Two dimensional (2D) systems with low carrier density is an outstanding platform for studying a wide spectrum of physics. These include both classical and quantum effects, arising from disorder, Coulomb interactions and even non-trivial topological properties of band-structure. In this thesis, we have explored the physics at low carrier number density in GaAs/AlGaAs heterostructure and bilayer graphene, by investigating in a larger phase space using a variety of electrical measurement tools. A two-dimensional electron system (2DES) formed in a GaAs/AlGaAs heterostructure offers an avenue to build a variety of mesoscopic devices, primarily because its surface gates can very effectively control its carrier density profile. In the first half of the thesis, we study the relevance of disorder in two kinds of devices made in a 2DES. A very strong negative gate voltage not only reduces the carrier density of the 2DES, but also drives it to a disordered state. In this state, we explore a new direction in parameter space by increasing in-plane electric field and investigating its magneto-resistance (MR). At sufficiently strong gate voltage and source-drain bias, we discover a remarkably linear MR. Its enormous magnitude and weak temperature dependence indicate that this is a classical effect of disorder. In another study, we examine a specially designed dual-gated device that can induce low number density in a periodic pattern. By applying appropriate gate voltages, we demonstrate the formation of an electrostatically tunable quantum dot lattice and study the impact of disorder on it. This work is important in paving way for solid state based platform for experimental simulations of artificial solids. The most striking property of bilayer graphene is the ability to open its band gap by a perpendicular electric field, giving the prospects of enabling a large set of de-vice applications. However, despite a band gap, a number of transport mechanisms are still active at very low densities that range from hopping transport through bulk to topologically protected 1D transport at the edges or along 1D crystal dislocations. In the second half of the thesis, we have used higher order statistical moment of resistance/conductance fluctuations, namely the variance of the fluctuations, to complement averaged resistance/conductance, and study and infer the dominant transport mechanism at low densities in a gapped bilayer graphene. Our results show possible evidence of percolative transport and topologically protected edge transport at different ranges of low number densities. We also explore the same phase space by studying its mesoscopic conductance fluctuations at very low temperatures. This is the first of its kind systematic experiment in a dual-gated bilayer graphene device. Its conductance fluctuations have several anomalous features suggesting non-universal behaviour which is at odds with conventional disordered systems.

<div>Strong electronic correlations in many-body systems are cradles of new physics. They give birth to novel collective states hosting emergent quasiparticles as well as intriguing geometrical charge patterns. Two-dimensional electron gas in GaAs/AlGaAs under perpendicular magnetic field is one of the most well-known hosts in condensed matter physics where a plethora of the collective states appear. In the strong magnetic field regime, strong Coulomb interactions among the electrons create emergent quasiparticles, i.e. composite fermions and Cooper-paired composite fermions. In the weak magnetic field regime, modified Coulomb interactions drive electron solid phases having geometrical charge patterns in the shape of stripes and bubbles and lower the spatial symmetry of the states.</div><div><br></div><div>The fascinating charge order in bubble geometry is the electron bubble phase predicted first by the Hartree-Fock theory. In a bubble phase, certain number of electrons cluster as an entity called bubble and the bubbles order into a crystal of triangular lattice. In addition to the Hartree-Fock theory, the density matrix renormalization group and the exact diagonalization methods further support the formation of electronic bubbles.</div><div><br></div><div>Reentrant integer quantum Hall states are commonly accepted as the manifestations of the bubble phases in transport experiment. Soon after the first prediction of the Hartree-Fock theory, the reentrant integer quantum Hall states were observed in the third and higher Landau levels. Since then, the association to the bubble phases has been tested with different experimental techniques for decades.</div><div><br></div><div>Although the experimental results from different methods support the bubble phase picture of the reentrant integer quantum Hall states, the electron confinement under the quantum well structure hindered direct scanning of bubble morphology. Thus none of the experiments could showcase the bubble morphology of the reentrant integer quantum Hall states. Meanwhile, a significant discrepancy still remained in between the bubble theories and the experiments. Even though the bubble theories predict the proliferation of bubble phases with increasing orbital index, none of the experiments could observe multiple reentrant integer quantum Hall states in a high Landau level, which signify the multiple bubble formation. Therefore, the proliferation of bubble phases with increasing Landau level index was pessimistic. </div><div><br></div><div>In this Dissertation, I present my research on solving this discrepancy. In chapter 4, we performed a magnetotransport measurement of reentrant integer quantum Hall states in the third and higher Landau levels at various different temperatures. Then, we scrutinized how each of the reentrant integer quantum Hall states develops with the gradual increase of the temperature. As a result, we observed multiple reentrant integer quantum Hall states in the fourth Landau level which are associated with the two- and three-electron bubble phases. This result strongly supports the bubble phase picture of the reentrant integer quantum Hall states by confirming the possibility of the proliferation of bubble phases in high Landau levels.</div><div><br></div><div>In chapter 5, I analyzed the energetics of newly resolved two- and three-electron bubble phases in the fourth Landau level as well as those of two-electron bubble phases in the third Landau level. Here, I first found, in the fourth Landau level, the three-electron bubbles are more stable than the two-electron bubbles indicating that the multi-electron bubbles with higher electron number are more stable within a Landau level. Secondly, I found distinct energetic features of two- and three-electron bubble phases which are independent of Landau level index throughout the third and the fourth Landau levels. These results highlight the effect of the number of electrons per bubble on the energetics of multi-electron bubble phases and are expected to contribute on improving the existing Hartree-Fock theories.</div>

