Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems

While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual interaction between composite fermions. We study the spin phase diagram of these states, motivated by the recent experimental observation by Liu {\em et al.} \cite{Liu14a,Liu14b} of several spin-polarization transitions at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the FQHE of composite fermions is much more prevalent in multicomponent systems, and consider the feasibility of such states for systems with ${\cal N}$ components for an SU(${\cal N}$) symmetric interaction. Our results apply to GaAs quantum wells, wherein electrons have two components, to AlAs quantum wells and graphene, wherein electrons have four components (two spins and two valleys), and to an H-terminated Si(111) surface, which can have six components. The aim of this article is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU(${\cal N}$) spin content, their energies, and their phase diagram as a function of the generalized "Zeeman" energy. We obtain results at three levels of approximation: from ground state wave functions of the composite fermion theory, from composite fermion diagonalization, and, whenever possible, from exact diagonalization. Effects of finite quantum well thickness and Landau level mixing are neglected in this study. We compare our theoretical results with the experiments of Liu {\em et al.} \cite{Liu14a,Liu14b} as well as of Yeh {\em et al.} \cite{Yeh99} for a two component system.Comment: 29 pages, 6 figure

Characterization of Zinc oxide & Aluminum Ferrite and Simulation studies of M-H plots of Cobalt/Cobaltoxide

Zinc oxide and Aluminum Ferrite were prepared Chemical route. The samples were characterized by XRD and VSM. Simulation of M-H plots of Co/CoO thin films were performed. Effect of parameters was observed on saturation magnetization.Comment: Working paper (11 pages, 8 figures

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde

Even denominator fractional quantum Hall states in higher Landau levels of graphene

An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from a chiral $p$-wave paired state of composite fermions which are topological bound states of electrons and quantized vortices. This state is theoretically described by a "Pfaffian" wave function or its hole partner called the anti-Pfaffian, whose excitations are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics. This has inspired ideas on fault-tolerant topological quantum computation and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even-denominator fractional quantum Hall physics in the $n=3$ Landau level. We numerically investigate the known candidate states for the even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistic

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E, 76 051115 (2007)] are in very good agreement with the proposed scaling relation.Comment: 4 pages, 3 figure

Coherent coupling between radio frequency, optical, and acoustic waves in piezo-optomechanical circuits

The interaction of optical and mechanical modes in nanoscale optomechanical systems has been widely studied for applications ranging from sensing to quantum information science. Here, we develop a platform for cavity optomechanical circuits in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency field through the piezo-electric effect, or optically through the strong photoelastic effect. We use this to demonstrate a novel acoustic wave interference effect, analogous to coherent population trapping in atomic systems, in which the coherent mechanical motion induced by the electrical drive can be completely cancelled out by the optically-driven motion. The ability to manipulate cavity optomechanical systems with equal facility through either photonic or phononic channels enables new device and system architectures for signal transduction between the optical, electrical, and mechanical domains

Fractional Quantum Hall Effect at ν=2+4/9\nu=2+4/9

Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $\nu=2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown quantum liquid, we propose that this state likely belongs in a parton sequence, put forth recently to understand the emergence of FQHE at $\nu=2+6/13$. While the $\nu=2+4/9$ state proposed here directly follows three simpler parton states, all known to occur in the second LL, it is topologically distinct from the Jain composite fermion (CF) state which occurs at the same $\nu=4/9$ filling of the lowest LL. We predict experimentally measurable properties of the $4/9$ parton state that can reveal its underlying topological structure and definitively distinguish it from the $4/9$ Jain CF state.Comment: 15 pages, 13 figures (includes supplemental material), published versio

Role of inter-edge tunneling in localizing Majorana zero modes at the ends of quasi one-dimensional p+ip systems

Potter and Lee have demonstrated the presence of Majorana zero modes at the ends of quasi one-dimensional (1-D) p+ip superconductors. We use conformal field theory (CFT) methods to show that inter-edge tunneling of the vortex excitations along the length of the channel is crucial for such localization. We show that localization of Majorana modes occurs also in quasi 1-D channels of the 5/2 fractional quantum Hall (FQH) systems when modeled, following Moore and Read, as the p+ip paired state of composite fermions. We propose a tunnel-interferometry experiment to detect these modes, which should show a \pi -phase shift of oscillations depending on whether a localized Majorana zero mode is present or not, which, in turn, can be controlled by varying the tunneling strength.Comment: 6 pages, 3 figures, published versio