Current and shot noise in a normal metal-superconductor junction driven by spin-dependent periodic pulse sequence

TL;DR

This paper investigates spin-dependent current and noise in a normal metal-superconductor junction under periodic drives, revealing symmetric spin currents and noise dependence on drive sum in the Andreev regime, with extensions beyond it.

Contribution

It introduces a detailed analysis of spin-resolved transport and noise in N-S junctions driven by different periodic signals, highlighting unique properties in the Andreev regime.

Findings

Spin-resolved currents are equal in the Andreev regime despite different drives.

Excess noise depends only on the sum of the periodic drives.

Properties change when moving beyond the Andreev regime.

Abstract

Andreev reflection is a fundamental transport process occurring at the junction between a normal metal and a superconductor (a N-S junction), when an incident electron from the normal side can only be transmitted in the superconductor as a Cooper pair, with the reflection of a hole in the normal metal. As a consequence of the spin singlet nature of the BCS Cooper pairs, the current due to Andreev reflection at a N-S junction is always symmetric in spin. Using a Keldysh Nambu Floquet approach, combining analytical and numerical calculations, we study in details the AC transport at a N-S junction, when the two spin components in the normal metal are driven by different periodic drives. We show that, in the Andreev regime, i.e. when the superconducting gap is much larger than the frequency of the drives, the spin-resolved photo-assisted currents are always equal even if the two drives are different. In addition, we show that in this regime the excess noise depends only on the sum of the periodic drives, and we consider in particular the case of Lorentzian pulses (Levitons). We also show how these properties get modified when going beyond the Andreev regime. Finally we give a simple analytical proof of the special properties of the Andreev regime using an exact mapping to a particular N-N junction.