Hamiltonian Theory of Disorder at 1/3

The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures

Field Theory of the Fractional Quantum Hall Effect-I

We provide details of a shorter letter and cond-mat/9702098 and some new results. We describe a Chern-Simons theory for the fractional quantum Hall states in which magnetoplasmon degrees of freedom enter. We derive correlated wavefunctions, operators for creating quasiholes and composite fermions and bosons (which are electrons bound to zeros). We show how the charge of these particles and mass gets renormalized to the final values and compute the effective mass approximately. By deriving a hamiltonian description of the composite fermions and bosons and their charge and current operators, we make precise and reconcile many notions that have been associated with them.Comment: 42 pages Latex To appear in Composite Fermions, edited by Olle Heinonen. Replacement has single spacin

The ν=12\nu={1\over2} Landau level: Half-full or half-empty?

We show here that an extension of the Hamiltonian theory developed by us over the years furnishes a composite fermion (CF) description of the $\nu =\frac{1}{2}$ state that is particle-hole (PH) symmetric, has a charge density that obeys the magnetic translation algebra of the lowest Landau level (LLL), and exhibits cherished ideas from highly successful wave functions, such as a neutral quasi-particle with a certain dipole moment related to its momentum. We also a provide an extension away from $\nu=\frac{1}{2}$ which has the features from $\nu=\frac{1}{2}$ and implements the the PH transformation on the LLL as an anti-unitary operator ${\cal T}$ with ${\cal T}^2=-1$. This extension of our past work was inspired by Son, who showed that the CF may be viewed as a Dirac fermion on which the particle-hole transformation of LLL electrons is realized as time-reversal, and Wang and Senthil who provided a very attractive interpretation of the CF as the bound state of a semion and anti-semion of charge $\pm {e\over 2}$. Along the way we also found a representation with all the features listed above except that now ${\cal T}^2=+1$. We suspect it corresponds to an emergent charge-conjugation symmetry of the $\nu =1$ boson problem analyzed by Read.Comment: 10 pages, no figures. Two references and a section on HF adde

Hamiltonian Theory of the Fractional Quantum Hall Effect: Effect of Landau Level Mixing

We derive an effective hamiltonian in the Lowest Landau Level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy. We then transcribe the hamiltonian to the composite fermion basis using our hamiltonian approach and compute the effect of LL mixing on transport gaps

Collective Edge Modes near the onset of a graphene quantum spin Hall state

Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. Possible experimental consequences are discussed.Comment: 5 pages, 2 figure