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Register a new userGround state and edge excitations of quantum Hall liquid at filling factor 2/3
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We present a numerical study of fractional quantum Hall liquid at Landau level filling factor $ u=2/3$ in a microscopic model including long-range Coulomb interaction and edge confining potential, based on the disc geometry. We find the ground state is accurately described by the particle-hole conjugate of a $ u=1/3$ Laughlin state. We also find there are two counter-propagating edge modes, and the velocity of the forward-propagating mode is larger than the backward-propagating mode. The velocities have opposite responses to the change of the background confinement potential. On the other hand changing the two-body Coulomb potential has qualitatively the same effect on the velocities; for example we find increasing layer thickness (which softens of the Coulomb interaction) reduces both the forward mode and the backward mode velocities.
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The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling $ u = 2$. Both mean-field theory and Luttinger liquid theory techniques are employed for the case of a null Zeeman energy splitting. The first calculation yields a stable spin-density wave state along the bar, while the second one predicts dominant Wigner-crystal correlations along the edges of the bar. We propose an antiferromagnetic Wigner-crystal groundstate for the edge electrons that reconciles the two results. A net Zeeman splitting is found to produce canting of the antiferromagnetic order.
We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $lambda$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlayer entanglement more effective and robust under perturbations than in the spin-frozen situation, mainly for a large number of flux quanta $lambda$. Interlayer entanglement of an equilibrium thermal state and its dependence with temperature and bias voltage is also studied for a pseudo-Zeeman interaction.
We studied neutral excitations in a two-dimensional electron system with an orbital momentum $Delta M = 1$ and spin projection over magnetic field axis $Delta S_z = 1$ in the vicinity of a filling factor of 3/2. It is shown that the 3/2 state is a singular point in the filling factor dependence of the spin ordering of the two-dimensional electron system. In the vicinity of $ u=3/2$, a significant increase in the relaxation time ($tau = 13$ $mutext{s}$) for the excitations to the ground state is exhibited even though the number of vacancies in the lowest energy level is macroscopically large. The decrease of the relaxation rate is related to the spin texture transformation in the ground state induced by spin flips and electron density rearrangement. We claim the 3/2 state is a locally incompressible fractional quantum Hall state.
We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $ u=2/lambda$ ($lambda$ odd) and we also study the large $SU(4)$ isospin-$lambda$ limit. The model Hamiltonian is an adaptation of the $ u=2$ case [Z.F. Ezawa {it et al.}, Phys. Rev. {B71} (2005) 125318] to the many-body situation (arbitrary $lambda$ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeeman, tunneling, etc, control parameters) is obtained by using previously introduced Grassmannian $mathbb{G}^4_{2}=U(4)/[U(2)times U(2)]$ coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any $lambda$, but the phase transition points depend on $lambda$, and the instance $lambda=1$ is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly $lambda$ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally FQHE has been observed in high mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
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