Long dephasing time and high temperature ballistic transport in an InGaAs open quantum dot

Abstract

We report on measurements of the magnetoconductance of an open circular InGaAs quantum dot between 1.3K and 204K. We observe two types of magnetoconductance fluctuations: universal conductance fluctuations (UCFs), and 'focusing' fluctuations related to ballistic trajectories between openings. The electron phase coherence time extracted from UCFs amplitude is larger than in GaAs/AlGaAs quantum dots and follows a similar temperature dependence (between T^-1 and T^-2). Below 150K, the characteristic length associated with 'focusing' fluctuations shows a slightly different temperature dependence from that of the conductivity. Comment: 6 pages, 4 figures, proceedings of ICSNN2002, to appear in Physica E

Full text

Page 1

Long dephasing time and high temperature ballistic transport in an
InGaAs open quantum dot
B. Hackensa,*, S. Faniela, F. Delfossea, C. Gustina, H. Boutrya, I. Huynena, X. Wallaertb,
S. Bollaertb, A. Cappyb, V. Bayota
aCERMIN, PCPM, DICE and EMIC Labs, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium
bIEMN, Cite scientifique, Villeneuve d Ascq, France
* Corresponding author. Tel.: +32-10-478191; fax: +32-10-473452; e-mail: hackens@pcpm.ucl.ac.be.
Abstract
We report on measurements of the magnetoconductance of an open circular InGaAs quantum dot between 1.3K and 204K.
We observe two types of magnetoconductance fluctuations: universal conductance fluctuations (UCFs), and focusing
fluctuations related to ballistic trajectories between openings. The electron phase coherence time extracted from UCFs
amplitude is larger than in GaAs/AlGaAs quantum dots and follows a similar temperature dependence (between T-1 and T-2).
Below 150K, the characteristic length associated with focusing fluctuations shows a slightly different temperature
dependence from that of the conductivity.
Keywords : quantum dots; ballistic effects; dephasing.

1. Introduction
Transport in semiconductor quantum dots (QDs) is mainly determined by two characteristic times: the phase
coherence time τφ and the elastic relaxation time τe. The phase coherence time is the key parameter which
determines whether a mesoscopic system either behaves in a classical way or exhibits quantum mechanical
effects, such as electron interferences. On the other hand, the ballistic transport regime is reached when τe
becomes comparable to the electron transit time through the QD. The ability to control and to increase both
timescales is essential in view of potential use in e.g. quantum information processing or high frequency
applications [1].
Here, we extract τφ from the magnetoconductance of an InGaAs open quantum dot, and find larger values
than previously reported in AlGaAs/GaAs quantum dots [2]. We also concentrate on the signatures of ballistic

Page 2

Submitted to Elsevier Science
2
electron behavior inside the dot. We study their temperature dependence and notice their persistence up to
unexpectedly high temperatures.
2. Experiment
The starting material for our sample is an InGaAs/InAlAs heterostructure, with an electron density ns = 1016
m-2 and a mobility ~3 m2/Vs at 4K (equivalent to an elastic mean free path lµ~ 500 nm). Using electron beam
lithography and wet etching, we define a circular quantum dot, with a lithographic diameter of 430 nm and
openings width of 60 nm. The depletion layer at the edges of the structure is approximately 25 nm wide. A
metallic gate deposited on the whole structure allows us to tune its shape and change the electron density. The
conductance of the sample is measured using a four-contacts lock-in technique. The measurements are performed
at temperatures between 1K and 204 K and in a magnetic field B up to 5T.
2.0
1.8
1.6
1.4
1.2
1.0
0.8
G(e2/h)
-1.0 -0.50.0
B(T)
0.5 1.0
1.3 K
23.5 K
83 K
Fig. 1. Temperature dependence of the magnetoconductance in units of e2/h.
3. Results
Fig. 1. shows the temperature dependence of the magnetoconductance G(B), with the gate grounded. The
average conductance of the cavity is ~ 1.4 e2/h to 1.6 e2/h, which means that there is at least one transverse mode

Page 3

Submitted to Elsevier Science
3
in the openings. The magnetoconductance exhibits two types of fluctuations, each with a different temperature
dependence. The first ones, also called universal conductance fluctuations (UCFs), are related to quantum
interference phenomena inside the dot and persist up to 30K. They are superimposed on a second type of
fluctuations, which occur on a much wider magnetic field range, and are more robust in temperature (observed up
to 204K). Most of these wide maxima and minima can be associated with direct focusing trajectories between
entrance and exit point contacts. Both types of fluctuations are symmetric with respect to B = 0.
1.70
1.65
1.60
1.55
1.50
G(e2/h)
1.6 1.20.8
B (T)
0.40.0
90 K
133 K
0.01
2
3
4
5
6
0.1
Amplitude (e2/h)
234567 8 9100
T(K)
2
peak 1
peak 2
Fig. 2. Top: high temperature magnetoconductance, with the magnetic field position of expected trajectories
inside the QD. Bottom: Temperature dependence of the amplitude of peaks 1 and 2.
Using the expression of the cyclotron radius rc = (h/eB)*(ns/2π)1/2, and given the size of the cavity, the
magnetic field position of the expected trajectories can easily be evaluated (Fig. 2). Two trajectories linking both
point contacts correspond to maxima at 0.81T and 1.47T, and the minimum at 0.49T is associated with an
electron trajectory reflecting electrons in the origin point contact. The uncertainty on the predicted peak positions
comes from the experimental error on ns and the cavity diameter, and from the direction for the carrier injection.
Following simple geometrical arguments, one could draw several other electron paths in the investigated
magnetic field range, which should give rise to other minima and maxima in the magnetoconductance. However,

