The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a level that is weakly coupled to the leads controls the molecular charge, while a strongly coupled one dominates the molecular conduction), and electron counting devices in which the current in a point contact is sensitive to the charging state of a nearby quantum dot. Here we consider the case where transport in the strongly coupled channel has to be described quantum mechanically (covering the full range between sequential tunneling and co-tunneling), while conduction through the weakly coupled channel is a sequential process that could by itself be described by a simple master equation. We compare the result of a full quantum calculation based on the pseudoparticle non-equilibrium Green function method to that obtained from an approximate mixed quantum-classical calculation, where correlations between the channels are taken into account through either the averaged rates or the averaged energy. We find, for the steady state current, that the approximation based on the averaged rates works well in most of the voltage regime, with marked deviations from the full quantum results only at the threshold for charging the weekly coupled level. These deviations are important for accurate description of the negative differential conduction behavior that often characterizes redox molecular junctions in the neighborhood of this threshold.

1.
M.
Galperin
,
M. A.
Ratner
, and
A.
Nitzan
,
Nano Lett.
5
,
125
130
(
2005
).
2.
M.
Galperin
,
A.
Nitzan
, and
M. A.
Ratner
,
J. Phys.: Condens. Matter
20
,
374107
(
2008
).
3.
M.
Galperin
,
A.
Nitzan
, and
M. A.
Ratner
, preprint arXiv:0909.0915 (
2009
).
4.
M. H.
Hettler
,
H.
Schoeller
, and
W.
Wenzel
,
Europhys. Lett.
57
,
571
(
2002
).
5.
B.
Muralidharan
and
S.
Datta
,
Phys. Rev. B
76
,
035432
(
2007
).
6.
R.
Hartle
and
M.
Thoss
,
Phys. Rev. B
83
,
115414
(
2011
).
7.
A.
Migliore
and
A.
Nitzan
,
ACS Nano
5
,
6669
(
2011
).
8.
K. F.
Albrecht
,
H.
Wang
,
L.
Mühlbacher
,
M.
Thoss
, and
A.
Komnik
,
Phys. Rev. B
86
,
081412
(
2012
).
9.
It should be emphasized that the theory addresses only locally stable states that will not persist beyond some finite lifetime, and do not imply multistability in the thermodynamic sense.
10.
M.
Field
,
C. G.
Smith
,
M.
Pepper
,
D. A.
Ritchie
,
J. E. F.
Frost
,
G. A. C.
Jones
, and
D. G.
Hasko
,
Phys. Rev. Lett.
70
,
1311
(
1993
).
11.
J. M.
Elzerman
,
R.
Hanson
,
L. H. W. v.
Beveren
,
B.
Witkamp
,
L. M. K.
Vandersypen
, and
L. P.
Kouwenhoven
,
Nature (London)
430
,
431
(
2004
).
12.
L. M. K.
Vandersypen
,
J. M.
Elzerman
,
R. N.
Schouten
,
L. H. W. v.
Beveren
,
R.
Hanson
, and
L. P.
Kouwenhoven
,
Appl. Phys. Lett.
85
,
4394
(
2004
).
13.
R.
Schleser
,
E.
Ruh
,
T.
Ihn
,
K.
Ensslin
,
D. C.
Driscoll
, and
A. C.
Gossard
,
Appl. Phys. Lett.
85
,
2005
(
2004
).
14.
T.
Fujisawa
,
T.
Hayashi
,
R.
Tomita
, and
Y.
Hirayama
,
Science
312
,
1634
(
2006
).
15.
S.
Gustavsson
,
R.
Leturcq
,
B.
Simovic
,
R.
Schleser
,
T.
Ihn
,
P.
Studerus
,
K.
Ensslin
,
D. C.
Driscoll
, and
A. C.
Gossard
,
Phys. Rev. Lett.
96
,
076605
(
2006
).
16.
S. A.
Gurvitz
and
Y. S.
Prager
,
Phys. Rev. B
53
,
15932
(
1996
).
17.
S. A.
Gurvitz
,
Phys. Rev. B
56
,
15215
(
1997
).
18.
G. Bulnes
Cuetara
,
M.
Esposito
, and
P.
Gaspard
,
Phys. Rev. B
84
,
165114
(
2011
).
19.
A.
Carmi
and
Y.
Oreg
,
Phys. Rev. B
85
,
045325
(
2012
).
20.
G.
Kießlich
,
P.
Samuelsson
,
A.
Wacker
, and
E.
Scholl
,
Phys. Rev. B
73
,
033312
(
2006
).
21.
G.
Kießlich
,
E.
Scholl
,
T.
Brandes
,
F.
Hohls
, and
R. J.
Haug
,
Phys. Rev. Lett.
99
,
206602
(
2007
).
22.
The “fast” channel carries all the current if the “slow” channel is coupled only to one of the leads.
23.
A.
Migliore
,
P.
Schiff
, and
A.
Nitzan
,
Phys. Chem. Chem. Phys.
14
,
13746
(
2012
).
24.
K. H.
Bevan
,
D.
Kienle
,
H.
Guo
, and
S.
Datta
,
Phys. Rev. B
78
,
035303
(
2008
).
25.
M.
Leijnse
,
W.
Sun
,
M. B.
Nielsen
,
P.
Hedegard
, and
K.
Flensberg
,
J. Chem. Phys.
134
,
104107
(
2011
).
26.
K.
Kaasbjerg
and
K.
Flensberg
,
Phys. Rev. B
84
,
115457
(
2011
).
27.
A.
Migliore
and
A.
Nitzan
, “
Irreversibility and hysteresis in redox molecular junctions
” (unpublished).
28.
P.
Coleman
,
Phys. Rev. B
29
,
3035
3044
(
1984
).
29.
N. E.
Bickers
,
Rev. Mod. Phys.
59
,
845
939
(
1987
).
30.
M.
Eckstein
and
P.
Werner
,
Phys. Rev. B
82
,
115115
(
2010
).
31.
J. H.
Oh
,
D.
Ahn
, and
V.
Bubanja
,
Phys. Rev. B
83
,
205302
(
2011
).
32.
M. H.
Hettler
,
J.
Kroha
, and
S.
Hershfield
,
Phys. Rev. B
58
,
5649
5664
(
1998
).
33.
T.
Schauerte
,
J.
Kroha
, and
P.
Wölfle
,
Phys. Rev. B
62
,
4394
4402
(
2000
).
34.
N. S.
Wingreen
and
Y.
Meir
,
Phys. Rev. B
49
,
11040
11052
(
1994
).
35.
N.
Sivan
and
N. S.
Wingreen
,
Phys. Rev. B
54
,
11622
1629
(
1996
).
36.
A. J.
White
and
M.
Galperin
,
Phys. Chem. Chem. Phys.
14
,
13809
13819
(
2012
).
37.
A. J.
White
,
B. D.
Fainberg
, and
M.
Galperin
,
J. Phys. Chem. Lett.
3
,
2738
2743
(
2012
).
38.
Note that while in quantum mechanics damping rates and level widths are synonymous, it is exactly the energetic consequence of the finite lifetime, that is, the level broadening, which is disregarded in the kinetic approximation.
39.
S.
Datta
,
Electric Transport in Mesoscopic Systems
(
Cambridge University Press
,
Cambridge
,
1995
).
40.
H.
Haug
and
A.-P.
Jauho
,
Quantum Kinetics in Transport and Optics of Semiconductors
(
Springer
,
2008
).
41.
M.
Esposito
and
M.
Galperin
,
Phys. Rev. B
79
,
205303
(
2009
).
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