Spin related transport phenomena in HgTe-based quantum well structures [Elektronische Ressource] / vorgelegt von Markus König

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• Physik

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• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2008
• Nombre de lectures: 37
• Poids de l'ouvrage: 5 Mo

Extrait

Spin-related transport phenomena
in HgTe-based
quantum well structures
Dissertation zur Erlangung des
naturwissenschaftlichen Doktorgrades der
Bayerischen Julius-Maximilians-Universit˜at Wurzburg˜
vorgelegt von
˜Markus Konig
aus Wurzburg˜
Wurzburg˜
Dezember 2007Eingereicht am 20.12.2007
bei der Fakult˜at fur˜ Physik und Astronomie
1. Gutachter: Prof. Dr. Hartmut Buhmann
2. Gutachter: PD Dr. Lukas Worschech
3. Gutachter: Prof. Dr. Sergey Ganichev
der Dissertation.
1. Prufer:˜ Prof. Dr. Hartmut Buhmann
2. Prufer:˜ PD Dr. Lukas Worschech
3. Prufer:˜ Prof. Dr. Bj˜orn Trauzettel
im Promotionskolloquium.
Tag des Promotionskolloquium: 04.04.2008
Doktorurkunde ausgeh˜andigt am:Contents
Introduction 1
1 HgTe based quantum wells 5
1.1 Band structure of HgTe-based quantum wells. . . . . . . . . . . . . . 7
1.2 Rashba spin-orbit interaction . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Sample fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Investigation of the band structure 21
2.1 Transition from n- to p-conductance. . . . . . . . . . . . . . . . . . . 22
2.2 Landau levels in HgTe . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 The Quantum Spin Hall Efiect 41
3.1 Introduction to the Quantum Spin Hall efiect . . . . . . . . . . . . . 42
3.2 Experimental observation of the Quantum Spin Hall insulator . . . . 45
3.3 QSH edge states in magnetic fleld . . . . . . . . . . . . . . . . . . . . 56
3.4 Temperature dependence of the QSH efiect . . . . . . . . . . . . . . . 70
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
iii CONTENTS
4 Spin Hall Efiects in doped HgTe QWs 81
4.1 Theory of Spin Hall Efiects. . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Experimental investigation of the Spin Hall Efiect . . . . . . . . . . . 88
4.3 Interplay of SHE and QSHE . . . . . . . . . . . . . . . . . . . . . . . 101
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 Transport in ring structures 115
5.1 General description of phase efiects . . . . . . . . . . . . . . . . . . . 117
5.2 Phase efiects in semiconductor ring structures . . . . . . . . . . . . . 120
5.3 Observation of the Aharonov-Casher efiect . . . . . . . . . . . . . . . 125
5.4 Measurements in high magnetic fleld . . . . . . . . . . . . . . . . . . 136
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Summary and Outlook 145
Zusammenfassung und Ausblick 149List of Publications
Parts of this thesis were already published in
† M.K˜onig,A.Tschetschetkin,E.M.Hankiewicz,J.Sinova,V.Hock,V.Daumer,
M. Sch˜afer, C. R. Becker, H. Buhmann, and L. W. Molenkamp
Direct Observation of the Aharonov-Casher Phase
Phys. Rev. Lett. 96, 076804 (2006).
† M. K˜onig, H. Buhmann, C. R. Becker, and L. W. Molenkamp
Phase efiects in HgTe quantum structures
phys. stat. sol. (c) 4, 3374 (2007).
† M.K˜onig,S.Wiedmann,C.Brune,˜ A.Roth,H.Buhmann,L.W.Molenkamp,
X L. Qi, and S. C. Zhang
Quantum Spin Hall Insulator State in HgTe Quantum Wells
Science 318, 766 (2007).
† M. K˜onig, H. Buhmann, L. W. Molenkamp, T. Hughes, C. X. Liu, X. L Qi,
and S. C. Zhang
The Quantum Spin Hall Efiect: Theory and Experiment
J. Phys. Soc. Jpn. 77, 031007 (2008).
iiiiv List of Publications
Further publications
† Y S. Gui, C. R. Becker, J. Liu, M. K˜onig, V. Daumer, M. N. Kiselev, H. Buh-
mann, and L. W. Molenkamp
Current heating of a magnetic 2DEG in Hg Mn Te/Hg Cd Te quantum1¡x x 0:3 0:7
wells
Phys. Rev. B 70, 195328 (2004).
† R. Scheibner, E. G. Novik, T. Borzenko, M. K˜onig, D. Reuter, A. Wieck,
H. Buhmann, and L. W. Molenkamp
Sequential and co-tunneling behavior in the temperature-dependent thermo-
power of few-electron quantum dots
Phys. Rev. B 75, 041301(R), (2007).
Submitted for publication
† R.Scheibner,M.K˜onig,D.Reuter,A.Wieck,H.Buhmann,andL.W.Molen-
kamp
Quantum dot as thermal rectifler
available on-line at arXiv:cond-mat/0703514.
Further parts of this thesis are considered for publication.Introduction
In recent years, spin-related phenomena have moved into the focus of solid state
research. The primary reason is that the spin properties became experimentally
accessible in electronic devices due to the ongoing progress in nanofabrication tech-
niques. Manifoldissuescannowbeaddressedinsolidstatesystemsfortheflrsttime
and studies are pursued for fundamental scientiflc purposes. Furthermore, an entire
