We report thermally activated transport resonances for biases below the superconducting energy gap in a carbon nanotube quantum dot (QD) device with a superconducting Pb and a normal metal contact. These resonances are due to the superconductor's finite quasi-particle population at elevated temperatures and can only be observed when the QD life-time broadening is considerably smaller than the gap. This condition is fulfilled in our QD devices with optimized Pd/Pb/In multi-layer contacts, which result in reproducibly large and “clean” superconducting transport gaps with a strong conductance suppression for subgap biases. We show that these gaps close monotonically with increasing magnetic field and temperature. The accurate description of the subgap resonances by a simple resonant tunneling model illustrates the ideal characteristics of the reported Pb contacts and gives an alternative access to the tunnel coupling strengths in a QD.
References
We use the Drude model to estimate the mean free path of our Pb strips from the measured low-temperature Pb strip resistivity. Assuming the bulk literature values of Pb23 for the coherence length ξ∞ ∼ 90 nm and the penetration depth λ∞ ∼ 40 nm in the clean limit (l = ∞), we estimate the coherence length and penetration depth of our Pb strips using the interpolation formulae suitable for the regime and ,42 respectively.
We use the equations and of Ref. 30, valid in the dirty limit l ≪ ξ and for , to calculate the dependence of the visible transport gap (the spectral quasiparticle gap) Δ as a function of B. Here, is the order parameter, Δ0 the experimentally determined transport gap at B = 0 and at base temperature, and the pair-breaking parameter with the exponent n.30,42 Note that we use Bc as adjustable parameter so that vanishes at the experimentally determined values.
We ascribe the small central subgap conductance peak between TL and TR to the thermally broadened DOS in the S contact, coinciding with . The analysis at VSD = ±1 mV shows that this finite subgap conductance at elevated temperatures has no influence on our analysis.
In the studied temperature range , the closing of the transport gap for plays already a significant role.
