In this dissertation, I present optical emission and light scattering studies on ultraclean two-dimensional electron systems. These studies focus on emerg- ing phases in the second Landau level. I report for the excitation spectrum for fractional quantum Hall states at filling factors ν = 2+1/3, ν = 2+3/8, and ν = 2+2/5 through resonant inelastic light scattering. Resonant Rayleigh scattering is used to demonstrate that these fractional quantum Hall states are anisotropic. This work provides new insights into the nature of quasiparticle interactions of these states. It also sets the stage for the subsequent discussions about competing and coexistent phases. I present studies of emergent phases in the filling factor range 2 ≤ ν ≤ 3 using weak optical emission from the second Landau level and resonant inelas- tic light scattering by spin wave excitations. A multiplet of optical emission peaks observed that exhibit striking filling factor dependence amnifest phase competition in the second Landau level. A correlation of emission peaks in the multiplet with anomalies observed in the spin wave spectrum uncover major impact of the spin degree of freedom on the emergent phases in the second Landau level. These experiments demonstrate the promise of optical emission from excited Landau levels as a probe of emergent phases. Results from optical emission and resonant inelastic light scattering stud- ies of the second Landau level conducted at higher temperatures (T ≈ 1 K) are also presented. Evidence that many phases observed at these higher temperatures are shown to be the same as those at lower (T ≈ 40 mK) temperatures. Striking and anomalous temperature-dependence of optical emission experiments is used to gain further insight into the nature of these competing phases.

Thesis (M.Sc.)--University of Wollongong, 2004. / Typescript. Includes bibliographical references: leaf 48-49.

Thesis (PhD)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The fractional quantum Hall effect represents a true many-body phenomenon in which the collective behaviour of interacting electrons plays a central role. In contrast to its integral counterpart, the appearance of a mobility gap in the fractional quantum Hall regime is due entirely to the Coulomb interaction and is not the result of a perturbed single particle gap. The bulk of our theoretical understanding of the underlying many-body problem is based on Laughlin’s ansatz wave function and the composite fermion picture proposed by Jain. In the latter the fractional quantum Hall effect of interacting electrons is formulated as the integral quantum Hall effect of weakly interacting quasiparticles called composite fermions. The composite fermion picture provides a qualitative description of the interacting system’s low-energy spectrum and leads to a generalisation of Laughlin’s wave functions for the electron ground state. These predictions have been verified through extensive numerical tests. In this work we present an alternative formulation of the composite fermion picture within a more rigorous mathematical framework. Our goal is to establish the relation between the strongly interacting electron problem and its dual description in terms of weakly interacting quasiparticles on the level of the microscopic Hamiltonian itself. This allows us to derive an analytic expression for the interaction induced excitation gap which agrees very well with existing numerical results. We also formulate a mapping between the states of the free particle and interacting descriptions in which the characteristic Jastrow-Slater structure of the composite fermion ansatz appears naturally. Our formalism also serves to clarify several aspects of the standard heuristic construction, particularly with regard to the emergence of the effective magnetic field and the role of higher Landau levels. We also resolve a long standing issue regarding the overlap of unprojected composite fermion trial wave functions with the lowest Landau level of the free particle Hamiltonian. / AFRIKAANSE OPSOMMING: Die fraksionele kwantum Hall-effek is ’n