Quantized charge pumping in superconducting double barrier structure : Non-trivial correlations due to proximity effect

TL;DR

This paper investigates quantum charge pumping in a superconducting double barrier system, revealing how resonance effects and electron interactions influence charge quantization, with implications for experimental realization.

Contribution

It demonstrates how superconducting gap modulation leads to quantized charge pumping and explores the impact of electron-electron interactions on this process.

Findings

Resonance in transmission causes quantized pumped charge.

Weak interactions suppress charge quantization at low temperatures.

Phase modulation does not reliably produce quantized charge.

Abstract

We consider quantum charge pumping of electrons across a superconducting double barrier structure in the adiabatic limit. The superconducting barriers are assumed to be reflection-less so that an incident electron on the barrier can either tunnel through it or Andreev reflect from it. In this structure, quantum charge pumping can be achieved (a) by modulating the amplitudes, $\Delta_1$ and $\Delta_2$ of the two superconducting gaps or alternatively, (b) by a periodic modulation of the order parameter phases, $\phi_1$ and $\phi_2$ of the superconducting barriers. In the former case, we show that the superconducting gap gives rise to a very sharp resonance in the transmission resulting in quantization of pumped charge, when the pumping contour encloses the resonance. On the other hand, we find that quantization is hard to achieve in the latter case. We show that inclusion of weak electron-electron interaction in the quantum wire leads to renormalisation group evolution of the transmission amplitude towards the perfectly transmitting limit due to proximity effects. Hence as we approach the zero temperature limit, we get destruction of quantized pumped charge. This is in sharp contrast to the case of charge pumping in a double barrier in a Luttinger liquid where quantized charge pumping is actually achieved in the zero temperature limit. We also propose an experimental set-up to study these effects.