Une étude expérimentale de gaz d'électrons bidimensionnel confinés dans des puits quantiques de CdTe et de CdMnTe est présentée. L'analyse de données est soutenue par des calculs numériques de la structure de bande des états confinés, utilisant l'approximation de densité locale et de fonction enveloppe. Un calcul de type k.p a été utilisé pour justifier l'approximation parabolique appliquée pour les bandes valence. Les échantillons ont été caractérisés par spectroscopie Raman et par spectroscopie d'absorption de la résonance cyclotron infrarouge. Le magnéto-transport à bas champ est dominé par la contribution semi-classique de Drude et révèle trois contributions plus faibles, qui sont la localisation faible, l'interaction électron-électron et les oscillations Shubnikov-De Haas. La contribution des interactions électron-électron est expliquée dans un modèle semi-classique à trajectoire circulaire. La forme des niveaux de Landau, leurs élargissement, les temps de vie transport et quantique de la diffusion et le mécanisme (long-portée) de la diffusion dominant ont été déterminés. Le magnéto-transport sous champs magnétiques intenses révèle la présence d'états Hall quantique fractionnaires dans les niveaux de Landau N=0 et N=1. Nous avons montré, que les états 5/3 et 4/3 étaient complètement polarisés en spin, en accord avec l'approche des fermions composites pour l'effet Hall quantique fractionnaire. La forme de la photoluminescence à champ magnétique nul et son évolution avec la température sont décrites par un modèle analytique simple. La dépendance en champ magnétique et en température de la photoluminescence indique que le gap de spin est amplifié dans les niveaux de landau entièrement occupés. Ces effets multi-corps de l'amplification du gap du spin ont été décrits avec succès par un modèle numérique simple. L'intensité de la photoluminescence a mise en évidence l'importance des processus non-radiatifs pendant la recombinaison, la dégénérescence des niveaux de Landau, leur taux d'occupation, les règles de sélection et l'influence de l'écrantage. Le mécanisme de la relaxation parallèle de spin d'électron et de trou a été identifié et attribué au mécanisme Bir-Aharonov-Pikus, assistée par les phonons acoustiques. Les spectres de photoluminescence d'excitation reflètent la densité des états caractéristique des systèmes bidimensionnels. Les résonances excitoniques, qui sont observées aux bords des sous-bandes électriques inoccupées, illustrent l'importance de l'écrantage et des champs électriques intrinsèques dans les puits asymétriquement dopés. / Experimental studies of two-dimensional electron gases confined in CdTe and CdMnTe quantum wells are presented. The data analysis is supported by numerical calculations of the band structure of confined states, using the local density and envelope function approximations. Four by four, k.p calculations have been performed to justify the parabolic approximation of valence bands. Samples were characterized by Raman scattering spectroscopy and far infrared cyclotron resonance absorption measurements. Low-field magneto-transport shows the dominant contribution of the semi-classical Drude conductivity and ten times weaker contributions of weak localization, electron-electron interaction and Shubnikov-de Haas oscillations. The contribution of electron-electron interactions is explained within a semi-classical model of circling electrons. The shape of Landau levels, broadening, transport and quantum lifetimes and dominant long-range scattering mechanism have been determined. High-field magneto-transport displays fractional quantum Hall states at Landau levels N=0 and N=1. The ground states 5/3 and 4/3 have been determined to be fully spin polarized, in agreement with the approach of composite fermions for the fractional quantum Hall effect. The form of the photoluminescence at zero magnetic field and its evolution with temperature have been described by simple analytical model. Magnetic field and temperature dependence of the photoluminescence has been found to display the enhanced spin splitting of fully occupied Landau levels. This many body enhanced spin gap has been successfully described by a numerical model. The intensity of the photoluminescence demonstrated the importance of the non-radiative recombination channel, degeneracy of Landau levels, their occupation, selection rules and screening. The mechanism of the simultaneous electron and hole spin-flip was recognized and attributed to the longitudinal acoustical phonon assisted Bir-Aharonov-Pikus spin relaxation mechanism. Photoluminescence excitation spectra embody the characteristic density of states of two-dimensional systems. The excitonic resonances, which are observed at the edges of unoccupied electric subbands, illustrate the importance of screening and internal electric fields in asymmetrically doped quantum wells.

