Dissertations / Theses on the topic 'Two Dimensional Electron Systems (2DES)'
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Rödel, Tobias. "Two-dimensional electron systems in functional oxides studied by photoemission spectroscopy." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS197/document.
Full textMany transition metal oxides (TMOs) show complex physics, ranging from ferroelectricity to magnetism, high-Tc superconductivity and colossal magnetoresistance. The existence of a variety of ground states often occurs as different degrees of freedom (e.g. lattice, charge, spin, orbital) interact to form different competing phases which are quite similar in energy. The capability to epitaxially grow heterostructures of TMOs increased the complexity even more as new phenomena can emerge at the interface. One typical example is the two-dimensional electron system (2DES) at the interface of two insulating oxides, namely LaAlO3/SrTiO3, which shows metal-to-insulator transitions, magnetism or gate-tunable superconductivity. The origin of this thesis was the discovery of a similar 2DES at the bare surface of SrTiO3 fractured in vacuum, making it possible to study its electronic structure by angle-resolved photoemission spectroscopy (ARPES).In this thesis, the study of well-prepared surfaces, instead of small fractured facets, results in spectroscopic data showing line widths approaching the intrinsic value. This approach allows a detailed analysis of many-body phenomena like the renormalization of the self-energy due to electron-phonon interaction.Additionally, the understanding of the electronic structure of the 2DES at the surface of SrTiO3(001) was given an additional turn by the surprising discovery of a complex spin texture measured by spin-ARPES. In this thesis data is presented which contradicts these conclusions and discusses possible reasons for the discrepancy.One major motivation of this thesis was the question if and how the electronic structure and the properties of the 2DES can be changed or controlled. In this context, the study of 2DESs at (110) and (111) surface revealed that the electronic band structure of the 2DES (orbital ordering, symmetry of the Fermi surface, effective masses) can be tuned by confining the electrons at different surface orientations of the same material, namely SrTiO3.A major achievement of this thesis is the generalization of the existence of a 2DES in SrTiO3 to many other surfaces and interfaces of TMOs (TiO2 anatase, CaTiO3, BaTiO3) and even simpler oxides already used in modern applications (ZnO). In all these oxides, we identify oxygen vacancies as the origin for the creation of the 2DESs.In anatase and other doped d0 TMOs, both localized and itinerant electrons (2DES) can exist due to oxygen vacancies. Which of the two cases is energetically favorable depends on subtle differences as demonstrated by studying two polymorphs of the same material (anatase and rutile).In CaTiO3, the oxygen octahedron around the Ti ion is slightly tilted. This symmetry breaking results in the mixing of different d-orbitals demonstrating again why and how the electronic structure of the 2DES can be altered.In BaTiO3, the creation of a 2DES results in the coexistence of the two, usually mutual exclusive, phenomena of ferroelectricity and metallicity in the same material by spatially separating the two.Moreover, this work demonstrates that the 2DES also exists in ZnO which is - compared to the Ti-based oxides - rather a conventional semiconductor as the orbital character of the itinerant electrons is of s and not d-type.The main result of this thesis is the demonstration of a simple and versatile technique for the creation of 2DESs by evaporating Al on oxide surfaces. A redox reaction between metal and oxide results in a 2DES at the interface of the oxidized metal and the reduced oxide. In this thesis the study of such interfacial 2DESs was limited to photoemission studies in ultra high vacuum. However, this technique opens up the possibility to study 2DESs in functional oxides in ambient conditions by e.g. transport techniques, and might be an important step towards cost-efficient mass production of 2DESs in oxides for future applications
Yoon, Hosang. "Two-Dimensional Plasmonics in Massive and Massless Electron Gases." Thesis, Harvard University, 2014. http://nrs.harvard.edu/urn-3:HUL.InstRepos:13070026.
Full textEngineering and Applied Sciences
Nahm, In Hyun. "Two dimensional disordered electron systems." Thesis, University of Southampton, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330179.
Full textMadhavi, S. "Carrier Mobility And High Field Transport in Modulation Doped p-Type Ge/Si1-xGex And n-Type Si/Si1-xGex Heterostructures." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/294.
Full textMadhavi, S. "Carrier Mobility And High Field Transport in Modulation Doped p-Type Ge/Si1-xGex And n-Type Si/Si1-xGex Heterostructures." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/294.
Full textOxley, John Paul. "Thermopower in two dimensional electron systems." Thesis, University of Nottingham, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293657.
Full textSiegert, Christoph. "Disorder effects in two dimensional electron systems." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612312.
Full textPeck, Andrew John. "Lateral tunnelling in two-dimensional electron systems." Thesis, University of Bath, 1994. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385345.
