Phonon-assisted tunneling and two-channel Kondo effect in
a vibrating molecular dot coupled to Luttinger liquid leads
Kai-Hua Yang
a,
n
, Bei-Yun Liu
a
, Huai-Yu Wang
b
, Xian He
a
a
College of Applied Sciences, Beijing University of Technology, Beijing 100122, China
b
Department of Physics, Tsinghua University, Beijing 100084, China
article info
Article history:
Received 16 July 2013
Received in revised form
6 October 2013
Accepted 28 October 2013
by Xincheng Xie
Available online 6 November 2013
Keywords:
A. Vibrating quantum dot
B. Luttinger liquid leads
C. Kondo regime
D. Density of state
abstract
We study the joint effects of the electron–phonon interaction (EPI) and intralead electron interaction
(IEI) on the density of states (DOS) of a single-molecular quantum dot weakly coupled to Luttinger liquid
leads in the Kondo regime by using the extended non-equilibrium Green's function method. The
introduction of the EPI yields satellite peaks around the Kondo peak. With the increase of the IEI, all the
peak heights reduce and then turn to dips. The full crossover in the DOS from the phonon-assisted one-
channel physics to two-channel physics is exhibited. The inelastic tunneling will dominate electron
transport for a certain region of interaction strength.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
The study of the behaviors of low-dimensional electronic
systems has become reality thanks to the progress in nanotech-
nology. The research is of crucial importance in extending our
knowledge of the strong electronic correlations in mesoscopic
physics. One of the most striking examples is the Kondo effect [1],
an interesting phenomenon of correlated electronic systems since
its discovery [2,3]. It is well known that the Kondo effect occurs
when a spin-1/2 local moment antiferromagnetically coupled to
only a single channel of conduction electrons [the single-channel
Kondo (1CK) effect], where the spin is completely screened by the
surrounding itinerant electrons to form a spin singlet state [4]. The
basic physics of the conduction electrons can be described by the
Fermi liquid (FL) theory [5]. As a result, the Kondo resonance-
peaks located at the Fermi-level in the density of states (DOS) arise
and the conductance is thus enhanced at very low temperature [4].
Nowadays the Kondo effect, as a prototypical many-body correla-
tion phenomenon, has been well understood experimentally and
theoretically [4–10]. However, when the screening channels
exceed twice of the impurity spin so that the local spin is coupled
to two or more screening channels, the spin is overscreened. Thus
the system exhibits non-Fermi liq uid properties [11,12].Thesimplest
version of the multi-channel Kondo phenomena is the two-channel
Kondo (2CK) effect, which has recently attracted much theoretical
[13–19] and experimental [20–24] attention.
On the other hand, because these nanometer scale systems are
spatially confined, their physical properties are sensitive to the
local molecular vibration. The influence of molecular vibrations
includes two basic types of the electron–phonon coupling. One is
the Holstein coupling between the molecular oscillator displace-
ment and the charge density of the dot. The main effect of
electron–phonon interaction (EPI) is to suppress the Coulomb
repulsion between the electrons on the dot and reduce the
hybridization between the dot and the conduction band. In this
case, the system can be described by the single-channel Anderson-
Holstein model. The corresponding Kondo effect has been also
observed in single molecules transistor (SMT) systems [25–28],
and the phonon-satellite structure has been clearly observed even
in the Kondo regime due to the EPI in such systems [29–32].
Theoretical efforts [33–38] have been devoted to investigate the
interplay of the EPI and the Kondo effect in the transport through
the SMT.
The other type of electron–phonon coupling affects the hop-
ping between the conductors and the oscillations of molecule,
which does not affect the effective Coulomb repulsion but affects
the hybridization. The system exhibits non-Fermi liquid properties
and can be described by a two-channel Anderson model with
phonon-assisted hybridization. The molecular local vibrational
modes play a significant role in the physical properties [39–42].
Up to this date, theoretical works involving the vibration of a
quantum dot (QD) have merely concerned noninteracting
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Solid State Communications
0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ssc.2013.10.025
n
Corresponding author. Tel.: þ86 010 67392201.
E-mail addresses: khy@bjut.edu.cn, khybjut@aliyun.com (K.-H. Yang).
Solid State Communications 178 (2014) 50–53