems in the linear response regime [44] :…”

Explicit connection between sample geometry and Hall response

“…Reverse-magneticfield reciprocity 20,21 implies that the first term is free of a linear dependence on B; thus, up to first order in B, it is equal to the constant I͐ 0 j a0 · j b0 dv, which in view of Eq. ͑1͒, we show first that V a = ͐j b · E a dv.…”

Real-time broadband subnoise level signal extraction in Hall sensors

“…Microscopic reversibility ensures that by permuting the current and voltage contacts in a device with 4 contacts labeled a, b, c and d, the transresistances V ac /I bd and V bd /I ac are equal, which is the definition of resistive reciprocity. From this, Sample et al deduced the theorem of reverse-magnetic-field-reciprocity [4], which states that if an external magnetic field is applied, it has to be inverted when permuting the source and sense contacts in order to ensure resistive reciprocity. This is the reason why the offset and the Hall voltage of a Hall device do not behave the same way under contact permutation: one sees its sign inverted and the other does not [5].…”

“…Its principle is derived from the universal Onsager relations [4]. Schematically speaking, in an isolated system, electromagnetic phenomena are invariant under time reversal.…”