In the present work, we theoretically study characteristics of the nonlinear Seebeck effect in a single-molecule junction with chain-like bridge of an arbitrary length. We have employed tight-binding models to compute the electron transmission through the system. We concentrate on the analysis of dependences of thermovoltage Vth and differential thermopower S on the bridge length. It is shown that Vth becomes stronger and S grows as the bridge lengthens. We discuss the effects of the bridge coupling to the electrodes and of specific characteristics of terminal sites on the bridge on the length-dependent Vth and S, which appear when the system operates beyond the linear response regime.

1.
C.
Joachim
,
J. K.
Gimzewski
, and
A.
Aviram
, “
Electronics using hybrid-molecular and mono-molecular devices
,”
Nature
408
,
541
(
2000
).
2.
J. C.
Cuevas
and
E.
Scheer
,
Molecular Electronics: An Introduction to Theory and Experiment
(
World Scientific
,
Singapore
,
2010
).
3.
Y.
Dubi
and
M.
Di Ventra
, “
Heat flow and thermoelectricity in atomic and molecular junctions
,”
Rev. Mod. Phys.
83
,
131
(
2011
).
4.
N. A.
Zimbovskaya
and
M. R.
Pederson
, “
Electron transport through molecular junctions
,”
Phys. Rep.
509
,
1
(
2011
).
5.
B.
Sothmann
,
D.
Sanchez
, and
A. N.
Jordan
, “
Thermoelectric energy harvesting with quantum dots
,”
Nanotechnology
26
,
032001
(
2015
).
6.
F.
Giazotto
,
T. T.
Heikkila
,
A.
Luukanen
,
A. M.
Savin
, and
J. P.
Pekola
, “
Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications
,”
Rev. Mod. Phys.
78
,
217
(
2006
).
7.
B.
Szukiewicz
and
K.
Wysokinski
, “
Quantum dot as spin current generator and energy harvester
,”
Eur. Phys. J. B
88
,
112
(
2015
).
8.
H.
Sadeghi
,
S.
Sangtarash
, and
C. J.
Lambert
, “
Oligoyne molecular junctions for efficient room temperature thermoelectric power generation
,”
Nano Lett.
15
,
7467
(
2015
).
9.
C. A.
Perroni
,
D.
Ninno
, and
V.
Cataudella
, “
Thermoelectric efficiency of molecular junctions
,”
J. Phys.: Condens. Matter
28
,
373001
(
2016
).
10.
N. A.
Zimbovskaya
, “
Seebeck effect in molecular junctions
,”
J. Phys.: Condens. Matter
28
,
183002
(
2016
).
11.
S.
Kruchinin
and
T.
Pruschke
, “
Thermopower for a molecule with vibrational degrees of freedom
,”
Phys. Lett. A
378
,
1157
(
2014
).
12.
M.
Leijnse
,
M. R.
Wegewijs
, and
K.
Flensberg
, “
Nonlinear thermoelectric properties of molecular junctions with vibrational coupling
,”
Phys. Rev. B
82
,
045412
(
2010
).
13.
L.
Simine
and
D.
Segal
, “
Vibrational cooling, heating, and instability in molecular conducting junctions: Full counting statistics analysis
,”
Phys. Chem. Chem. Phys.
14
,
13820
(
2012
).
14.
R.
Swirkowicz
,
M.
Wilczynski
, and
J.
Barnas
, “
The Kondo effect in quantum dots coupled to ferromagnetic leads with noncollinear magnetizations: Effects due to electron-phonon coupling
,”
J. Phys.: Condens. Matter
20
,
255219
(
2008
).
15.
B. K.
Agarwalla
,
B.
Li
, and
J. S.
Wang
, “
Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems
,”
Phys. Rev. E
85
,
051142
(
2012
).
16.
M.
Galperin
,
M. A.
Ratner
, and
A.
Nitzan
, “
Inelastic effects in molecular junction transport: Scattering and self-consistent calculations for the Seebeck coefficient
,”
Mol. Phys.
106
,
397
(
2008
).
17.
N. A.
Zimbovskaya
, “
Nonlinear thermoelectric transport in single-molecule junctions: The effect of electron-phonon interactions
,”
J. Phys.: Condens. Matter
28
,
295301
(
2016
).
