Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
Benedikt Frieß
Spin and Charge
Ordering in the
Quantum Hall Regime
Springer Theses
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ß
Benedikt Frie
Spin and Charge Ordering
in the Quantum Hall
Regime
Doctoral Thesis accepted by
the Technical University of Munich, Germany
123
Author Supervisor
Dr. BenediktFrieß Prof. KlausvonKlitzing
MaxPlanckInstitute for SolidState MaxPlanckInstitute for SolidState
Research Research
Stuttgart Stuttgart
Germany Germany
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-33535-3 ISBN978-3-319-33536-0 (eBook)
DOI 10.1007/978-3-319-33536-0
LibraryofCongressControlNumber:2016937505
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Artisticrenderingofthespinandcharge
orderinginasemiconductorheterostructure
’
Supervisor s Foreword
QuantumHallphysicsstartedmorethan35yearsagoandisstillanexpandingfield,
thanks to new high-quality materials such as graphene and zinc oxide, new theo-
retical concepts including topological insulators and topological quantum compu-
tation, and last but not least, due to important applications in metrology that will
lead to a new international system of units based on constants of nature.
Themostimportantingredientinthisresearchfieldismerelyatwo-dimensional
electronsystem(2DES)inastrongperpendicularmagneticfieldleading(inanideal
system) to a discrete energy spectrum. The 2DES is not a mathematical simplifi-
cation of a three-dimensional system; it truly opens a new dimension in science,
especially if magnetic flux quanta are added. New quasiparticles called composite
bosons, composite fermions, or anions are realized with new electronic properties.
Insomecases,quasiparticleswithnon-abelianstatisticsareexpectedthatmaywell
revolutionize quantum information technology. The host material in this research
fieldofbasic scienceplays asecondary role andthe influenceof thecrystal onthe
2DESisnormallyincludedinparameterssuchastheeffectivemassandtheg-factor
of the electrons. Unfortunately, even high-quality crystals are never perfect, and
their residual defects and impurities very often mask the intrinsic properties of the
electronic system. A two-dimensional electron layer on the clean surface of liquid
helium is very nearly an ideal system for basic science in the two-dimensional
world,buttheelectronconcentrationsintheseexperimentsarelimitedtoverysmall
values so that the diversity of quantum Hall physics cannot be exploited in these
systems.
Atpresent,thebest-controlled2DESforbasicresearchisrealizedattheinterface
betweenGaAsandAlGaAs,andeverytimethequalityofthissystem(characterized
by the mobility of electrons) has been increased, new phenomena were observed.
The integer quantum Hall effect can be discussed within a simple
independent-electron picture, where the discrete energy levels for electrons in a
strong magnetic field (Landau levels) are fully occupied and an incompressible
electronsystemisformed.Disorderdoesnotdestroythiseffect.Quitethecontrary,
it stabilizes this quantum phenomenon. However, many other fascinating electron
vii
viii Supervisor’sForeword
phases based on electron–electron interactions such as the fractional quantum Hall
effect,Wignercrystals,orexcitoncondensationbecomevisibleonlyifthedisorder
isnegligiblysmall.Twootherprominentphenomenabasedoncorrelatedelectrons,
namelytheformationofbubblesandstripes,arethefocusoftheresearchperformed
by Benedikt Frieß as described in this thesis.
ContrarytotheintuitivepictureofelectronsinaplanewithCoulombrepulsion,
the expected homogeneous electron concentration can be drastically changed by
redistributing the electrons if, for example, the increase in Coulomb energy is
overcompensated by the gain in exchange energy. The electrons in a half-filled
Landau level may redistribute in stripes representing a mixture of fully occupied
Landau levels with alternating numbers of completely filled energy levels. The
resulting electronic anisotropy can clearly be seen in angular-dependent resistivity
measurements, but another technique used by Benedikt Frieß, the analysis of the
velocity change of surface acoustic waves due to the screening properties of the
electron system, yields unexpectedly new information about the compressibility
of the spatially varying electron system. Such density-modulated phases are of
generalinterestbecausetheyexistinnatureinmanycases,includingsomehigh-T
C
superconductors. Contrary to other systems, the control of the electron concentra-
tion in GaAs/AlGaAs heterostructures offers a unique opportunity to study these
phases in detail. Very sensitive probes are available for characterizing the
density-modulated phases because the charge-modulated system is generally con-
nected to a spin-density modulation, which can be detected sensitively by local
probes via the Knight shift.
