Collective excitations in the Ginzburg-Landau theory of the fractional quantum Hall effect

Counterpropagating Fractional Hall States in Mirror-Symmetric Dirac Semimetals

The Landau bands of mirror symmetric 2D Dirac semimetals (e.g., odd layers of ABA graphene) can be identified by their parity with respect to mirror symmetry. This symmetry facilitates a new class of counterpropagating Hall states. We predict the presence of a Laughlin-like correlated liquid state, at the charge neutrality point, with opposite but equal electron and hole filling factors |ν_{±}|=1/m (m odd). This state exhibits fractionally charged quasiparticle-hole pair excitations and counterpropagating edge states with opposite parity. Using a bosonized one-dimensional edge state theory, we show that the fractionally quantized two-terminal longitudinal conductance, σ_{xx}=2e^{2}/(mh), is robust to short-ranged intermode interactions.

Nonlinear hydrodynamics and fractionally quantized solitons at the fractional quantum Hall edge

We argue that the dynamics of fractional quantum Hall (FQH) edge states is essentially nonlinear and that it features fractionally quantized solitons with charges -νe propagating along the edge. The observation of solitons would be direct evidence of fractional charges. We show that the nonlinear dynamics of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation. Nonlinear dynamics of gapless edge states is determined by gapped modes in the bulk of FQH liquid and is traced to the double boundary layer "overshoot" of FQH states. The dipole moment of the layer η=1-ν/4π is obtained in paper. Quantum hydrodynamics of FQH liquid is outlined.

Hamiltonian theory of disorder at nu = 1/3

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter 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.

Quantum Hall to insulator transition in the bilayer quantum Hall ferromagnet

We describe a phase transition of the bilayer quantum Hall ferromagnet at nu=1. In the presence of static disorder (modeled by a periodic potential), bosonic S=1/2 spinons undergo a superfluid-insulator transition while preserving ferromagnetism. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Consequences for charge and counterflow conductivity and for interlayer tunneling conductance are discussed.

Splitting of long-wavelength modes of the fractional quantum hall liquid at nu = 1/3

Resonant inelastic light scattering experiments at nu = 1/3 reveal a novel splitting of the long-wavelength modes in the low energy spectrum of quasi-particle excitations in the charge degree of freedom. We find a single peak at small wave vectors that splits into two distinct modes at larger wave vectors. The evidence of well-defined dispersive behavior at small wave vectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long-wavelength modes of the electron liquid.

Model for the voltage steps in the breakdown of the integer quantum Hall effect

In samples used to maintain the U.S. resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magnetoexcitons when the quantum Hall fluid flows past an ionized impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.