Full textYeung, Yan Mui Kitty. "Engineering Plasmonic Waves in Two-Dimensional Electron Systems." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467363.
Full textEngineering and Applied Sciences - Applied Physics
Li, Hongtao. "Electron-electron correlations and lattice frustration in quasi-two-dimensional systems." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/202769.
Full textBao, Yunjuan. "Resonant spin Hall effect in two-dimensional electron systems." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B34627819.
Full textCastleton, I. M. "Electron transport in coupled one- and two-dimensional systems." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597365.
Full textBao, Yunjuan, and 暴云娟. "Resonant spin Hall effect in two-dimensional electron systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B34627819.
Full textBaenninger, Matthias. "Interaction effects and disorder in two-dimensional electron systems." Thesis, University of Cambridge, 2008. https://www.repository.cam.ac.uk/handle/1810/280142.
Full textSubbiah, Suresh. "Macroscopic dressing of electron states in a two dimensional ballistic electron waveguide /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004381.
Full textShaukat, Muhammad Usman. "Microwave and terahertz studies of the electron dynamics in two-dimensional electron systems." Thesis, University of Leeds, 2012. http://etheses.whiterose.ac.uk/3410/.
Full textNikolaev, Valentin. "Many-particle correlations in quasi-two-dimensional electron-hole systems." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248096.
Full textLi, Lijun. "Transport properties of single and double two dimensional electron systems." Thesis, University of Exeter, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269749.
Full textTyson, Robin Edward. "Far-infrared optical studies of low-dimensional electron systems." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338068.
Full textRenken, Volker. "Electron confinement and quantum well states in two-dimensional magnetic systems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985573546.
Full textKlironomos, Filippos. "Tunneling between two dimensional electron systems in a high magnetic field and crystalline phases of a two dimensional electron system in a magnetic field." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0009801.
Full textRaith, Martin. "Orbital effects of transverse magnetic fields in quasi two-dimensional electron systems." kostenfrei, 2009. http://epub.uni-regensburg.de/8285/.
Full textHowell, D. F. "Studies of two-dimensional electron systems in semiconductors at high magnetic fields." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253390.
Full textRichards, David Robert. "The electronic structure and optical properties of GaAs two-dimensional electron systems." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359697.
Full textCaldwell, Joshua D. "Investigation of electron-nuclear spin interactions in two-dimensional electron systems via magnetoresistively detected magnetic resonance." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008397.
Full textGalaktionov, Evgeniy A. "Transport and thermodynamic properties of low-density two-dimensional electron and hole systems." Thesis, University of Exeter, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.439126.
Full textJones, Christopher Lee. "Magnetisation and optical studies of two-dimensional electron systems in high magnetic fields." Thesis, University of Exeter, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294472.
Full textSoumyanarayanan, Anjan. "A nanoscale probe of the quasiparticle band structure for two dimensional electron systems." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/83821.
Full textPage 138 blank. Cataloged from PDF version of thesis.
Includes bibliographical references (pages 121-137).
The advent of a broad class of two-dimensional (2D) electronic materials has provided avenues to create and study designer electronic quantum phases. The coexistence of superconductivity, magnetism, density waves, and other ordered phases on the surfaces and interfaces of these 2D materials are governed by interactions which can be experimentally tuned with increasing precision. This motivates the need to develop spectroscopic probes that are sensitive to these tuning parameters, with the objective of studying the electronic properties and emergence of order in these materials. In the first part of this thesis, we report on spectroscopic studies of the topological semimetal antimony (Sb). Our simultaneous observation of Landau quantization and quasiparticle interference phenomena on this material enables their quantitative reconciliation - after two decades of their study on various materials. We use these observations to establish momentum-resolved scanning tunneling microscopy (MR-STM) as a robust nanoscale band structure probe, and reconstruct the multi-component dispersion of Sb(111) surface states. We quantify surface state parameters relevant to spintronics applications, and clarify the relationship between bulk conductivity and surface state robustness. At low momentum, we find a crossover in the single particle behavior from massless Dirac to massive Rashba character - a unique signature of topological surface states. In the second part of this thesis, we report on the spectroscopic study of charge density wave (CDW) order in the dichalcogenide 2H-NbSe2 - a model system for understanding the interplay of coexisting CDW and superconducting phases. We detail the observation of a previously unknown unidirectional (stripe) CDW smoothly interfacing with the familiar triangular CDW on this material. Our low temperature measurements rule out thermal fluctuations and point to local strain as the tuning parameter for this quantum phase transition. The distinct wavelengths and tunneling spectra of the two CDWs, in conjunction with band structure calculations, enable us to resolve two longstanding debates about the anomalous spectroscopic gap and the role of Fermi surface nesting in the CDW phase of NbSe2. Our observations motivate further spectroscopic studies of the phase evolution of the CDW, and of NbSe 2 as a prototypical strong coupling density wave system in the vicinity of a quantum critical point.
by Anjan Soumyanarayanan.