veeldeeltjie verskynsel waarin die kollektiewe gedrag van wisselwerkende elektrone ’n sentrale rol speel. In teenstelling met die heeltallige kwantum Hall-effek is die ontstaan van ’n energie gaping in die fraksionele geval nie ’n enkeldeeltjie effek nie, maar kan uitsluitlik aan die Coulomb wisselwerking toegeskryf word. Die teoretiese raamwerk waarbinne hierdie veeldeeltjie probleem verstaan word is grootliks gebaseer op Laughlin se proefgolffunksie en die komposiete-fermion beeld van Jain. In laasgenoemde word die fraksionele kwantum Hall-effek van wisselwerkende elektrone geformuleer as die heeltallige kwantum Hall-effek van swak-wisselwerkende kwasi-deeljies wat as komposiete-fermione bekend staan. Hierdie beeld lewer ’n kwalitatiewe beskrywing van die wisselwerkende sisteem se lae-energie spektrum en lei tot ’n veralgemening van Laughlin se golffunksies vir die elektron grondtoestand. Hierdie voorspellings is deur verskeie numeriese studies geverifieer. In hierdie tesis ontwikkel ons ’n alternatiewe formulering van die komposiete-fermion beeld binne ’n strenger wiskundige raamwerk. Ons doel is om die verband tussen die sterk-wisselwerkende elektron sisteem en sy duale beskrywing in terme van swak-wisselwerkende kwasi-deeltjies op die vlak van die mikroskopiese Hamilton-operator self te realiseer. Hierdie konstruksie lei tot ’n analitiese uitdrukking vir die opwekkingsenergie wat baie goed met bestaande numeriese resultate ooreenstem. Ons identifiseer ook ’n afbeelding tussen die vrye-deeltjie en wisselwerkende toestande waarbinne die Jastrow-Slater struktuur van die komposiete-fermion proefgolffunksies op ’n natuurlike wyse na vore kom. Verder werp ons formalisme nuwe lig op kwessies binne die standaard heuristiese konstruksie, veral met betrekking tot die oorsprong van die effektiewe magneetveld en die rol van ho¨er effektiewe Landau vlakke. Ons lewer ook uitspraak oor die vraagstuk van die oorvleueling van ongeprojekteerde komposiete-fermion golffunksies met die laagste Landau vlak van die vrye-deeltjie Landau probleem.

Graphene – a two-dimensional honeycomb lattice of sp2-bonded carbon atoms – possesses unusual zero-gap band structure with linear band dispersions, accommodating photon-like, massless electrons that have exhibited a variety of surprising phenomena, primarily in DC transport, in the last several years. In this thesis dissertation, we investigate graphene’s AC or infrared properties in the presence of an ultrahigh magnetic field, produced by a destructive pulsed method. The linear dispersions of graphene lead to unequally spaced Landau levels in a magnetic field, which we probe through cyclotron resonance (CR) spectroscopy in the magnetic quantum limit. Specifically, using magnetic fields up to 170 T and polarized midinfrared radiation with tunable wavelengths from 9.22 to 10.67 μm, we experimentally investigated CR in large-area graphene grown by chemical vapor deposition. Circular-polarization-dependent studies revealed strong p-type doping for as-grown graphene, and the dependence of the CR fields on the radiation wavelength allowed for an accurate determination of the Fermi energy. Upon annealing the sample to remove physisorbed molecules, which shifts the Fermi energy closer to the Dirac point, we made the unusual observation that hole and electron CR emerges in the magnetic quantum limit, even though the sample is still p-type. We theoretically show that this non-intuitive phenomenon is a direct consequence of the unusual Landau level structure of graphene. Namely, if the Fermi energy lies in the n = 0 Landau level, then CR is present for both electron-active and hole-active circular polarizations. Furthermore, if the Fermi level lies in the n = 0 Landau level, the ratio of CR absorption between the electron-active and hole-active peaks allows one to accurately determine the Fermi level and carrier density. Hence, high-field CR studies allow not only for fundamental studies but also for characterization of large-area, low-mobility graphene samples.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references and index.

