Related papers: W-infinity Symmetry in the Quantum Hall Effect Bey…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
We study the transition between sharp and smooth density distributions at the edges of Quantum Hall Liquids in the presence of interactions. We find that, for strong confining potentials, the edge of a $\nu=1$ liquid is described by the…
We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard…
We study the quantum dynamics in response to time-dependent external potentials of the edge modes of a small fractional quantum Hall fluid composed of few particles on a lattice in a bosonic Laughlin-like state at filling {\nu} = 1/2. We…
Edge states in the integral quantum Hall effect on a lattice are reviewed from a topological point of view. For a system with edges which is realized inevitably in an experimental situation, the Hall conductance $\sigma_{xy}$ is given by a…
We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum…
The tunneling between the Laughlin state and its quasihole excitations are studied by using the Jack polynomial. We find a universal analytical formula for the tunneling amplitude, which can describe both bulk and edge quasihole…
The edge structure of a gate-defined compressible quantum Hall fluids in the filling fraction range 2/3 to 1 is studied using the three reconstructed $e^2/3h$ fractional edge modes of unity filling integer quantum Hall state. We find that…
We algebraically analysis the quantum Hall effect of a system of particles living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field $B$. For this, we identify the non-compact disc with the coset space $SU(1,1)/U(1)$. This…
There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires analytic continuation beyond the…
Quantum Hall universality classes can be classified by $W_{1+\infty}$ symmetry. We show that this symmetry also governs the dynamics of quantum edge excitations. The Hamiltonian of interacting electrons in the fully-filled first Landau…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
We consider quantum Hall droplets on complex projective spaces with a combination of abelian and nonabelian background magnetic fields. Carrying out an analysis similar to what was done for abelian backgrounds, we show that the effective…
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct…
We extend our ensemble density functional approach to quantum Hall systems to include non-collinear spins to study charge-spin textures in inhomogeneous quantum Hall systems. We have studied the edge reconstruction in quantum dots at unit…
Two dimensional inversion symmetry ($180^{\circ}$ rotations in the ``Hall plane'' that hosts the incompressible electron fluid that exhibits the quantized Hall effect) is identified as its fundamental unbroken symmetry. A consequence is…
We study theoretically the two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of inter-edge correlated liquid (IECL) without the spin gap is found. This liquid shows the diverging density…
The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall effect is studied in the presence of a confining potential. We review the bulk properties of the model and discuss how the plateau formation emerges without any…
In quantum anomalous Hall (QAH) systems, the Hall conductance is quantized and the corresponding effective topological theory of the system is the Chern-Simons theory. The conductance quantum is given by the universal constant $e^2/h$ --…