Ph.D.
Elbahrawy, Mohammed. "High field electron magnetic resonance in complex correlated spin systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-39380.
Full textRamanayaka, Aruna N. "Magnetotransport in Two Dimensional Electron Systems Under Microwave Excitation and in Highly Oriented Pyrolytic Graphite." Digital Archive @ GSU, 2012. http://digitalarchive.gsu.edu/phy_astr_diss/54.
Full textBrener, Sergej. "Coulomb Drag and Jahn-Teller effect in two-dimensional electron systems in strong magnetic fields." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-26345.
Full textYang, Chunlei. "Studies of the spintronic systems of ferromagnetic GaMnAs and non-magnetic InGaAs/InAlAs two dimensional electron gas /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202005%20YANG.
Full textKerridge, Gregg Charles. "Magneto-optical investigations of two-dimensional electron systems in GaAs-Alâ†xGaâ†1â†-â†xAs single heterojunctions." Thesis, University of Exeter, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286493.
Full textTobita, Motoi. "Development of efficient electron correlation methods for one- and two-dimensional extended systems and their applications." [Gainesville, Fla.] : University of Florida, 2002. http://purl.fcla.edu/fcla/etd/UFE1000168.
Full textTitle from title page of source document. Document formatted into pages; contains x, 109 p.; also contains graphics. Includes vita. Includes bibliographical references.
Zhang, Yao. "Experimental Measurements by Antilocalization of the Interactions between Two-Dimensional Electron Systems and Magnetic Surface Species." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/49020.
Full textPh. D.
Dai, Ji. "Low-dimensional electron systems studied by angle- and spin-resolved photoemission spectroscopy." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS345.
Full textMaterials in which many-body interactions, low-dimensional confinement, and/or strong spin-orbit coupling are present show a rich variety of phenomena, but are still poorly understood. Essential information about the origin of such phenomena can be obtained by measuring their electronic structure. This thesis presents an experimental study of the electronic structure of some low-dimensional and/or strongly correlated materials of current fundamental interest, using angle- and spin-resolved photoemission spectroscopy (ARPES and SARPES). In the introductory part, I present my work on two innovative textbook examples showing how interactions affect the band structure of a material: the coupling of electrons with phonons in a Debye distribution in a two-dimensional electron system (2DES) in ZnO, a wide-band-gap oxide semiconductor used in photovoltaic applications, and the splitting induced by strong spin-orbit coupling (SOC) in the bulk valence band of ZnTe, another important semiconductor used in optoelectronic devices. Then, in the rest of this thesis, I discuss my original results in three different low-dimensional systems of current interest: 1.The realisation of a 2DES at the (110) surface of SnO₂, the first of its kind in a rutile structure. Tunability of its carrier density by means of temperature or Eu deposition and robustness against surface reconstructions and exposure to ambient conditions make this 2DES promising for applications. By means of a simple redox reaction on the surface, this work has proven that oxygen vacancies can dope the conduction band minimum at the surface of SnO₂, solving a long-debated issue about their role in n-type doping in SnO₂. 2.The study of topological surface states in M₂Te₂X (with M = Hf, Zr, or Ti; and X = P or As), a new family of three-dimensional topological metals, originating from SOC and being protected by time-reversal symmetry. Their electronic structure and spin texture, studied by ARPES and SARPES, reveal the presence of massless Dirac fermions giving rise to Dirac-node arcs. 3.The investigation of the quasi-one-dimensional heavy-fermion material YbNi₄P₂, which presents a second-order quantum phase transition from a ferromagnetic to a paramagnetic phase upon partial substitution of phosphorous by arsenide. Such a transition is expected to occur only in zero- or one-dimensional systems, but a direct measurement of the electronic structure of ferromagnetic quantum-critical materials was missing so far. By careful in-situ preparation and cleaning of the surface of YbNi₄P₂ single crystals, which are impossible to cleave, their electronic structure has been successfully measured by ARPES, thus effectively unveiling the quasi-one-dimensionality of YbNi₄P₂. Moreover, the protocol used to make this material accessible to ARPES can be readily generalised to other exotic materials lacking a cleavage plane
Höpfner, Philipp Alexander [Verfasser], and Ralph [Akademischer Betreuer] Claessen. "Two-Dimensional Electron Systems at Surfaces — Spin-Orbit Interaction and Electronic Correlations / Philipp Alexander Höpfner. Betreuer: Ralph Claessen." Würzburg : Universitätsbibliothek der Universität Würzburg, 2013. http://d-nb.info/1037093488/34.
