Photon-Assisted Single-Particle Tunneling Between Superconductors

Abstract

Before attempting to describe what effect a microwave photon might be expected to have on the tunneling current I would like to review briefly the gross features of the usual single-particle tunneling between dissimilar superconductors. If we assume that the energy gaps are ε _g1 = 2Δ ₁ and ε _g2 = 2Δ ₂ and for convenience take Δ ₁ > Δ ₂, then for T = 0°K there will be no tunneling current for an applied voltage e V _o < Δ ₁ + Δ ₂. At eV _o = Δ ₁ + Δ ₂ there will be an abrupt rise, with an approximately linear increase in the current for all values of eV _o ≥ Δ ₁ + Δ ₂. The effect of finite temperatures on this abrupt rise, or tunneling edge, will be to broaden the transition and give it a definite width. In addition, due to the thermal excitation of electrons across the gap there will be electrons able to tunnel at voltages less than eV _o = Δ ₁ + Δ ₂ , giving rise to a cusp in the current with the peak occurring at eV _o = Δ ₁ − Δ ₂. The magnitude of the current below the tunneling edge, being related to the number of thermally excited electrons, can be made arbitrarily small by going to progressively lower temperatures.