Thermoelectric properties of few electron quantum dots [Elektronische Ressource] / vorgelegt von Ralf Scheibner

Sujets

• Physik

Informations

• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2008
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

Thermoelectric Properties of Few-Electron
Quantum Dots
Dissertation zur Erlangung des
naturwissenschaftlichen Doktorgrades
der Bayerischen Julius-Maximilians-Universit˜at
Wurzburg˜
vorgelegt von
Ralf Scheibner
geboren in Ebern
Wurzburg˜ 2007Eingereicht am: 30.08.2007
bei der Fakult˜at fur˜ Physik und Astronomie
der Julius-Maximillians-Universit˜at Wurzburg˜
Prof. Dr. Hartmut Buhmann1. Gutachter:
Prof. Dr. Vladimir Dyakonov2. Gutachter:
Prof. Dr. Kornelius Nielsch3. Gutachter:
Tag des Promotionskolloquiums: 16.01.2008
Prof. Dr. Hartmut Buhmann1. Prufer:˜
Prof. Dr. Vladimir Dyakonov2. Prufer:˜
Prof. Dr. Kornelius Nielsch3. Prufer:˜
Prof. Dr. Bj˜orn Trauzettel4. Prufer:˜Meiner FamilieList of Publications i
Parts of this thesis have been published in:
† R. Scheibner, H. Buhmann, D. Reuter, M.N. Kiselev, and L.W. Molenkamp
’Thermopower of a Kondo spin-correlated quantum dot’,
Phys. Rev. Lett. 95, 176602 (2005)
recited in ’Virtual Journal of Nanoscale Science & Technology’, 31. Oct. 2005.
† R. Scheibner, E.G. Novik, T. Borzenko, M. K˜onig, D. Reuter, A.D. Wieck, H.
Buhmann, and L.W. Molenkamp
’Sequential and cotunneling behavior in the temperature-dependent thermopower of
few-electron quantum dots’,
Phys. Rev. B 75, 041301 (2007).
Submitted for publication:
† R. Scheibner, M. K˜onig, D. Reuter, A.D. Wieck, H. Buhmann, and L.W.
Molenkamp, ’Quantum dot as a thermal rectifler’,
arXiv:cond-mat=0703514v1 (2007); submitted to Phys. Rev. Lett.
Further Chapters of this thesis are considered for publication.ii ContentsContents
Introduction 1
1 Fundamentals of Coulomb-blockade in quantum dots 7
1.1 Theoretical description of a quantum dot . . . . . . . . . . . . . . . . . . . 8
1.1.1 Hamiltonian for transport through a quantum dot . . . . . . . . . . 8
1.1.2 Constant interaction model . . . . . . . . . . . . . . . . . . . . . . 9
1.2 First and second order transport . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.1 First order linear transport. . . . . . . . . . . . . . . . . . . . . . . 11
1.2.2 Elastic and inelastic cotunneling . . . . . . . . . . . . . . . . . . . . 13
1.3 Nonlinear transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 Coulomb Blockade Diamonds . . . . . . . . . . . . . . . . . . . . . 17
1.3.2 Transport via excited states in the SET regime . . . . . . . . . . . 18
1.3.3 Cotunneling in the CB regime . . . . . . . . . . . . . . . . . . . . . 18
2 Fundamentals of thermoelectric transport 23
2.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Thermodynamics of irreversible processes . . . . . . . . . . . . . . . 24
2.1.2electric transport in microstructures . . . . . . . . . . . . . 26
2.1.3 Remark on Mott’s law . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Thermoelectric transport in the Coulomb-blockade . . . . . . . . . . . . . 28
2.2.1 Sequential tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Cotunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Experimental setup 33
3.1 Quantum dot sample design . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.2 Split gate quantum dot structure . . . . . . . . . . . . . . . . . . . 35
3.2 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2 Electrical characterization . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.3 Thermoelectrical characterization . . . . . . . . . . . . . . . . . . . 40
3.3 Current-heating technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Basic principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Temperature calibration . . . . . . . . . . . . . . . . . . . . . . . . 46
iiiiv Contents
4 Cotunneling contribution to the thermopower of few-electron quantum
dots 55
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Model calculations and comparison . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Thermoelectric transport in the presence of asymmetries 73
5.1 Energy dependence of tunnel barriers . . . . . . . . . . . . . . . . . . . . . 74
5.2 Unidirectional thermoelectric transport in a SET conductance peak . . . . 77
5.2.1 Experimental observation . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.3 Comparison of thermovoltage and nonlinear difierential conductance 84