Full textDodoo-Amoo, Nii Amoo. "The nature of critical phenomena of the scaling theory of quantum Hall transitions in two-dimensional electron systems." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/4764/.
Full textLynass, Mark Ronald. "Novel physics in two dimensional charge carrier structures : anisotropc magneto-transport at Landau-level crossings in aluminium arsenide quantum wells and coupled two dimensional electron and hole systems." Thesis, University of Bath, 2006. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428382.
Full textKärcher, Daniel [Verfasser], and Bernhard [Akademischer Betreuer] Keimer. "Transport in two-dimensional electron systems in ZnO under the influence of microwave radiation / Daniel Kärcher. Betreuer: Bernhard Keimer." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2016. http://d-nb.info/1084636115/34.
Full textBrasse, Matthias [Verfasser], Dirk [Akademischer Betreuer] Grundler, and PETER [Akademischer Betreuer] BOENI. "Magnetization of correlated electron systems: MnSi thin films, CrB2 single crystals and two-dimensional electron systems in MgZnO/ZnO / Matthias Brasse. Gutachter: Dirk Grundler ; Peter Böni. Betreuer: Dirk Grundler." München : Universitätsbibliothek der TU München, 2014. http://d-nb.info/1047883554/34.
Full textGriesbeck, Michael [Verfasser], and Christian [Akademischer Betreuer] Schüller. "Spin dynamics in high-mobility two-dimensional electron systems embedded in GaAs/AlGaAs quantum wells / Michael Griesbeck. Betreuer: Christian Schüller." Regensburg : Universitätsbibliothek Regensburg, 2012. http://d-nb.info/1028958951/34.
Full textRösch, Matthias. "Kopplung von kollektiven Anregungen in einlagigen und doppellagigen quasi-zweidimensionalen Elektronensystemen Coupling of collective excitations in monolayer and bilayer quasi two-dimensional electron systems /." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974407658.
Full textSchmalzbauer, Michael [Verfasser], Dominique [Akademischer Betreuer] Bougeard, Dieter [Akademischer Betreuer] Weiss, Milena [Akademischer Betreuer] Grifoni, and Karsten [Akademischer Betreuer] Rincke. "Heterostructure design of Si/SiGe two-dimensional electron systems for field-effect devices / Michael Schmalzbauer. Betreuer: Dominique Bougeard ; Dieter Weiss ; Milena Grifoni ; Karsten Rincke." Regensburg : Universitätsbibliothek Regensburg, 2015. http://d-nb.info/1070423521/34.
Full textStegmann, Thomas [Verfasser], Dietrich E. [Akademischer Betreuer] Wolf, Orsolya [Akademischer Betreuer] Ujsághy, and Jürgen [Akademischer Betreuer] König. "Quantum transport in nanostructures : From the effects of decoherence on localization to magnetotransport in two-dimensional electron systems / Thomas Stegmann. Gutachter: Orsolya Ujsághy ; Jürgen König. Betreuer: Dietrich E. Wolf." Duisburg, 2014. http://d-nb.info/1060631873/34.
Full textPeters, John Archibald. "Ballistic Magnetotransport and Spin-Orbit Interaction InSb and InAs Quantum Wells." Ohio University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1143487911.
Full textChickering, William Elbridge. "Thermopower in Two-Dimensional Electron Systems." Thesis, 2016. https://thesis.library.caltech.edu/9320/2/thesis.pdf.
Full textThe subject of this thesis is the measurement and interpretation of thermopower in high-mobility two-dimensional electron systems (2DESs). These 2DESs are realized within state-of-the-art GaAs/AlGaAs heterostructures that are cooled to temperatures as low as T = 20 mK. Much of this work takes place within strong magnetic fields where the single-particle density of states quantizes into discrete Landau levels (LLs), a regime best known for the quantum Hall effect (QHE). In addition, we review a novel hot-electron technique for measuring thermopower of 2DESs that dramatically reduces the influence of phonon drag.
Early chapters concentrate on experimental materials and methods. A brief overview of GaAs/AlGaAs heterostructures and device fabrication is followed by details of our cryogenic setup. Next, we provide a primer on thermopower that focuses on 2DESs at low temperatures. We then review our experimental devices, temperature calibration methods, as well as measurement circuits and protocols.
