Tuning the Thermoelectric Properties of a Single-Molecule Junction
by Mechanical Stretching
†
Alberto Torres,
a∗
Renato B. Pontes,
b
Antˆ onio J. R. da Silva,
a‡
and A. Fazzio
a
Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX
First published on the web Xth XXXXXXXXXX 200X
DOI: 10.1039/b000000x
Supplementary Information
Electronic Transport Calculations
The transport calculations were performed on TRANSAMPA
code which employs non-equilibrium Green’s function com-
bined with density functional theory (NEGF-DFT). To per-
form these calculations the system is divided in three parts:
left lead(L), scattering region(CC) and right lead(R) (see Fig.
1). We also assume that the leads only couple with the scatter-
ing region, but do not with each other.
Fig. 1 Ball-and-stick representation of the set up used in the
transport calculations.
The Hamiltonian matrix H for the system is an infinite Her-
mitian matrix. Firstly, we have to define principal layer(PL).
A principal layer is the smallest cell that repeats periodically
in the direction of the transport. For example, in this paper, it
is composed by the atoms in the three outermost Au layers on
each side of the system, as can be seen in Fig. 1.
a
Instituto de F´ ısica, Universidade de S˜ ao Paulo, CP 66318, 05315-970, S˜ ao
Paulo, SP, Brazil. E-mail: fazzio@if.usp.br, E-mail: ajrsilva@if.usp.br
b
Instituto de F´ ısica, Universidade Federal de Goi´ as, CP 131, 74001-970,
Goiˆ ania, GO, Brazil; E-mail: pontes@ufg.br
∗
Present Address: Departmento de F´ ısica, Universidade Federal de
Santa Catarina, 88040-900, Florian´ opolis, SC, Brazil; E-mail: al-
berto.trj@gmail.com
‡
Laborat´ orio Nacional de Luz Sincroton LNLS, 13083-970 Campinas-SP,
Brazil
The Hamiltonian matrix for the system is
H =
H
LL
H
LC
0
H
CL
H
CC
H
CR
0 H
RC
H
RR
(1)
where, H
LL
(H
RR
) are infinite block-diagonal matrices with the
following form:
H
LL
=
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0 H
−1
H
0
H
1
0
... 0 H
−1
H
0
H
1
... ... 0 H
−1
H
0
(2)
where H
0
is a matrix describing all interactions within a PL,
and H
1(−1)
is a N × N matrix that describes the interaction
between two PLs. N is the total number of basis function in
the PL. It is assumed that there is no coupling between the
left and the right leads (H
LR
= H
RL
= 0). The atoms in these
regions were held fixed at their ideal bulk positions. H
LL
(H
RR
)
are obtained in a bulk electronic structure calculation. H
CC
stands for a M × M matrix that describes the interaction in the
scattering region and, H
RC
e H
LC
stand for the matrices
H
LC
=
.
.
.
0
H
1
(3)
which contains the interaction between the PL and the scat-
tering region. For a system with time-reversal symmetry
H
RC
= H
†
CR
and H
LC
= H
†
CL
.
In the Landauer-B¨ uttiker formalism, the current is given by
I =
2e
h
T (E )[ f
L
(E ) − f
R
(E )] dE , (4)
where T (E ) stands for the transmission coefficient, f (E ) is
the Fermi-Dirac distribuction function. The conductance of
the system, G, can be written as
G =
2e
2
h
T (E )
−
∂ f
∂ E
dE . (5)
(6)
1–5 | 1
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