Transition from metallic to tunneling-type conductance in metal-metal and normal-metal-superconductor point contacts

Abstract

We have investigated the microshort-to-tunneling crossover in normal-normal (N-N) and normal-metal-superconductor (N-S) point-contact junctions at 4.2 K as the junction conductance (G₀) is varied. The microshort (or "metallic") point contact with the dynamic conductance G (V) having a negative derivative with respect to bias V (i.e., ∂G/∂V<0) changes over to a tunneling-type junction with ∂G/∂V>0 when G₀≃3-5 mS. We show that this is the region where the contact radius a is a few times k_F⁻¹ (k_F is the Fermi wave vector) and the crossover in the sign of ∂G/∂V occurs due to electron confinement in a length scale comparable to k_F⁻¹. The effect of confinement is to make the electrons crossing the constriction evanescent in nature as the junction size is reduced progressively and the energy for lateral confinement becomes comparable to E_F. We argue that in this extreme ballistic regime, the classical Sharvin approach breaks down as quantum effects due to electron confinement takes over. This happens much before "single-atom" contact is reached which signals the onset of vacuum tunneling. As a further test of the electron confinement effects in point contacts, we investigated clean N-S microshorts showing near-ideal Andreev reflection. We find that in N-S junctions, the Andreev reflection (which is a manifestation of superconductivity) gradually vanishes when the contact radius α≃0.1ξ (ξ is the coherence length) and the energy cost of electron confinement is larger than the superconducting energy gap Δ.