new area of applications opened up and the fleld of spintronics (= spin + electron-
ics)developed[1,2]. Spintronicdevicestakeadvantageoftheelectronspin, whereas
conventional ones rely solely on the charge. The main improvements compared to
conventional devices include the reduced or maybe even vanishing dissipation in
the system and decreased electrical power consumption. For the realization of spin-
tronicdevices, themajoraspectsarethecreation, transportation, manipulationand
detection of the electronic spin polarization.
It turned out that these tasks are more di–cult to realize than expected. This
is particularly the case, if spintronic applications are supposed to be implemented
on semiconductor materials. For example, the injection of spin-polarization from
a ferromagnetic metal is highly ine–cient due to the difierence in the density of
states for the two components [3]. The search for ferromagnetic semiconductors,
e.g., GaMnAs[4], ore–cientspininjection, e.g., bytunnelcontacts[5], guidedmost
research projects.
A rather new idea is to use the intrinsic spin-orbit interaction for creation,
manipulationanddetectionofspinaccumulationorspincurrents. Two-dimensional
electrongasesformedinsemiconductorheterostructuresarehighlysuitablesystems.
12 Introduction
Theadvantageofthisapproachisthatthestrengthofthespin-orbitinteractioncan
be locally controlled by the Rashba efiect [6]. This rather direct method to afiect
the electron spin not only initiated considerable experimental efiort, but also was
very attractive to theoreticians and triggered the prediction of various efiects and
devices [7{10]. A prominent example is the Spin Hall efiect [11{13]. When a charge
current is driven in a system with a strong spin-orbit interaction, a transverse spin
current is generated and results in a spin imbalance at the sample edges. This
efiect may be utilized for the creation of pure spin current and spin polarization.
Furthermore, the spin-orbit interaction can afiect the phase of the electron wave
functioninformofadditionalphasefactors, theBerryphase[14]andtheAharonov-
Casherphase[15]. Thismodulationoftheelectronphaseledtotheconceptofanew
type of spin-interference device [16]. The proposed ring structure represents a kind
ofspin-interferencefleldefiecttransistor,inwhichthetransmissioncanbecontrolled
by spin-orbit induced phases. A spin fleld efiect transistor had been suggested by
Datta and Das [17], but ferromagnetic contacts are required in the latter device,
which has proven to be an obstacle for the realization.
Recently, a new state of matter in a topological sense, the Quantum Spin Hall
efiect,hasbeenproposed[18,19]. Thisnovelstateischaracterizedbynon-dissipative
transport of spin-polarized electrons in one-dimensional edge channels and thus has
equivalently high potential for spintronic applications.
Quantum well structures based on HgTe appear to be very suitable for the in-
vestigation of fundamental spin-orbit efiects. HgTe as a bulk material is a zero-gap
semimetal, whereas a narrow energy gap opens up in a quantum well. First of all,
two-dimensional electron gases in HgTe quantum wells exhibit high carrier mobili-
ties. These result in a large mean free path comparable to the characteristic sample
dimensions, which is a prerequisite for the manifestation of spin-related transport
phenomena. In addition, the Rashba energy can reach values of up to 30 meV,
which is several times larger than for any other semiconductor material, and can be
tuned over a wide range [20{22]. Both attributes help to identify efiects due to theIntroduction 3
spin-orbit interaction like the spin Hall efiect or phase efiects. Finally, HgTe quan-
tum wells feature very peculiar band structure properties. Depending on the actual
well width, the band structure is either normal or inverted, i.e., the ordering of the
energystatesin thequantumwellisreversed compared commonsemiconductors for
the latter case. For samples with an inverted band structure, the existence of the
quantum spin Hall efiect was explicitly predicted [23].
Within the scope of this thesis, the transport properties of HgTe-based quantum
well structures are studied with an emphasis on various spin-orbit efiects. A gen-
eral introduction to the speciflc properties of this material is provided in Chapter 1.
Duetorecentadvancesinthegrowthandfabrication,whicharealsodescribed,high
mobility devices with characteristic dimensions of only a few 100 nm were available,
meeting the requirements for the observation of spin-related efiects.
In Chapter 2, transport phenomena are discussed, which arise from the narrow
energy gap and the peculiar band structure, respectively. The Fermi energy can be<