Even-Odd Effect in Andreev Transport through a Carbon Nanotube Quantum Dot

Abstract

We have measured the current(I)-voltage(V ) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance dI/dV due to the Kondo resonance is observed in the normal state, this feature around zero bias voltage is absent in the superconducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the dI/dV sub-gap structure caused by Andreev reflection. The first-order Andreev peak appearing around V = ∆/e is markedly enhanced in gate-voltage regions, in which the charge state of the quantum dot is odd. This enhancement is explained by a 'hidden' Kondo resonance, pinned to one contact only. A comparison with a single-impurity Anderson model, which is solved numerically in a slave-boson meanfield ansatz, yields good agreement with the experiment. There is a growing interest in the exploration of correlated charge transport through nanoscaled lowdimensional systems involving both superconductors and normal metals [1,2,3,4,5,6]. The penetration of the pair amplitude ∆ from a superconductor (S) into a normal metal (N), the proximity effect, is a manifestation of correlated charge transport mediated by Andreev processes taking place at the S-N interface [7] and leading in S-N-S junctions to the Josephson effect [8] and sup-gap current peaks due to multiple Andreev reflection (MAR) [9]. The superconducting proximity effect has been studied in great detail in the mesoscopic size regime of diffusive, but phase coherent conductors [10]. Andreev transport has also been the key quantity in experiments elucidating charge transport in single atom contacts [5,11]. On the other hand, Andreev transport through a quantum dot coupled to superconductors, is just emerging now [12,13,14,15]. If the dot is weakly coupled to the leads, Andreev processes are suppressed by the charging energy U of the dot [3,16,17]. If the dot is sufficiently small, size quantization takes place, forming a quantum dot (QD) with discrete eigenstates ('levels') at energies E {i} . Transport then occurs through individual levels [3]. Since the level 'positions' E {i} , and sometimes also the coupling strengths of the levels to both source and drain contacts Γ 1,2 , can be tuned through gate voltages, a physically tunable model system of the Anderson 'impurity problem' is realized. With one electron on the QD (half-filling), a many-electron ground-state forms, involving both the dot-state and conduction electrons from the leads in an energy window given by the the Kondo temperature T K [18,19].

Josephson current through a single Anderson impurity coupled to BCS leads

“…[14][15][16][17][18][19][20][21][22][23] The microscopic parameters of such nanoscale systems (e.g. the energy ǫ of the quantum dot) can be easily tuned, thereby allowing to study the physics in a controlled way.…”

Subgap features due to quasiparticle tunneling in quantum dots coupled to superconducting leads

“…Another method based on nonequilibrium Green's function was used by Yeyati et al 17 and Kang 18 to describe resonant tunneling through an effective single level quantum dot in the limit of very strong Coulomb repulsion in the dot (U → ∞ limit), where transport is governed by quasiparticle tunneling; the corresponding I -V curves show an intrinsic broadening of the BCS-like feature in the current in agreement with experimental observation. 8 For small Coulomb repulsion, higher order processes lead to Josephson current 9 and Andreev reflections, [2][3][4][5]7,10,15 which appear as subgap features in the experiments. Both effects were studied intensely experimentally and theoretically 4,17,19,20 and were recently summarized in review articles of Refs.…”

“…8 For small Coulomb repulsion, higher order processes lead to Josephson current 9 and Andreev reflections, [2][3][4][5]7,10,15 which appear as subgap features in the experiments. Both effects were studied intensely experimentally and theoretically 4,17,19,20 and were recently summarized in review articles of Refs. 21 and 22.…”

To Screen or Not to Screen, That is the Question!

“…6,7,[14][15][16][17][18] In this work, instead of relying on transport through a QD, we perform tunneling spectroscopy of a single QD (coupled to a superconducting reservoir) in order to investigate this interplay in a direct way. In particular, we explore how the Kondo resonance, observed when the QD's occupancy is odd and the reservoir is in the normal state, is replaced by ABS within the gap as the reservoir becomes superconducting.…”