18.
F.
Pauly
,
J. K.
Viljas
, and
J. C.
Cuevas
, “
Length-dependent conductance and thermopower in single-molecule junctions of dithiolated oligophenylene derivatives: A density functional study,
,”
Phys. Rev. B
78
,
035315
(
2008
).
19.
C. M.
Finch
,
V. M.
Garcia-Suarez
, and
C. J.
Lambert
, “
Giant thermopower and figure of merit in single-molecule devices
,”
Phys. Rev. B
79
,
033405
(
2009
).
20.
A.
Tan
,
J.
Balachandran
,
S.
Sadat
,
V.
Gavini
,
B. D.
Dunietz
,
S.-Y.
Jang
, and
P.
Reddy
, “
Effect of length and contact chemistry on the electronic structure and thermoelectric properties of molecular junctions
,”
J. Am. Chem. Soc.
133
,
8838
(
2011
).
21.
M.
Tsutsui
,
K.
Yokota
,
T.
Morikawa
, and
M.
Taniguchi
, “
Roles of vacuum tunnelling and contact mechanics in single-molecule thermopower
,”
Sci. Rep.
7
,
44276
(
2017
).
22.
Z.
Golsanamlou
,
S. I.
Vishkayi
,
M. B.
Tagani
, and
H. R.
Soleimani
, “
Thermoelectric properties of metal/molecule/metal junction for different lengths of polythiophene
,”
Chem. Phys. Lett.
594
,
51
(
2014
).
23.
P.
Murphy
,
S.
Mukerjee
, and
J.
Moore
, “
Optimal thermoelectric figure of merit of a molecular junction
,”
Phys. Rev. B
78
,
161406
(
2008
).
24.
B.
Kubala
,
J.
Konig
, and
J.
Pekola
, “
Violation of the Wiedemann-Franz law in a single-electron transistor
,”
Phys. Rev. Lett.
100
,
066801
(
2008
).
25.
D.
Nozaki
,
H.
Sevincli
,
W.
Li
,
R.
Gutierrez
, and
G.
Cuniberti
, “
Engineering the figure of merit and thermopower in single-molecule devices connected to semiconducting electrodes
,”
Phys. Rev. B
81
,
235406
(
2010
).
26.
A. L.
Monteros
,
G. S.
Uppal
,
S. R.
McMillan
,
M.
Crisan
, and
I.
Tifrea
, “
Thermoelectric transport properties of a T-shaped double quantum dot system in the Coulomb blockade regime
,”
Euro. Phys. J. B
87
,
50656
(
2014
).
27.
J.
Azema
,
A.-M.
Dare
,
S.
Schafer
, and
P.
Lombardo
, “
Kondo physics and orbital degeneracy interact to boost thermoelectrics on the nanoscale
,”
Phys. Rev. B
86
,
075303
(
2012
).
28.
N. A.
Zimbovskaya
, “
The effect of Coulomb interactions on thermoelectric properties of quantum dots
,”
J. Chem. Phys.
140
,
104706
(
2014
).
29.
Y.
Yan
,
H.
Wu
,
F.
Jiang
, and
H.
Zhao
, “
Electron interaction effects on the thermoelectric power of a quantum dot at T > TK
,”
Euro. Phys. J. B
87
,
244
(
2014
).
30.
M. A.
Sierra
,
M.
Saiz-Bretin
,
F.
Dominguez-Adame
, and
D.
Sanchez
, “
Interactions and thermoelectric effects in a parallel-coupled double quantum dot
,”
Phys. Rev. B
93
,
235452
(
2016
).
31.
N. R.
Abdullah
,
C. S.
Tang
,
A.
Manolescu
, and
V.
Gudmundsson
, “
Cavity-photon controlled thermoelectric transport through a quantum wire
,”
ACS Photonics
3
,
249
(
2016
).
32.
M.
Wierzbicki
and
R.
Swirkowicz
, “
Electric and thermoelectric phenomena in a multilevel quantum dot attached to ferromagnetic electrodes
,”
Phys. Rev. B
82
,
165334
(
2010
).
33.
R.
Swirkowicz
,
M.
Wierzbicki
, and
J.