Modulation doped heterostructures have revolutionized the operation of field effect devices by increasing the speed of operation. One of the factors that affects the speed of operation of these devices is the mobility of the carriers, which is intrinsic to the material used. Mobility of electrons in silicon based devices has improved drastically over the years, reaching as high as 50.000cm2/Vs at 4.2K and 2600cm2/Vs at room temperature. However, the mobility of holes in p-type silicon devices still remains comparatively lesser than the electron mobility because of large effective masses and complicated valence band structure involved. Germanium is known to have the largest hole mobility of all the known semiconductors and is considered most suitable to fabricate high speed p-type devices. Moreover, it is also possible to integrate germanium and its alloy (Si1_zGex ) into the existing silicon technology. With the use of sophisticated growth techniques it has been possible to grow epitaxial layers of silicon and germanium on Si1_zGex alloy layers grown on silicon substrates. In tills thesis we investigate in detail the electrical properties of p-type germanium and n-type silicon thin films grown by these techniques. It is important to do a comparative study of transport in these two systems not only to understand the physics involved but also to study their compatibility in complementary field effect devices (cMODFET). The studies reported in this thesis lay emphasis both on the low and high field transport properties of these systems. We report experimental data for the maximum room temperature mobility of holes achieved m germanium thin films grown on Si1_zGex layers that is comparable to the mobility of electrons in silicon films. We also report experiments performed to study the high field degradation of carrier mobility due to "carrier heating" in these systems. We also report studies on the effect of lattice heating on mobility of carriers as a function of applied electric field. To understand the physics behind the observed phenomenon, we model our data based on the existing theories for low and high field transport. We report complete numerical calculations based on these theories to explain the observed qualitative difference in the transport properties of p-type germanium and ii-type silicon systems. The consistency between the experimental data and theoretical modeling reported in this work is very satisfactory.

No description available.

KurHigh mobility two-dimensional electron gas in CdTe quantum wells: High magnetic field studies Experimental studies of two-dimensional electron gases confined in CdTe and CdMnTe quantum wells are presented. The data analysis is supported by numerical calcula- tions of the band structure of confined states, using the local density and envelope func- tion approximations. Four by four, k.p calculations have been performed to justify the parabolic approximation of valence bands. Samples were characterized by Raman scatter- ing spectroscopy and far infrared cyclotron resonance absorption measurements. Low-field magneto-transport shows the dominant contribution of the semi-classical Drude conduc- tivity and three orders of magnitude weaker contributions of weak localization, electron- electron interaction and Shubnikov-de Haas oscillations. The contribution of electron- electron interactions is explained within a semi-classical model of circling electrons. The shape of Landau levels, broadening, transport and quantum lifetimes and dominant long- range scattering mechanism have been determined. High-field magneto-transport displays fractional quantum Hall states at Landau levels N = 0 and N = 1. The ground states 5/3 and 4/3 have been determined to be fully spin polarized, in agreement with the approach of composite...