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.

1.
M. R.
Gräber
,
T.
Nussbaumer
,
W.
Belzig
, and
C.
Schönenberger
,
Nanotechnology
15
,
S479
(
2004
).
2.
V.
Mourik
,
K.
Zuo
,
S. M.
Frolov
,
S. R.
Plissard
,
E. P. A. M.
Bakkers
, and
L. P.
Kouwenhoven
,
Science
336
,
1003
(
2012
).
3.
S.
Das Sarma
,
M.
Freedman
, and
C.
Nayak
,
NPJ Quantum Inf.
1
,
15001
(
2015
).
4.
P.
Recher
,
E. V.
Sukhorukov
, and
D.
Loss
,
Phys. Rev. B
63
,
165314
(
2001
).
5.
L.
Hofstetter
,
S.
Csonka
,
J.
Nygård
, and
C.
Schönenberger
,
Nature
461
,
960
(
2009
).
6.
L. G.
Herrmann
,
F.
Portier
,
P.
Roche
,
A.
Levy Yeyati
,
T.
Kontos
, and
C.
Strunk
,
Phys. Rev. Lett.
104
,
026801
(
2010
).
7.
J.
Schindele
,
A.
Baumgartner
, and
C.
Schönenberger
,
Phys. Rev. Lett.
109
,
157002
(
2012
).
8.
A.
Das
,
Y.
Ronen
,
M.
Heiblum
,
D.
Mahalu
,
A. V.
Kretinin
, and
H.
Shtrikman
,
Nat. Commun.
3
,
1165
(
2012
).
9.
J.
Gramich
,
A.
Baumgartner
, and
C.
Schönenberger
,
Phys. Rev. Lett.
115
,
216801
(
2015
).
10.
J.-D.
Pillet
,
C. H. L.
Quay
,
P.
Morfin
,
C.
Bena
,
A.
Levy Yeyati
, and
P.
Joyez
,
Nat. Phys.
6
,
965
(
2010
).
11.
T.
Dirks
,
T. L.
Hughes
,
S.
Lal
,
B.
Uchoa
,
Y.-F.
Chen
,
C.
Chialvo
,
P. M.
Goldbart
, and
N.
Mason
,
Nat. Phys.
7
,
386
(
2011
).
12.
E. J. H.
Lee
,
X.
Jiang
,
M.
Houzet
,
R.
Aguado
,
C. M.
Lieber
, and
S.
De Franceschi
,
Nat. Nanotechnol.
9
,
79
(
2014
).
13.
J.
Schindele
,
A.
Baumgartner
,
R.
Maurand
,
M.
Weiss
, and
C.
Schönenberger
,
Phys. Rev. B
89
,
045422
(
2014
).
14.
L.
Bretheau
,
Ç. Ö.
Girit
,
H.
Pothier
,
D.
Esteve
, and
C.
Urbina
,
Nature
499
,
312
(
2013
).
15.
C.
Janvier
,
L.
Tosi
,
L.
Bretheau
,
Ç. Ö.
Girit
,
M.
Stern
,
P.
Bertet
,
P.
Joyez
,
D.
Vion
,
D.
Esteve
,
M. F.
Goffman
,
H.
Pothier
, and
C.
Urbina
,
Science
349
,
1199
(
2015
).
16.
M.
Gaass
,
S.
Pfaller
,
T.
Geiger
,
A.
Donarini
,
M.
Grifoni
,
A. K.
Hüttel
, and
C.
Strunk
,
Phys. Rev. B
89
,
241405
(
2014
).
17.
S.
Ratz
,
A.
Donarini
,
D.
Steininger
,
T.
Geiger
,
A.
Kumar
,
A. K.
Hüttel
,
C.
Strunk
, and
M.
Grifoni
,
New J. Phys.
16
,
123040
(
2014
).
18.
A. P.
Higginbotham
,
S. M.
Albrecht
,
G.
Kirsanskas
,
W.
Chang
,
F.
Kuemmeth
,
P.
Krogstrup
,
T. S.
Jespersen
,
J.
Nygård
,
K.
Flensberg
, and
C. M.
Marcus
,
Nat. Phys.
11
,
1017
(
2015
).
19.
W.
Chang
,
S. M.
Albrecht
,
T. S.
Jespersen
,
F.
Kuemmeth
,
P.
Krogstrup
,
J.
Nygård
, and
C. M.
Marcus
,
Nat. Nanotechnol.
10
,
232
(
2015
).
20.
M.
Taupin
,
P.
Krogstrup
,
H. Q.
Nguyen
,
E.
Mannila
,
S. M.
Albrecht
,
J.
Nygård
,
C. M.
Marcus
, and
J. P.
Pekola
, e-print arXiv:1601.01149.
21.
K.
Grove-Rasmussen
,
H. I.
Jørgensen
,
B. M.
Andersen
,
J.
Paaske
,
T. S.
Jespersen
,
J.
Nygård
,
K.
Flensberg
, and
P. E.
Lindelof
,
Phys. Rev. B
79
,
134518
(
2009
).
22.
G.
Fülöp
,
F.
Domínguez
,
S.
d'Hollosy
,
A.
Baumgartner
,
P.
Makk
,
M. H.
Madsen
,
V. A.
Guzenko
,
J.
Nygård
,
C.
Schönenberger
,
A.
Levy Yeyati
, and
S.
Csonka
,
Phys. Rev. Lett.
115
,
227003
(
2015
).
23.
C. P.
Poole
,
Handbook of Superconductivity
, edited by
C. P.
Poole
(
Academic Press
,
San Diego, CA
,
2000
).
24.
Y.-F.
Chen
,
T.
Dirks
,
G.
Al-Zoubi
,
N. O.
Birge
, and
N.
Mason
,
Phys. Rev. Lett.
102
,
036804
(
2009
).
25.
N.
Bronn
and
N.
Mason
,
Phys. Rev. B
88
,
161409
(
2013
).
26.
T.
Dirks
,
Y.-F.
Chen
,
N. O.
Birge
, and
N.
Mason
,
Appl. Phys. Lett.
95
,
192103
(
2009
).
27.
I. V.
Borzenets
,
Y.
Shimazaki
,
G. F.
Jones
,
M. F.
Craciun
,
S.
Russo
,
Y.
Yamamoto
, and
S.
Tarucha
,
Sci. Rep.
6
,
23051
(
2016
).
28.
C. B.
Whan
and
T. P.
Orlando
,
Phys. Rev. B
54
,
R5255
(
1996
).
29.
S.
Pfaller
,
A.
Donarini
, and
M.
Grifoni
,
Phys. Rev. B
87
,
155439
(
2013
).
30.
S.
Skalski
,
O.
Betbeder-Matibet
, and
P. R.
Weiss
,
Phys. Rev.
136
,
A1500
(
1964
).
31.
R.
Yang
,
L.
Zhang
,
Y.
Wang
,
Z.
Shi
,
D.
Shi
,
H.
Gao
,
E.
Wang
, and
G.
Zhang
,
Adv. Mater.
22
,
4014
(
2010
).
32.
J.
Samm
,
J.
Gramich
,
A.
Baumgartner
,
M.
Weiss
, and
C.
Schönenberger
,
J. Appl. Phys.
115
,
174309
(
2014
).
33.
J. M.
Eldridge
,
Y. J.
Van der Meulen
, and
D. W.
Dong
,
Thin Solid Films
12
,
447
(
1972
).
34.
J.
Kim
,
V.
Chua
,
G. A.
Fiete
,
H.
Nam
,
A. H.
MacDonald
, and
C.-K.
Shih
,
Nat. Phys.
8
,
464
(
2012
).
35.
L.
Serrier-Garcia
,
J. C.
Cuevas
,
T.
Cren
,
C.
Brun
,
V.
Cherkez
,
F.
Debontridder
,
D.
Fokin
,
F. S.
Bergeret
, and
D.
Roditchev
,
Phys. Rev. Lett.
110
,
157003
(
2013
).
36.
A.
Levy Yeyati
,
J. C.
Cuevas
,
A.
López-Dávalos
, and
A.
Martín-Rodero
,
Phys. Rev. B
55
,
R6137
(
1997
).
37.
D. J.
Thouless
,
Phys. Rev.
117
,
1256
(
1960
).
38.
D. H.
Douglass
, Jr.
and
L. M.
Falicov
, “
The superconducting energy gap
,” in
Progress in Low Temperature Physics
, edited by
C.
Gorter
(
Elsevier
,
1964
), Vol.
4
, pp.
97
193
.
39.
R. F.
Gasparovic
,
B. N.
Taylor
, and
R. E.
Eck
,
Solid State Commun.
4
,
59
(
1966
).
40.

