AC response of Chklovskii-Halperin quantum Hall step-up transformer

The junction of quantum Hall(QH) edge states has attracted significant interest in recent days due to their applicability as the basic building blocks of quantum circuitry. Chklovskii and Halperin theoretically predicted that a quantum point contact between filling fractions ν= 1 and 1/3 could act as a DC step-up transformer with an amplification factor of 3/2 (Phys. Rev. B 57, 3781 (1998)), which was observed recently in experiments(arXiv:2212.01374). This amplification is intimately connected to the Andreev reflection-type processes (Phys. Rev. B 57, 12324 (1998) occurring due to the mismatch of quasi-particle charge on the two sides of the junction, even in the absence of a pairing mechanism like superconductivity. In this presentation, I will discuss a recent work of ours (arXiv:2306.00939) pertaining to a study for an AC transformer action of a quantum point contact separating quantum Hall states with distinct filling fractions (ν₁, ν₂₎. We carried out an analytic calculation in the frequency domain using the Kubo formula and established its consistency with a time domain calculation carried out in terms of plasmon wave packet dynamics. We show that the AC gain (g_ν1,ν2 (ω)) of this setup exceeds its DC bound for a certain range of frequency in the presence of appropriate inter-electron interactions owing to displacement current induced by the ambient gate electrodes. This setup is also endowed with the unique possibility of having frequency-tunable resonances and anti-resonances across the QPC.