George Simion

The hierarchy of incompressible fractional quantum Hall states

Abstract The correlations that give rise to incompressible quantum liquid (IQL) states in fractional quantum Hall systems are determined by the pseudopotential V ( R ) describing the interaction of a pair of Fermions in a degenerate Landau level (LL) as a function of relative pair angular momentum R . V ( R ) is known for a number of different Fermion systems, e.g.xa0electrons in the lowest Landau level (LL0) or the first excited Landau level (LL1), and for quasiparticles of Laughlin–Jain IQL states. Laughlin correlations, the avoidance of pair states with the smallest values of R , occur only when V ( R ) satisfies certain conditions. We show that Jain’s composite Fermion (CF) picture is valid only if the conditions necessary for Laughlin correlations are satisfied, and we present a rigorous justification of the CF picture without the need of introducing an “irrelevant” mean-field energy scale. Electrons in LL1 and quasielectrons in IQL states (e.g.xa0QEs in CF LL1) do not necessarily support Laughlin correlations. Numerical diagonalization studies for small systems of Fermions (electrons in LL0 or in LL1, and QEs in CF LL1), with the use of appropriate pseudopotentials V ( R ) , show clear evidence for different types of correlations. The relation between LL degeneracy g = 2 l + 1 and number of Fermions N at which IQL states are found is known for a limited range of N values. However, no simple intuitive models that we have tried satisfactorily describe all of the systems we have studied. Successes and shortcomings of some simple models are discussed, and suggestions for further investigation are made.

Spin phase diagram of the ve=4/ 11 composite fermion liquid

Spin polarization of the second generation nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.

Electrostatic control of quantum Hall ferromagnetic transition: A step toward reconfigurable network of helical channels

Ferromagnetic transitions between quantum Hall states with different polarization at a fixed filling factor can be studied by varying the ratio of cyclotron and Zeeman energies in tilted magnetic field experiments. However, an ability to locally control such transitions at a fixed magnetic field would open a range of attractive applications, e.g. formation of a reconfigurable network of one-dimensional helical domain walls in a two-dimensional plane. Coupled to a superconductor, such domain walls can support non-Abelian excitation. In this article we report development of heterostructures where quantum Hall ferromagnetic (QHFm) transition can be controlled locally by electrostatic gating. A high mobility two-dimensional electron gas is formed in CdTe quantum wells with engineered placement of paramagnetic Mn impurities. Gate-induced electrostatic field shifts electron wavefunction in the growth direction and changes overlap between electrons in the quantum well and d-shell electrons on Mn, thus controlling the s-d exchange interaction and the field of the QHFm transition. The demonstrated shift of the QHFm transition at a filling factor

Mesoscopic Transport in Electrostatically Defined Spin-Full Channels in Quantum Hall Ferromagnets

nu=2

Friedel oscillations in a two dimensional Fermi liquid

is large enough to allow full control of spin polarization at a fixed magnetic field.

Non-Abelian ν=12 quantum Hall state in Γ8 valence band hole liquid

In this work, we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to the hybridization of two counterpropagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with a localization length of 4-6u2009u2009μm. In shorter DWs, the resistance saturates to a nonzero value at low temperatures. Mesoscopic resistance fluctuations in a magnetic field are investigated. The theoretical model of transport through impurity states within the gap induced by spin-orbit interactions agrees well with the experimental data. Helical DWs have the required symmetry for the formation of synthetic p-wave superconductors. The achieved electrostatic control of a single helical domain wall is a milestone on the path to their reconfigurable network and ultimately to a demonstration of the braiding of non-Abelian excitations.

Fractional Quantum Hall Effect and Electron Correlations in Partially Filled First Excited Landau Level

Within linear response the long range oscillations caused by short or long ranged impurities embedded in an otherwise homogeneous electron gas reflect the singularities of the static response function. By making use of the theory of the many-body local fields and the results of recent quantum Monte Carlo studies we have calculated the exact dependence of the amplitude of these oscillations on the density in a two dimensional electron Fermi liquid.

Chirality, charge and spin-density wave instabilities of a two-dimensional electron gas in the presence of Rashba spin-orbit coupling

In search of states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional charge carrier holes. We propose a new method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. This method provides single-particle hole states used in exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions. An incompressible fractional quantum Hall state emerges in a hole liquid at the half-filling of the ground state in a magnetic field in the range of fields where single-hole states cross. This state has a negligible overlap with the Halperin 331 state, but a significant overlap with the Moore-Read Pfaffian state. Excited fractional quantum Hall states for small systems have sizable overlap with non-Abelian excitations of the Moore-Read Pfaffian state.

Gate control of spin polarization in a quantum Hall regime toward reconfigurable network of helical channels(Conference Presentation)

Abstract We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the electron–electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states ν = 5 2 , 7 3 and 8 3 are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors 14 5 , 16 7 , 11 5 , 19 7 are Laughlin correlated electron or hole states and fit Jains sequence of filled CF 4 levels.

Excitations of the v=5/2 fractional quantum Hall state and the generalized composite fermion picture

We show that a result equivalent to Overhauser’s famous Hartree-Fock instability theorem can be established for the case of a two-dimensional electron gas in the presence of Rashba spin-obit coupling. In this case it is the spatially homogeneous paramagnetic chiral ground state that is shown to be differentially unstable with respect to a certain class of distortions of the spin-density-wave and charge-density-wave type. The result holds for all densities. Basic properties of these inhomogeneous states are analyzed.