Page 4

Submitted to Elsevier Science
4
all trajectories do not contribute equally to the magnetoconductance. As electron reflections on device boundaries
are not always specular, trajectories involving a small number of such reflections have a larger contribution than
more complicated paths.
7
8
9
1
2
3
L f / L f,204 K
3456 7 8 9100
T(K)
23
7
8
9
1
2
3
G2DEG / G2DEG,204 K
peak 1
peak 2
T -1
Fig. 3. Temperature dependence of the change in Lf and in the longitudinal conductance of the 2DEG (both
normalized to the value at 204 K). The dashed line represents a T-1 law.
Focusing measurements [3] evidenced that the focusing peak amplitude Ap depends on the trajectory length Le
and the focusing mean free path Lf according to the following expression :
Ap = A0 exp (-Le/Lf),(1)
where A0 is a constant. The maxima at B=0.81T (peak 1) and 1.47T (peak 2) correspond respectively to
trajectory lengths Le ~ 596 nm and 700 nm, both larger than the electron mean free path, even at low temperature.
However, ballistic effects can still be observed when Le is larger than lµ, as evidenced by Hirayama and Tarucha
[4]. The peak amplitude Ap, shown on Fig. 2 as a function of the temperature, is obtained after substracting from
each value of G(B) the value of the conductance linearly interpolated between each side of the peak. As this
method adds the amplitude of a maximum to that of the adjacent minima, it only gives an indication on the
temperature dependence of Ap and Lf, but not on their absolute value. Note also that the extraction of Ap was not
performed below 20 K, because UCFs amplitude becomes comparable to the amplitude of the focusing
fluctuations.
In order to calculate Lf from equ. (1), the value of A0 has to be determined. This requires a reference value for
Lf at a given temperature, which is not available. Therefore, we only calculate the change in Lf with respect to its

Page 5

Submitted to Elsevier Science
5
value at 204K, Lf/Lf,204K. Fig. 3 compares these data to the relative change in the longitudinal conductance of the
unpatterned two-dimensional electron gas, G2DEG, with respect to the conductance at 204K, G2DEG,204K.
G2DEG/G2DEG,204K is directly proportional to the elastic mean free path lµ. First, one sees that G2DEG/G2DEG,204K
saturates below ~50K, while Lf/Lf,204K increases continuously as T decreases. This difference may come from a
different sensitivity of lµ and Lf to small angle elastic scattering mechanisms, as already evidenced by Heremans
and co-workers in different types of experiments [3,5]. Despite this small discrepancy, the temperature
dependence and the absolute values of both G2DEG/G2DEG,204K and Lf/Lf,204K are similar.
4
6
8
10
2
4
6
8
100
τφ (ps)
2345 6 7
10
T (K)
T -1
T -2
Fig. 4. Temperature dependence of the phase coherence time inside the cavity.
Dashed lines indicate T-1 and T-2 law.
Then, we focus on the phase coherence time τφ. We use the results of the random matrix theory applied to
chaotic ballistic dots [6] to extract τφ from the variance of UCFs [7]. The variance of the fluctuations is evaluated
on high-pass filtered G(B) traces in order to remove the background contribution. As shown on Fig. 4, we find a
temperature dependence of the form τφ ∝ T-b, where 1<b<2, comparable to previous results in GaAs
heterostructures [2]. This temperature dependence is qualitatively consistent with the 2D model of decoherence
by electron-electron interactions in a diffusive system [2,8]. However, the absolute value of τφ is larger than in
ref. [2] by a factor of 2 to 4. This enhancement is likely to be due to the higher electron concentration of our
substrate which plays an important role in electron-electron interaction effects.

Page 6

Submitted to Elsevier Science
6
4. Conclusion
In summary, we investigate the magnetoconductance of an InGaAs quantum dot. Our sample exhibits wide
magnetoconductance fluctuations up to 204 K, caused by ballistic trajectories inside the dot. We calculate the
temperature dependence of the focusing mean free path Lf. We find that Lf follows approximately the same
temperature dependence as that of the mobility mean free path, although Lf does not saturate at low temperature.
We calculate the electron phase coherence time up to 18 K, and find a roughly comparable temperature
dependence as in GaAs heterostructure quantum dots, but with a larger absolute value by a factor of 2 to 4.
B.H., S.F. and C.G. acknowledge financial support from the F.R.I.A. This work was also supported by the
Interuniversity attraction Pole (PAI-IUAP) program of the Belgian Government and by the Action de Recherche
Concertee of the Communaute Francaise de Belgique .
5. References
[1] A.M. Song, P. Omling, L. Samuelson, W. Seifert, I. Shorubalko, H. Zirath, Appl. Phys. Lett. 79 (2001) 1357.
[2] A.G. Huibers et al., Phys. Rev. Lett. 81 (1998) 200.
[3] P.C. van Son, H. van Kempen and P. Wyder, Phys. Rev. Lett. 58 (1987) 1567; J. Heremans, B.K. Fuller, C.M.
Thrush and D.L. Partin, Phys. Rev. B 52 (1995) 5767.
[4] Y. Hirayama and S. Tarucha, Appl. Phys. Lett. 63 (1993) 2366.
[5] J. Heremans et al., Phys. Rev. B 54 (1996) 2685.
[6] P. Brouwer et al., Phys. Rev. B 65 (2002) 081302; K. Frahm, Europhys. Lett. 30 (1995) 457.
[7] B. Hackens et al., to be published.
[8] B.L. Altshuler, A.G. Aronov and D.E. Khmelnitzky, J. Phys. C 15 (1982) 7367; K.K. Choi, D.C. Tsui and K.
Alavi, Phys. Rev. B 36 (1987) 7751.