Thisthesisprovidesnotonlyacomprehensiveintroductiontomodernaspectsof
quantum Hall physics but also an impressive overview of experimental details and
techniques for characterizing quantum Hall systems with a focus on new methods
based on electron–nuclear spin interactions.
Stuttgart Prof. Dr. Dr. h.c. mult.
January 2016 Klaus von Klitzing
Acknowledgments
Thepresentthesiswouldhavelackedmuchofitsprofundityifitweren’tforthegreat
supportIhavereceivedfrommanypeople.Inparticular,Iamhighlyindebtedto…
(cid:129) Professor Klaus von Klitzing for giving me the privilege to become one of his
students and for providing exceptional support in many regards. I highly value
the many insightful discussions and constructive suggestions. His enthusiasm
and supportive mind has been greatly inspiring to me.
(cid:129) Dr. habil. Jurgen Smet for guiding me through all the ups and downs of the
recent years. His extensive support combined with all necessary liberties pro-
videdbestpossibleresearchconditionsandpushedmetoexcel.Icouldnothave
wished for a better environment.
(cid:129) my external supervisor Prof. Bernd Rosenow (Universität Leipzig) for the
numerous helpful discussions. The present work strongly benefited from his
wealth of experience and profound knowledge.
(cid:129) Professor Rudolf Gross (TU München), who kindly agreed to become the
second referee of my doctoral exam.
(cid:129) Dr. Vladimir Umansky (Weizmann Institute of Science) for providing some
of the world’s best 2DES.
(cid:129) thecleanroomteamforbringingthe2DESintoshape.Mostofall,Iwouldlike
to thank Marion Hagel for her persistent help in sample processing.
(cid:129) our skillful technicians, Steffen Wahl, Gunther Euchner, Steffen Pischke, Ingo
Hagel and Manfred Schmid, for their invaluablehelpwhen it comes tocooling
the samples to ultra-low temperatures.
(cid:129) Dr.JohannesNüblerforintroducingmetothebroadsweepoflow-temperature
physics.Ilearnedalot from him,from theintricacies oflabworktothedetails
of quantum Hall physics.
(cid:129) allmyfriendsandcolleaguesintheSmetgroup.Thejoyyoubroughtmeinthe
past years beggars description. I highly appreciate the many scientific, philo-
sophical and mundane discussions. Most prominently I would like to mention
Matthias Kühne, Ding Zhang, Federico Paolucci, Daniel Kärcher, Thomas
Weitz, Youngwook Kim, Johannes Geurs and Patrick Herlinger.
ix
xx AAcckknnoowwlleeddggmmeennttss
(cid:129) Joseph Falson (University ofToyko, now at MPI) for bringingthe rich physics
of ZnO/MgZnO heterostructures and himself to Stuttgart.
(cid:129) Professor Daniel Loss (Universität Basel) for inviting me to Basel and sharing
his knowledge about nuclear magnetic ordering.
(cid:129) ProfessorYongqingLi(ChineseAcademyofSciences)forfruitfulcollaboration
on thefield oftopological insulatorsand quantumHall spin physics. Iam truly
grateful for the invitation to Beijing.
(cid:129) Dr. Yang Peng and Prof. Felix von Oppen (both FU Berlin) for helping us to
develop a theoretical understanding of the surface acoustic wave experiments
(cid:129) Christian Reichl and Prof. Werner Wegscheider (ETH Zürich) for providing
additional high-quality samples.
(cid:129) Ruth Jenz for keeping the bureaucracy at bay and for her friendly nature.
(cid:129) the financial and non-material support by the Studienstiftung des deutschen
Volkes during my undergraduate studies.
(cid:129) my friends and family for their invaluable support throughout my life. Most of
all, I feel deeply obliged to my parents. They sparked in me the excitement for
nature and technology early on and taught me to think critically.
(cid:129) Julia for enriching my daily life. Thank you for being so patient and under-
standingthroughthickandthinandforcheeringmeupwhenthingswentwrong
in the lab.