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 lξ,ξ(l)ξ(1+ξ/l)0.5 and λ(l)λ(1+ξ/l)0.5,42 respectively.

41.

We use the equations Δ(α)=Δ̃(α)[1(α/Δ̃(α))2/3]3/2 and ln(Δ̃(α)/Δ0)=π/4·α/Δ̃(α) of Ref. 30, valid in the dirty limit lξ and for αΔ̃(α), to calculate the dependence of the visible transport gap (the spectral quasiparticle gap) Δ as a function of B. Here, Δ̃ is the order parameter, Δ0 the experimentally determined transport gap at B = 0 and at base temperature, and α=0.5Δ0(B/Bc)n the pair-breaking parameter with the exponent n.30,42 Note that we use Bc as adjustable parameter so that Δ(B) vanishes at the experimentally determined values.

42.
M.
Tinkham
,
Introduction to Superconductivity
, 2nd ed. (
Dover
,
2004
).
43.

We ascribe the small central subgap conductance peak between TL and TR to the thermally broadened DOS in the S contact, coinciding with μQD=μN. The analysis at VSD = ±1 mV shows that this finite subgap conductance at elevated temperatures has no influence on our analysis.

44.
We carefully controlled that no structures are lost or created in the averaging procedure.
45.

In the studied temperature range kTΔkTc, the closing of the transport gap for TTc plays already a significant role.

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