Symmetry breaking of the admittance of a classical two-dimensional electron system in a magnetic field

Magnetic-field symmetry of dynamic capacitances

“…Below we show that the dynamic-capacitance matrix is in general not an even function of the magnetic field but obeys only the weaker Onsager-Casimir reciprocity symmetry. This result is in agreement with a recent experiment by Sommerfeld et al 8 Linear electrical transport is characterized by a quadraticadmittance matrix G ␣␤ with a dimension equal to the number of contacts which are connected to the sample under investigation. The Fourier amplitudes, ␦I ␣ , of the current through contact ␣ are then related to the Fourier amplitudes of the voltage oscillation, ␦V ␤ exp(Ϫit), at contact ␤ by…”

“…Obviously, this is only possible if NϾ3, and provided that there are contacts with a nonvanishing dc conductance. This last condition was not satisfied in the experiment by Sommerfeld et al, 8 where apparently only capacitive contacts were present. Their sample, however, was macroscopic in size such that electron motion is not phase coherent.…”

“…In the case of a spatially dependent potential along a conductor ͑e.g., in the presence of a voltage probe͒, the emittance of capacitive contacts is symmetric but higher-order terms in frequency are not ͑row 3 of Table I͒: this corresponds to the experiment of Ref. 8. In a measurement for which at least one of the conductors is connected to two or more contacts ͑and thus permits transmission from one of its contacts to another͒, one finds an emittance 10 which is not an even function of the magnetic field ͑row 4 of …”

“…In the present work, we show that the above-mentioned theory of low-frequency admittance predicts the observed result. In particular, we show that the dynamic capacitance between two conductors, which are both capacitively coupled to the rest of the sample and to each other, can be asymmetric, and we discuss an example similar to the experiment of Sommerfeld et al 8 Consider a general multiterminal sample consisting of conductors jϭ1, . .…”

“…Edge-plasma modes, as discussed in Ref. 8, are a possible mechanism but not necessary for the existence of asymmetric capacitances. 16 To conclude, we summarize the main results on the symmetry properties of capacitances in Table I for two-and three-terminal samples.…”