Barnas
, “
Thermoelectric effects in transport through quantum dots attached to ferromagnetic leads with noncollinear magnetic moments
,”
Phys. Rev. B
80
,
195409
(
2009
).
34.
L.
Karwacki
and
P.
Trocha
, “
Spin-dependent thermoelectric effects in a strongly correlated double quantum dot
,”
Phys. Rev. B
94
,
085418
(
2016
).
35.
L.
Xu
,
Z.-J.
Li
,
P.
Niu
, and
Y.-H.
Nie
, “
Nonequilibrium spin-polarized thermal transport in ferromagnetic quantum dotmetal system
,”
Phys. Lett. A
42
,
3553
(
2016
).
36.
M. B.
Tagani
and
H. R.
Soleimani
, “
Thermoelectric effects in a quantum dot coupled to ferromagnetic leads and subject to microwave fields
,”
J. Appl. Phys.
113
,
143709
(
2013
).
37.
R.
Hartle
and
M.
Thoss
, “
Vibrational instabilities in resonant electron transport through single-molecule junctions
,”
Phys. Rev. B
83
,
125419
(
2011
).
38.
G. T.
Craven
and
A.
Nitzan
, “
Electron transfer at thermally heterogeneous molecule-metal interfaces
,”
J. Chem. Phys.
146
,
092305
(
2017
).
39.
J.
Arguello-Luengo
,
D.
Sanchez
, and
R.
Lopez
, “
Heat asymmetries in nanoscale conductors: The role of decoherence and inelasticity
,”
Phys. Rev. B
91
,
165431
(
2015
).
40.
N. A.
Zimbovskaya
, “
The effect of dephasing on the thermoelectric efficiency of molecular junctions
,”
J. Phys.: Condens. Matter
26
,
275303
(
2014
).
41.
N. A.
Zimbovskaya
, “
Scattering theory of thermocurrent in quantum dots and molecules
,”
Phys. E
74
,
213
(
2015
).
42.
B.
De
and
B.
Muralidharan
, “
Thermoelectric study of dissipative quantum-dot heat engines
,”
Phys. Rev. B
94
,
165416
(
2016
).
43.
P.
Trocha
and
J.
Barnas
, “
Large enhancement of thermoelectric effects in a double quantum dot system due to interference and Coulomb correlation phenomena
,”
Phys. Rev. B
85
,
085408
(
2012
).
44.
L.
Simine
,
W. J.
Chen
, and
D.
Segal
, “
Can the Seebeck coefficient identify quantum interference in molecular conduction?
,”
J. Phys. Chem. C
119
,
12097
(
2015
).
45.
P.
Reddy
,
S. Y.
Jang
,
R. A.
Segalman
, and
A.
Majumdar
, “
Thermoelectricity in molecular junctions
,”
Science
315
,
1568
(
2007
).
46.
J. A.
Malen
,
P.
Doak
,
K.
Baheti
,
T. D.
Tilley
,
R. A.
Segalman
, and
A.
Majumdar
, “
Identifying the length dependence of orbital alignment and contact coupling in molecular heterojunctions
,”
Nano Lett.
9
,
1164
(
2009
).
47.
S. Y.
Quek
,
H. J.
Choi
,
S. G.
Louie
, and
J. B.
Neaton
, “
Length dependence of conductance in aromatic single-molecule junctions
,”
Nano Lett.
9
,
3949
(
2009
).
48.
S. Y.
Quek
,
H. J.
Choi
,
S. G.
Louie
, and
J. B.
Neaton
, “
Thermopower of amine−gold-linked aromatic molecular junctions from first principles
,”
ACS Nano
5
,
551
(
2011
).
49.
A.
Mishchenko
,
D.
Vonlanthen
,
V.
Meded
,
M.
Burkle
,
C.
Li
,
I. V.
Pobelov
,
A. I.
Bagrets
,
J. K.
Viljas
,
F.
Pauly
,
F.
Evers
,
M.
Mayor
, and
T.
Wandlowski
, “
Influence of conformation on conductance of biphenyl-dithiol single-molecule contacts
,”
Nano Lett.
10
,
156
(
2010
).
50.
J. R.
Widawsky
,
W.