Latter chapters focus on the physics and thermopower results in the QHE regime. After reviewing the basic phenomena associated with the QHE, we discuss thermopower in this regime. Emphasis is given to the relationship between diffusion thermopower and entropy. Experimental results demonstrate this relationship persists well into the fractional quantum Hall (FQH) regime.
Several experimental results are reviewed. Unprecedented observations of the diffusion thermopower of a high-mobility 2DES at temperatures as high as T = 2 K are achieved using our hot-electron technique. The composite fermion (CF) effective mass is extracted from measurements of thermopower at LL filling factor ν = 3/2. The thermopower versus magnetic field in the FQH regime is shown to be qualitatively consistent with a simple entropic model of CFs. The thermopower at ν = 5/2 is shown to be quantitatively consistent with the presence of non-Abelian anyons. An abrupt collapse of thermopower is observed at the onset of the reentrant integer quantum Hall effect (RIQHE). And the thermopower at temperatures just above the RIQHE transition suggests the existence of an unconventional conducting phase.
Huang, Jian-Zhe, and 黃健哲. "transport in two-dimensional GaN electron systems." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/05735658938187878178.
Full text國立臺灣大學
物理研究所
95
Abstract This thesis describes the measurements on the low-temperature electron transport properties in a two-dimensional GaN electron system. This thesis consists of the following two parts: 1. Electron-electron interaction in a perpendicular magnetic field: We report on experimental studies of Al0.15Ga0.85N/GaN high electron mobility transistor (HEMT) structures grown on p-type Si (111) substrates. By introducing an ultra thin SiN layer during the crystal growth, the Hall mobility of the HEMT structure can be greatly enhanced (>3 times). This SiN treatment technique also allows the observation of Shubnikov-de Haas oscillations which is not possible in the untreated HEMT structure. Our experimental results pave way to integration of AlxGa1-xN/GaN HEMT structures with the mature Si technology in industry. 2. Weak localization effect in a perpendicular magnetic field: We can illustrate weak localization by the constructive interference of wave functions which back to the origin after transmitting along time-reversed paths. Electrons will be localized by weal localization. The dephasing time , which determines the time scale kept the constructive interference of wave functions, limits the length of the time-reversed paths. It is known that weak localization causes a negative magnetoresistivity.
Huang, Jian-Zhe. "transport in two-dimensional GaN electron systems." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-0307200716200600.
Full textHuang, Tsai-Yu, and 黃才育. "Transport properties in two-dimensional GaAs electron systems." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/09048648273325713081.
Full text國立臺灣大學
物理研究所
93
We have investigated the low-temperature magnetotransport measurements in two-dimensional GaAs electron systems. This dissertation consists of the following four topics. 1. On the low-field insulator-quantum Hall transitions We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor /nu=4 on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the /nu=4 quantum Hall state directly from the low-field insulator, the system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall conductor transition. 2. On the various Hall insulators We have studied the various Hall insulators (HIs) in a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. It is shown that the quantized HI is not necessarily accompanied by the insulator-quantum Hall (I-QH) transition. From our study, the semicircle law can become invalid in the QH liquid so that the quantized Hall plateau is absent at the I-QH transition. The appearance and breakdown of the semicircle law in the insulating phase can be both observed when the QH liquid is destroyed by disorder. 3. Direct measurement of the spin gaps in a gated two-dimensional GaAs electron gas We have investigated magneto transport in gated GaAs two-dimensional electron gases. From the evolution of spin-split Landau levels (LLs) in the Energy (E)-magnetic field (B) plane, we can perform direct measurements of the spin gap for different LLs. The measured g-factor is greatly enhanced over its bulk value in GaAs (0.44) due to electron-electron (e-e) interactions. As the LL index decreases, the g-factor increases, suggesting that the strength of e-e interactions increases as the number of occupied LL decreases. Moreover, the g-factor determined from the conventional activation energy studies is ~ 2.5 times smaller than that deduced from the direct measurements. 4. “Mobility gap” of a spin-split GaAs two- dimensional electron system We have performed magnetotransport measurements of the electron g-factor in a two-dimensional GaAs electron gas. In order to obtain the spin gap△S, we measure the spin-split longitudinal resistivity minimum which shows an activated behavior. From the spin gaps at different odd filling factors, we can obtain the effective g-factor which is greatly enhanced over its bare value (0.44) in GaAs. This enhancement is due to many-body electron-electron interactions. Our experimental results provide compelling evidence that conventional activation energy studies yield a “mobility gap” which can be very different from the real spin gap in the energy spectrum.