Disorder and interactions in graphene and other quantum systems

This thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the body centred cubic and face centred cubic lattices. We obtain high precision results for the critical disorder at the band centre and the critical exponent using the transfer-matrix method and finite size scaling. Comparing the critical disorder between the simple cubic, body centred cubic and face centred cubic lattices, an increase in the critical disorder is observed as a function of the coordination number of the lattice. The critical exponent is found to be v ≃ 1:5 in agreement with the value for the simple cubic lattice. Energy-disorder phase diagrams are plotted for both lattice types. Next, we consider the Aharonov-Bohm effect for an exciton in a 1D ring geometry. The aim is to determine how the addition of a constant electric field in the plane of the ring effects the Aharonov-Bohm oscillations, which occur as a function of the magnetic ux threading the ring. We develop a self consistent equation for the ground state energy, which is then solved numerically. Oscillations in the ground state energy have an increasing amplitude as a function of electric field strength until a critical electric field value. At this point, oscillations in the oscillator strength become inverted, with the oscillation minimum reaching zero at half a magnetic ux quantum. This suggests a possible process for controlling the formation and recombination of excitons through tuning the applied fields. The final and largest section of the thesis is concerned with collective excitations of graphene in a strong perpendicular magnetic field. The excitations, which are most strongly mixed are identified and used as a basis to diagonalise the Hamiltonian, which includes the Coulomb interaction between electrons and holes. In this way the oscillator strengths and energies of collective excitations are obtained. The good quantum numbers for collective excitations are identified. In particular, we study those arising from the SU(4) symmetry, which is due to two spin and two valley pseudospin projections. This enables us to determine the multiplet structure of the states. In addition to neutral collective excitations or excitons, we investigate the possible formation of charged collective excitations or trions from nearly full or nearly empty Landau levels. The localisation of neutral collective excitations upon a single Coulomb or δ-function impurity is also examined

Disorder and interactions in graphene and other quantum systems

This thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the body centred cubic and face centred cubic lattices. We obtain high precision results for the critical disorder at the band centre and the critical exponent using the transfer-matrix method and finite size scaling. Comparing the critical disorder between the simple cubic, body centred cubic and face centred cubic lattices, an increase in the critical disorder is observed as a function of the coordination number of the lattice. The critical exponent is found to be v ≃ 1:5 in agreement with the value for the simple cubic lattice. Energy-disorder phase diagrams are plotted for both lattice types. Next, we consider the Aharonov-Bohm effect for an exciton in a 1D ring geometry. The aim is to determine how the addition of a constant electric field in the plane of the ring effects the Aharonov-Bohm oscillations, which occur as a function of the magnetic ux threading the ring. We develop a self consistent equation for the ground state energy, which is then solved numerically. Oscillations in the ground state energy have an increasing amplitude as a function of electric field strength until a critical electric field value. At this point, oscillations in the oscillator strength become inverted, with the oscillation minimum reaching zero at half a magnetic ux quantum. This suggests a possible process for controlling the formation and recombination of excitons through tuning the applied fields. The final and largest section of the thesis is concerned with collective excitations of graphene in a strong perpendicular magnetic field. The excitations, which are most strongly mixed are identified and used as a basis to diagonalise the Hamiltonian, which includes the Coulomb interaction between electrons and holes. In this way the oscillator strengths and energies of collective excitations are obtained. The good quantum numbers for collective excitations are identified. In particular, we study those arising from the SU(4) symmetry, which is due to two spin and two valley pseudospin projections. This enables us to determine the multiplet structure of the states. In addition to neutral collective excitations or excitons, we investigate the possible formation of charged collective excitations or trions from nearly full or nearly empty Landau levels. The localisation of neutral collective excitations upon a single Coulomb or δ-function impurity is also examined.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)University of WarwickInstitute of Physics (Great Britain)C. R. Barber TrustGBUnited Kingdo

Disorder and interactions in graphene and other quantum systems

This thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the body centred cubic and face centred cubic lattices. We obtain high precision results for the critical disorder at the band centre and the critical exponent using the transfer-matrix method and finite size scaling. Comparing the critical disorder between the simple cubic, body centred cubic and face centred cubic lattices, an increase in the critical disorder is observed as a function of the coordination number of the lattice. The critical exponent is found to be v ≃ 1:5 in agreement with the value for the simple cubic lattice. Energy-disorder phase diagrams are plotted for both lattice types. Next, we consider the Aharonov-Bohm effect for an exciton in a 1D ring geometry. The aim is to determine how the addition of a constant electric field in the plane of the ring effects the Aharonov-Bohm oscillations, which occur as a function of the magnetic ux threading the ring. We develop a self consistent equation for the ground state energy, which is then solved numerically. Oscillations in the ground state energy have an increasing amplitude as a function of electric field strength until a critical electric field value. At this point, oscillations in the oscillator strength become inverted, with the oscillation minimum reaching zero at half a magnetic ux quantum. This suggests a possible process for controlling the formation and recombination of excitons through tuning the applied fields. The final and largest section of the thesis is concerned with collective excitations of graphene in a strong perpendicular magnetic field. The excitations, which are most strongly mixed are identified and used as a basis to diagonalise the Hamiltonian, which includes the Coulomb interaction between electrons and holes. In this way the oscillator strengths and energies of collective excitations are obtained. The good quantum numbers for collective excitations are identified. In particular, we study those arising from the SU(4) symmetry, which is due to two spin and two valley pseudospin projections. This enables us to determine the multiplet structure of the states. In addition to neutral collective excitations or excitons, we investigate the possible formation of charged collective excitations or trions from nearly full or nearly empty Landau levels. The localisation of neutral collective excitations upon a single Coulomb or δ-function impurity is also examined.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)University of WarwickInstitute of Physics (Great Britain)C. R. Barber TrustGBUnited Kingdo

