Abstract:
The author investigates the nature of quantum Hall states for (sigma)H = 0; (+) or (-) 1, hence the review of the reported experimental works is centered around these states. The quantum Hall experiments for graphene on boron nitride substrate and suspended graphene are most relevant to this work. Chapter 2, provides analytical and numerical solutions to the problem of electrons
in graphene subjected to cross electric and magnetic field. Within the continuum model,
the obtained spectrum for graphene subjected to cross electric and magnetic field. The present study utilizes the relativistic structure of continuum theory and trick of Lorentz boost to obtain exact analytical solutions. These solutions reveal collapse of Landau level spectrum for
a critical electric field. This work also presents numerical calculations for the same problem on lattice to show that the electric field effects on the Landau levels are not artifacts of continuum theory.
In Chapter 3 it is shown that a systematic continuum approximation for the interacting lattice model for graphene and provided motivation for the choice of continuum interacting model
studied in this thesis.
Chapter 4 presents a discussion on the choice of Landau levels for massive Dirac to construct the variational wave functions. Using the heat kernel method developed a suitable expression for two point correlator for massive Dirac particle in magnetic field. The two point correlator are used to evaluate the mean
field energies and particle-hole excitation gaps. Chapter 5 presents the results of mean field calculation for the SU(4) symmetric model, which only takes into account the kinetic and long ranged Coulomb interaction.
It is shown that Coulomb interactions spontaneous break the SU(4) symmetry. Results of particle-hole excitation within symmetric model is presented.
Chapter 6 presents the effects of symmetry breaking terms on the nature of ground
states and excitation for the ground states. The role of various symmetry
breaking terms in obtaining the SU(4) polarization for the ground states is illustrated. The effects of tilted magnetic field effects on the gaps is shown and connected the present results with those
reported in experiments.
Chapter 7 presents summary of findings.