The electron-electron interaction is the origin of many interesting phenomena in condensed matter. These phenomena post challenges to theoretical physics and can lead to important future applications. Transition metal dichalcogenide heterostructures provide excellent platforms to study these phenomena because of the two-dimensional nature, large effective mass and tunable bandwidth with moiré potential. As electron bands become narrower such that the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. This dissertation describes the realization of this platform and probing of correlated phenomena with low- temperature transport measurements. As the first step, the electrical contact problem of few-layer transition metal dichalcogenides, which prohibits low-temperature transport measurements, needs to be solved. Two different contact schemes have been used to attack this problem. For p-type transition metal dichalcogenide, prepatterned platinum is used to bottom contact transition metal dichalcogenides. This method prevents channel from deterioration due to electron beam evaporation and the high workfunction platinum can place the Fermi level underneath the material valence band. Alternatively, for n-type transition metal dichalcogenides, a single layer of boron nitride is put on transition metal dichalcogenide before cobalt evaporation. This way, the boron nitride layer protects the transition metal dichalcogenide from the process of evaporation and can decrease the work function of cobalt thus putting Fermi level above the conduction band. With these contact methods, Ohmic contacts can be achieved at cryogenic temperature and probing the transition metal dichalcogenide heterostructures with transport measurements become accessible. Then, the magnetotransport properties of monolayer molybdenum disulphide and bilayer tungsten diselenide encapsulated with boron nitride with graphite dual-gate were measured. There are three unique features underlie this two dimensional electron gas system. First, the system is strong correlated. The Landau level spectrum reveals strong correlated signatures, such as enhanced spin-orbit coupling splitting and enhanced effective g-factor. Second, the longitudinal resistance/conductance at half-filling of Landau levels are found to depend on the spin orientation. The minority spin Landau level become totally localized at higher magnetic field. Third, in bilayer device the two layers are weak coupled and can be independently controlled by two gates. All this features establish transition metal dichalcogenide a unique platform for studying correlated physics. Finally, to achieve higher level of correlation, two layers of tungsten diselenide are stacked together with a small twist angle. With the help of moiré potential and layer hybridization, the bandwidth can be continuously tuned by the twist angle. In the range of 3 degree to 5.1degree, with moderate correlation strength, correlated insulating states are shown at half-filled flatband and are highly tunable with vertical electric field.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posed an intriguing question to theorists: Why is the quantization of conductance so precise, given the imperfections of the measured samples? The question was answered a few years later, when a connection was uncovered between the quantum Hall effect and topological quantities associated with the band structure of the material in which it is observed. The Hall conductance was revealed to be an integer topological invariant, implying its robustness to certain perturbations. The topological theory went further than explaining only the usual integer quantum Hall effect in a perpendicular magnetic field. Soon it was realized that it also applies to certain systems in which the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect without Landau levels. We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recent studies suggest that the application of an electric field parallel to the magnetic field would induce a gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensional nature of the carbon nanotube, the gapped state supports a quantum Hall effect and is associated with a non zero topological invariant. This result is revealed when an additional magnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to this magnetic field is varied by one flux quantum, exactly one electron is transported between the ends of the carbon nanotube. / AFRIKAANSE OPSOMMING: Die eksperimentele waarneming van die kwantum Hall effek in ’n twee-dimensionele elektron gas laat ’n interessante vraag aan teoretiese fisikuste: Waarom sou die kwantisasie van die geleiding so presies wees al bevat die monsters, waarop die meetings gedoen word, onsuiwerhede? Hierdie vraag word ’n paar jaar later geantwoord toe ’n konneksie tussen die kwantum Hall effek en topologiese waardes, wat verband hou met die bandstruktuur van die monster, gemaak is. Dit is aan die lig gebring dat die Hall geleiding ’n heeltallige topologiese invariante is wat die robuustheid teen sekere steurings impliseer. Die topologiese teorie verduidelik nie net die gewone kwantum Hall effek wat in ’n loodregte magneetveld waargeneem word nie. Dit is ook moontlik om ’n kwantum Hall effek waar te neem in sekere sisteme waar die totale magneetvloed nul is. Dit is dus moontlik om ’n gekwantiseerde Hall effek sonder Landau levels te hˆe. Ons bestudeer ’n koolstofnanobuis in ’n magneetveld loodreg tot die aksiale rigting. Onlangse studies dui daarop dat die toepassing van ’n elektriese veld parallel aan die magneetveld ’n gaping in die elektroniese spektrum van ’n metaliese koolstofnanobuis induseer. Ten spyte van die een-dimensionele aard van die koolstofnanobuis ondersteun die gapings-toestand steeds ’n kwantum Hall effek en hou dit verband met ’n nie-nul topologiese invariante. Hierdie resultaat word openbaar wanneer ’n bykomende magneetveld parallel tot die as van die koolstofnanobuis toegedien word. Indien die vloed as gevolg van hierdie magneetveld met een vloedkwantum verander word, word presies een elektron tussen die twee kante van die koolstofnanobuis vervoer.