5.2.4 Thermal rectiflcation . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Asymmetric thermoelectric transport induced by excited states . . . . . . . 90
5.3.1 Fine structure of flrst order transport via states . . . . . . . 92
5.3.2 Thermoelectric signature of blocked excited states . . . . . . . . . . 94
5.3.3 Asymmetric cotunneling . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Thermoelectric transport in the spin-correlated regime 99
6.1 Kondo-efiect in quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Magnetically induced chessboard pattern . . . . . . . . . . . . . . . . . . . 103
6.3 Contributions of spin-correlations to the thermopower . . . . . . . . . . . . 109
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.4.1 Kinetic spin-correlation contribution to the thermopower . . . . . . 112
6.4.2 Spin-entropy ux . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Summary 126
A Sample information 131
Zusammenfassung 131
B Cryogenic flltering 133
Bibliography 148Introduction
The information technology based society has an increasing demand for e–cient comput-
ing power. A gain in e–ciency can be achieved by reduced production costs for single
logic devices, by an increased number of computational operations per given time in-
terval, or by reduced energy consumption in relation to the number of logic operations.
These goals are achievable by means of size reduction of conventional logic components,
which are based on the laws of classical information theory, and by the application of
quantum information theory. The latter allows a high degree of parallel information
processing to be attained. The fundamental limit of the size of new information pro-
cessing and storing devices is given by the properties of single particles, or to be more
precise, the spacial extension of single quantum states. The particle states are charac-
terized by a given set of quantum numbers and these states yield the information that
has to be stored or processed. Modern semiconductor fabrication technologies make it
possible for these geometric limits to be approached, and consequently ofier the prospect
of scalable semiconductor quantum processing devices; hence, the intense interest in the
study of quantum dot (QD) structures that contain only a few electrons [LD98]. For the
development of these devices, a detailed knowledge of the underlying electron transport
processes is of crucial importance. So far, most of the transport experiments have fo-
+cused on the electrical conductance [KMM 97]. Besides the proofs that semiconductor
QD structures can be used for (coherent) single particle and quantum state manipula-
+ +tion [EHWvB 04, KBT 06], measurements have shown that the dynamic and magnetic
quantum mechanical properties of the QD electrons govern the electrical transport at low
+ +temperatures [GGSAM 98, COK98, vdWDFF 00], and that (QD) systems containing
conflned electrons are a useful tool for studying fundamental transport phenomena, e.g.
the quantum Hall efiect [KDP80, vKGW05]. These, as well as many other experiments
on the electrical conductance, have made few electron QDs a magniflcent model system
for testing the charge transport properties on the scale of a single lattice site, or single
impurity, respectively.
Although thermoelectrical transport measurements are known to be more sensitive to
the details of the electronic structure than conventional transport measurements [Zim63],
little experimental attention has so far been paid to this kind ofts on QDs.
Thus it is desirable that such measurements be done, since the measurement of the ther-
moelectricpower(thermopower)allowsadirectanalysisofthechargetransportdynamics
12 Introduction
to be carried out. Moreover, it is an important measurement due to the close connection
between the thermopower and the heat transport, i.e. entropy transport. Experiments
show that diverse behaviors are found for the thermopower of simple metals, where even
the sign of this quantity shows no regularity. Although there has been extensive work
on this topic, the low temperature theory even in metals has still not been well under-
stood [Mah81]. Thus, it is highly desirable to establish a complete microscopic picture of
thermoelectric transport in mesoscopic and quantum systems.
Recently, the fleld of thermoelectricity has gained large renewed attention. Much in-
terest has been focused on understanding thermoelectric tra