Thermal noise correlations in quantum Hall effect devices: experimental check of a theorem by Battiker

Johnson-Nyquist expression for the mean-square voltage spectral density function of thermal noise in a two-terminal element has been extensively verified in over wide ranges of temperature, frequency and resistance of the two-terminal element. Most accurate investigations are given by Johnson noise thermometry experiments, where a base accuracy of a few parts per million was recently achieved. A generalization of the Johnson-Nyquist expression was derived in 1990 by Markus Büttiker (Phys. Rev. Lett., 65, 2901). Buttiker's expression is a statement about equilibrium noise correlations in multiterminal devices, and predicts the cross-spectral density functions between noise voltages measured at different terminal couples. The proof of Buttiker's expression deals also with the case of nonreciprocal electrical networks, for which the expression has its most interesting form. Quantum Hall effect (QHE) gives an ideal physical model to verify Büttiker's expression. QHE devices are multiterminal and exhibit a high degree of nonreciprocity. With the same devices, different networks can be obtained by short-circuiting together two or more terminals; the resulting network transresistances are simple fractions of the quantized Hall resistance. Measurements of voltage noise correlations have been carried out with a digital correlator and ultra-low-noise amplifier on a 6-terminal quantum Hall effect device. The device was in a screened probe provided with coaxial leads, kept at 1.3 K and under a magnetic field of 9 T. For all the configurations tested, the predictions of Büttiker's expression were verified within the experimental uncertainty of a few percent.