Nesta tese, apresentamos estudos de magnetotransporte em poços quânticos duplos (DQWs) a campos magnéticos de baixo e sob a aplicação de um campo elétrico externo (potencial de porta). Medidas de magnetorresistência foram realizadas tanto no regime linear quanto no regime não linear. Relatamos a observação de oscilações magnéticas de inter-sub-banda (MIS) pela primeira vez. Estas oscilações MIS já foram estudadas em poços quânticos simples (QWs) com duas sub-bandas ocupadas; um DQW´e o sistema mais apropriado para o estudo das oscilações MIS. As oscilações MIS são atribuídas ao espalhamento inter-sub-banda, e a intensidade delas depende da largura da barreira (relacionada ao gap de energia entre as duas sub-bandas ocupadas, SAS). O estudo das oscilações MIS é uma ferramenta importante para poder acessar ao tempo de vida quântico dos elétrons a temperaturas onde as oscilações Shubnikov-de Haas (SdH) já não são observadas. Em nossas amostras, as oscilações MIS persistem até 25 K. Explicamos estes resultados num modelo teórico considerando um potencial de espalhamento de curto alcance com uma contribuição significativa do tempo de espalhamento elástico dos elétrons e uma contribuição do espalhamento elétron-elétron (e-e) com o aumento da temperatura. A aplicação de um campo elétrico externo (correntes dc) modifica fortemente as oscilações MIS. Descrevemos este efeito não linear causado pelo campo elétrico dc com uma função de distribuição oscilatória. Considerando o aquecimento dos elétrons pelo campo elétrico, é extraído o tempo de espalhamento inelástico. Para correntes dc grandes são encontradas discrepâncias entre o experimento e a teoria. Finalmente, consideramos medidas de magnetotransporte como função de potenciais de porta (porta na superficie) levando ao desbalance do DQW. Encontramos que as contribuições clássica e quântica são necessárias para a descrição teórica da magnetorresistência. Descrevemos as contribuições da magnetorresistência em termos das taxas de espalhamento inter e intra sub-banda utilizando uma função gaussiana como função da correlação do potencial. / In this thesis we present studies of magnetotransport in double quantum wells (DQWs) in low magnetic fields and under application of an external electric field (gate potential). Measurements of magnetoresistance have been carried out in both linear and non-linear regime. We report on the observation of magneto-intersubband (MIS) oscillations for the first time. These MIS oscillations have been studied already in quantum wells (QWs) with two occupied subbands, DQW is the most convenient system for studies of MIS oscillations. They are attributed to intersubband scattering and the strength of MIS oscillations depends on the barrier width (´delta´SAS). Analysis of MIS oscillations is an important tool to access quantum lifetime of electrons at high temperatures where Shubnikov-de Haas (SdH) oscillations are already absent. For our samples, MIS oscillations still exist up to 25 K. We explain these results in a theoretical model considering short-range scattering potential with a significant contribution of el´astic scattering time of electrons and a contribution of electron-electron (e-e) scattering if one increases temperature. Application of an external electric field (here a dc currents) strongly modifies the MIS oscillations. We describe this non-linear effect caused by a dc electric field with nonequilibrium part of the electron distribution function. Including the heating of electrons by the electric field, we are able to extract inelastic scattering time. For a strong dc current, a discrepancy between experiment and theory is found. Finally, we consider gate-dependent (top gate) magnetotransport measurements and drive de DQWs out of balance. We find that both cl´assical and quantum contributions are necessary for theoretical description of the magnetoresistance. We express both contributions in terms of inter and intrasubband scattering rates using a gaussian function as correlation function of the potential.