Localized collective excitations in doped graphene in strong magnetic fields

We consider collective excitations in graphene with filled Landau levels (LL’s) in the presence of an external potential due to a single charged donor D+ or acceptor A− impurity. We show that localized collective modes split off the magnetoplasmon continuum and, in addition, quasibound states are formed within the continuum. A study of the evolution of the strengths and energies of magneto-optical transitions is performed for integer filling factors ν=1,2,3,4 of the lowest LL. We predict impurity absorption peaks above as well as below the cyclotron resonance. We find that the single-particle electron-hole symmetry of graphene leads to a duality between the spectra of collective modes for the D+ and A−. The duality shows up as a set of the D+ and A− magnetoabsorption peaks having the same energies but active in different circular polarizations

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find $\theta = -0.275(5)$ and $\theta \approx 0.2$ respectively in two and three dimensions. These results show that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions our data strongly support the absence of spontaneous magnetization in the infinite-volume limit

Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.Comment: 24 pages, 12 figure

Feedback in the Antennae Galaxies (NGC 4038/9): I. High-Resolution Infrared Spectroscopy of Winds from Super Star Clusters

We present high-resolution (R ~ 24,600) near-IR spectroscopy of the youngest super star clusters (SSCs) in the prototypical starburst merger, the Antennae Galaxies. These SSCs are young (3-7 Myr old) and massive (10^5 - 10^7 M_sun for a Kroupa IMF) and their spectra are characterized by broad, extended Br-gamma emission, so we refer to them as emission-line clusters (ELCs) to distinguish them from older SSCs. The Brgamma lines of most ELCs have supersonic widths (60-110 km/s FWHM) and non-Gaussian wings whose velocities exceed the clusters' escape velocities. This high-velocity unbound gas is flowing out in winds that are powered by the clusters' massive O and W-R stars over the course of at least several crossing times. The large sizes of some ELCs relative to those of older SSCs may be due to expansion caused by these outflows; many of the ELCs may not survive as bound stellar systems, but rather dissipate rapidly into the field population. The observed tendency of older ELCs to be more compact than young ones is consistent with the preferential survival of the most concentrated clusters at a given age.Comment: Accepted to Ap

Tropospheric ozone production and chemical regime analysis during the COVID-19 lockdown over Europe

The COVID-19 (coronavirus disease 2019) European lockdowns have led to a significant reduction in the emissions of primary pollutants such as NO (nitric oxide) and NO$_2$ (nitrogen dioxide). As most photochemical processes are related to nitrogen oxide (NO$_x$≡ NO + NO$_2$) chemistry, this event has presented an exceptional opportunity to investigate its effects on air quality and secondary pollutants, such as tropospheric ozone (O$_3$). In this study, we present the effects of the COVID-19 lockdown on atmospheric trace gas concentrations, net ozone production rates (NOPRs) and the dominant chemical regime throughout the troposphere based on three different research aircraft campaigns across Europe. These are the UTOPIHAN (Upper Tropospheric Ozone: Processes Involving HO$_x$ and NO$_x$) campaigns in 2003 and 2004, the HOOVER (HO$_x$ over Europe) campaigns in 2006 and 2007, and the BLUESKY campaign in 2020, the latter performed during the COVID-19 lockdown. We present in situ observations and simulation results from the ECHAM5 (fifth-generation European Centre Hamburg general circulation model, version 5.3.02)/MESSy2 (second-generation Modular Earth Submodel System, version 2.54.0) Atmospheric Chemistry (EMAC), model which allows for scenario calculations with business-as-usual emissions during the BLUESKY campaign, referred to as the “no-lockdown scenario”. We show that the COVID-19 lockdown reduced NO and NO$_2$ mixing ratios in the upper troposphere by around 55 % compared to the no-lockdown scenario due to reduced air traffic. O$_3$ production and loss terms reflected this reduction with a deceleration in O$_3$ cycling due to reduced mixing ratios of NO$_x$, while NOPRs were largely unaffected. We also study the role of methyl peroxyradicals forming HCHO ($^α$CH$_3$O$_2$) to show that the COVID-19 lockdown shifted the chemistry in the upper-troposphere–tropopause region to a NO$_x$-limited regime during BLUESKY. In comparison, we find a volatile organic compound (VOC)-limited regime to be dominant during UTOPIHAN