Chen
,
H.
Vazquez
,
T.
Kim
,
R.
Breslow
,
M. S.
Hybertsen
, and
L.
Venkataraman
, “
Length-dependent thermopower of highly conducting AuC bonded single molecule junctions
,”
Nano Lett.
13
,
2889
(
2013
).
51.
Y.-H.
Wang
,
X.-Y.
Zhou
,
Y.-Y.
Sun
,
D.
Han
,
J.-F.
Zheng
,
Z.-J.
Niu
, and
X.-S.
Zhou
, “
Conductance measurement of carboxylic acids binding to palladium nanoclusters by electrochemical jump-to-contact STM break junction
,”
Electrochim. Acta
123
,
205
(
2014
).
52.
R. X.
Li
,
Y.
Ni
,
H. D.
Li
,
X. L.
Tian
,
K. L.
Yao
, and
H. H.
Fu
, “
Thermoelectric transport through a zigzag like chain: Influence of the chain length, the interdot tunneling and the intradot Coulomb interaction
,”
Phys. B
493
,
1
(
2016
).
53.
N. A.
Zimbovskaya
, “
Communication: Length-dependent thermopower of single-molecule junctions
,”
J. Chem. Phys.
145
,
221101
(
2016
).
54.
S. F.
Svensson
,
E. A.
Hoffmann
,
N.
Nakpathomkun
,
P. M.
Wu
,
H. Q.
Xu
,
H. A.
Nilsson
,
D.
Sanchez
,
V.
Kashcheyevs
, and
H.
Linke
, “
Nonlinear thermovoltage and thermocurrent in quantum dots
,”
New J. Phys.
15
,
105011
(
2013
).
55.
Y.
Dubi
and
M.
Di Ventra
, “
Thermoelectric effects in nanoscale junctions
,”
Nano Lett.
9
,
97
(
2009
).
56.
R. S.
Whitney
, “
Nonlinear thermoelectricity in point contacts at pinch off: A catastrophe aids cooling,
,”
Phys. Rev. B
88
,
064302
(
2013
).
57.
M. A.
Sierra
and
D.
Sanchez
, “
Strongly nonlinear thermovoltage and heat dissipation in interacting quantum dots
,”
Phys. Rev. B
90
,
115313
(
2014
).
58.
J.
Azema
,
P.
Lombardo
, and
A.-M.
Dare
, “
Conditions for requiring nonlinear thermoelectric transport theory in nanodevices
,”
Phys. Rev. B
90
,
205437
(
2014
).
59.
D.
Sanchez
and
R.
Lopez
, “
Scattering theory of nonlinear thermoelectric transport
,”
Phys. Rev. Lett.
110
,
026804
(
2013
).
60.
R.
Lopez
and
D.
Sanchez
, “
Nonlinear heat transport in mesoscopic conductors: Rectification, Peltier effect, and Wiedemann-Franz law
,”
Phys. Rev. B
88
,
045129
(
2013
).
61.
N. A.
Zimbovskaya
, “
The effect of Coulomb interactions on nonlinear thermovoltage and thermocurrent in quantum dots
,”
J. Chem. Phys.
142
,
244310
(
2015
).
62.
D.
Sanchez
and
R.
Lopez
, “
Nonlinear phenomena in quantum thermoelectrics and heat
,”
C. R. Phys.
17
,
1060
(
2016
).
63.
D.
Nozaki
,
H. M.
Pastawski
, and
G.
Cuniberti
, “
Controlling the conductance of molecular wires by defect engineering New
,”
New J. Phys.
12
,
063004
(
2010
).
64.
V.
Mujica
,
M.
Kemp
, and
M. A.
Ratner
, “
Electron conduction in molecular wires. I. A scattering formalism
,”
J. Chem. Phys.
101
,
6849
(
1994
).
65.
J. L.
d’Amato
and
H. M.
Pastawski
, “
Conductance of a disordered linear chain including inelastic scattering events
,”
Phys. Rev. B
41
,
7411
(
1990
).
66.
J.
Fransson
and
M.
Galperin
, “
Spin Seebeck coefficient of a molecular spin pump
,”
Phys. Chem. Chem. Phys.
13
,
14350
(
2011
).
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