In this thesis we study the effect of electron-electron interactions on Chiral two-dimensional electron gas (C2DEGs). C2DEGs are a very good description of the low-energy electronic properties of single layer and multilayer graphene systems. The low-energy properties of single layer and multilayer graphene are described by Chiral Hamiltoninans whose band eigenstates have definite chirality. In this thesis we focus on the effect of electron-electron interactions on two of these systems: monolayer and bilayer graphene. In the first half of this thesis we use the massless Dirac Fermion model and random-phase-approximation to study the effect of interactions in graphene sheets. The interplay of graphene's single particle chiral eigenstates along with electron-electron interactions lead to a peculiar supression of spin susceptibility and compressibility, and also to an unusual velocity renormalization. We also report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene. We find that level repulsion between quasiparticle and plasmaron resonances gives rise to a gap-like feature near the Dirac point. In the second half we anticipate interaction driven integer quantum Hall effects in bilayer graphene because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate q[superscrit 3/2] dispersion. We speculate on the possibility of unusual localization physics associated with these modes. / text

Nesta tese, apresentamos estudos de magnetotransporte em poços quânticos duplos (DQWs) a campos magnéticos de baixo e sob a aplicação de um campo elétrico externo (potencial de porta). Medidas de magnetorresistência foram realizadas tanto no regime linear quanto no regime não linear. Relatamos a observação de oscilações magnéticas de inter-sub-banda (MIS) pela primeira vez. Estas oscilações MIS já foram estudadas em poços quânticos simples (QWs) com duas sub-bandas ocupadas; um DQW´e o sistema mais apropriado para o estudo das oscilações MIS. As oscilações MIS são atribuídas ao espalhamento inter-sub-banda, e a intensidade delas depende da largura da barreira (relacionada ao gap de energia entre as duas sub-bandas ocupadas, SAS). O estudo das oscilações MIS é uma ferramenta importante para poder acessar ao tempo de vida quântico dos elétrons a temperaturas onde as oscilações Shubnikov-de Haas (SdH) já não são observadas. Em nossas amostras, as oscilações MIS persistem até 25 K. Explicamos estes resultados num modelo teórico considerando um potencial de espalhamento de curto alcance com uma contribuição significativa do tempo de espalhamento elástico dos elétrons e uma contribuição do espalhamento elétron-elétron (e-e) com o aumento da temperatura. A aplicação de um campo elétrico externo (correntes dc) modifica fortemente as oscilações MIS. Descrevemos este efeito não linear causado pelo campo elétrico dc com uma função de distribuição oscilatória. Considerando o aquecimento dos elétrons pelo campo elétrico, é extraído o tempo de espalhamento inelástico. Para correntes dc grandes são encontradas discrepâncias entre o experimento e a teoria. Finalmente, consideramos medidas de magnetotransporte como função de potenciais de porta (porta na superficie) levando ao desbalance do DQW. Encontramos que as contribuições clássica e quântica são necessárias para a descrição teórica da magnetorresistência. Descrevemos as contribuições da magnetorresistência em termos das taxas de espalhamento inter e intra sub-banda utilizando uma função gaussiana como função da correlação do potencial. / In this thesis we present studies of magnetotransport in double quantum wells (DQWs) in low magnetic fields and under application of an external electric field (gate potential). Measurements of magnetoresistance have been carried out in both linear and non-linear regime. We report on the observation of magneto-intersubband (MIS) oscillations for the first time. These MIS oscillations have been studied already in quantum wells (QWs) with two occupied subbands, DQW is the most convenient system for studies of MIS oscillations. They are attributed to intersubband scattering and the strength of MIS oscillations depends on the barrier width (´delta´SAS). Analysis of MIS oscillations is an important tool to access quantum lifetime of electrons at high temperatures where Shubnikov-de Haas (SdH) oscillations are already absent. For our samples, MIS oscillations still exist up to 25 K. We explain these results in a theoretical model considering short-range scattering potential with a significant contribution of el´astic scattering time of electrons and a contribution of electron-electron (e-e) scattering if one increases temperature. Application of an external electric field (here a dc currents) strongly modifies the MIS oscillations. We describe this non-linear effect caused by a dc electric field with nonequilibrium part of the electron distribution function. Including the heating of electrons by the electric field, we are able to extract inelastic scattering time. For a strong dc current, a discrepancy between experiment and theory is found. Finally, we consider gate-dependent (top gate) magnetotransport measurements and drive de DQWs out of balance. We find that both cl´assical and quantum contributions are necessary for theoretical description of the magnetoresistance. We express both contributions in terms of inter and intrasubband scattering rates using a gaussian function as correlation function of the potential.