Related papers: Dynamical Group for the Quantum Hall Effect
Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat and topologically non-trivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
We present activation gap measurements of the fractional quantum Hall effect (FQHE) in the second Landau level. Signatures for 14 (5) distinct incompressible FQHE states are seen in a high (low) mobility sample with the enigmatic 5/2 even…
The two-dimensional interacting electron gas at Landau level filling factor $\nu =1$ and temperature $T=0$ is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on a theoretical study of…
We construct an effective Hamiltonian for electrons in the fractional quantum Hall regime for GaAs and graphene that takes into account Landau level mixing (for both GaAs and graphene) and subband mixing (for GaAs, due to the nonzero width…
An approach to electron correlation effects in atoms that uses quantum trajectories is presented. A comparison with the exact quantum mechanical results for 1D Helium atom shows that the major features of the correlated ground state…
Using a $W_{N}$-gauge theory to describe electromagnetic interactions of spinless fermions in the lowest Landau level, where the $W_{N}$ transformations are nonlinear realizations of U(1) gauge transformations, we construct the effective…
In a recent article, we were motivated by the question of whether any of the remarkable condensed matter phenomena, such as the quantum Hall effect (QHE), the Integer quantum Hall effect (IQHE) etc., could potentially be observed in the…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a…
The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order…
Several recent works have proposed that electron-electron interactions in bilayer graphene can be tuned with the help of external parameters, making it possible to stabilize different fractional quantum Hall states. In these prior works,…
The energy gaps appearing in the fractional quantum Hall effect (FQHE) remain an essential aspect of the investigation. Moreover, the plateau widths in the Hall resistance have been considered simply an effect of disorder as in the integral…
The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of $e^2/h$. Here we show that the…
The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at…
Intra-cell motion endows rich non-trivial phenomena to a wide variety of quantum materials. The most prominent example is a transverse current in the absence of a magnetic field (i.e. the anomalous Hall effect). Here we show that, in…
Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states in higher Landau levels and those in the lowest Landau level,…