Eur. Phys. J. B 78, 481–488 (2010)
DOI: 10.1140/epjb/e2010-10698-2
Regular Article
T
HE
E
UROPEAN
P
HYSICAL
J
OURNAL
B
Manipulating the Tomonaga-Luttinger exponent by electric field
modulation
H. Shima
1,2,a
,S.Ono
3
,andH.Yoshioka
4
1
Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628 Hokkaido, Japan
2
Department of Applied Mathematics 3, LaC`aN, Universitat Polit`echnica de Catalunya, 08034 Barcelona, Spain
3
Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628 Hokkaido, Japan
4
Department of Physics, Nara Women’s University, 630-8506 Nara, Japan
Received 13 September 2010 / Received in final form 29 October 2010
Published online 6 December 2010 –
c
EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2010
Abstract. We establish a theoretical framework for artificial control of the power-law singularities in
Tomonaga-Luttinger liquid states. The exponent governing the power-law behaviors is found to increase
significantly with an increase in the amplitude of spatially periodic electrostatic field applied to the system.
This field-induced shift in the exponent indicates the tunability of the transport properties of quasi-one-
dimensional electron systems.
1 Introduction
Interacting electrons in one-dimensional (1D) metals con-
stitute a highly collective state of matter: the Tomonaga-
Luttinger liquid (TLL) state [1–4]. The collective nature
of the TLL states is what distinguishes them from their
higher-dimensional counterparts. Interacting electrons in
two or three dimensions form a Fermi liquid, wherein the
only effects of interaction are the modification of their ef-
fective mass and the possibility of being scattered. In one
dimension, however, even the slightest correlation between
electron motions has a dramatic effect, leading to distinc-
tive features that cannot be explained by the Fermi liquid
theory. To date, physical consequences of the TLL states
have been experimentally observed in various systems, in-
cluding carbon nanotubes [5–10], semiconducting quan-
tum wires [11–16], quasi-1D organic conductors [17–19],
quantum Hall edge states [20], and other materials having
highly anisotropic conductivity [21–28]. From the theoret-
ical viewpoint, a more general TLL theory with a non-
linear dispersion [29,30], dynamical transport of mechani-
cally vibrating TLL wires in a magnetic field [31,32], and a
novel wave-packed dynamics through Y-shaped TLL junc-
tions [33] have been recently suggested.
A hallmark of TLL states is a pseudogap in the one-
particle density of states ν(ε) at the Fermi energy ε
F
.In-
jection of an additional electron in the TLL ground state
disrupts the pre-existing correlation, thus requiring excita-
tion of an infinite number of collective modes. This results
in a power-law singularity of the form ν(ε) ∝|ε − ε
F
|
α
,
where α(>0) is called the TLL exponent. The same
a
e-mail: shima@eng.hokudai.ac.jp
power-law arises in the case of a differential tunneling
current dI/dV ∝|V |
α
at high bias voltages (eV k
B
T )
and a temperature-dependent conductance G(T ) ∝ T
α
at
low voltages (eV k
B
T )[5], although α may change due
to environment effects [34]. These power-law behaviors are
in strong contrast with the behavior of Fermi liquids in
which ν(ε)closetoε
F
and dI/dV become constant
1
.
The TLL exponent α is nonuniversal; it is dependent
on the interaction strength [4], the geometric shape of the
system [37,38], and the position of tunneling [39]. In fact,
different values of α were obtained in carbon nanotube
experiments when each electron tunneled into the end or
bulk of the system [5,6,40]; the variability in α was also
predicted in carbon nanotube networks under external
pressure [41], and may be enhanced by deforming isolated
nanotubes [42–44] due to strong correlation between their
electronic and machanical properties. A further non-trivial
shift in α was suggested in multiwalled nanotubes, where
α varies in a continuous manner under the application of
a high transverse magnetic field [45]. Continuous varia-
tion in α was also found in a nuclear magnetic resonance
study of CuBr
4
(C
5
H
12
N)
2
crystals [46]; in this case, an ex-
ternal magnetic field acted as the chemical potential. Such
field-induced variations in α can be exploited for achiev-
ing artificial control of transport properties in quasi-1D
conductors, which would play a fundamental role in the
development of next-generation quantum devices.
1
It should be noted that the power-laws in transport men-
tioned here are not unique to the TLL states but can take
place by different mechanism. See references [35]and[36]for
examples.