335 research outputs found
New universal gates for topological quantum computation with Fibonacci- composite Majorana edge modes on topological superconductor multilayers
We propose a new design of universal topological quantum computer device
through a hybrid of the 1-, 2- and 7-layers of chiral topological
superconductor (TSC) thin films. Based on the coset
construction, strongly correlated Majorana fermion edge modes on the 7-layers
of TSC are factorized into the composite of the Fibonacci -anyon
and -anyon modes in the tricritical Ising model. Furthermore, the
deconfinement of and via the interacting potential gives
the braiding of either or . Topological phase gates are
assembled by the braidings. With these topological phase gates, we find a set
of fully topological universal gates for the composite
Majorana-Ising-type quantum computation. Because the Hilbert space still
possesses a tensor product structure of quibts and is characterized by the
fermion parities, encoding quantum information in this machine is more
efficient and substantial than that with Fibonacci anyons. The computation
results is easier to be read out by electric signals, so are the initial data
inputted.Comment: 6 pages, 3 figues, revised versio
Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect
We study the quantum anomalous Hall effect described by a class of
two-component Haldane models on square lattices. We show that the latter can be
transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long
wave length limit, the ground state wave function is described by Halperin's
(1,1,-1) state of neutral fermions analogous to the double layer quantum Hall
effect. The vortex excitations are charge e/2 abelian anyons which carry a
neutral Dirac fermion zero mode. The superconducting proximity effect induces
`tunneling' between `layers' which leads to topological phase transitions
whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge
in the edge states. The charge e/2 vortex excitation carrying a Majorana zero
mode is a non-abelian anyon. The proximity effect can also drive a conventional
insulator into a quantum anomalous Hall effect state with a Majorana edge mode
and the non-abelian vortex excitations.Comment: 6 pages, 4 figures, accepted by Phys. Rev.
Correlation-hole induced paired quantum Hall states in lowest Landau level
A theory is developed for the paired even-denominator fractional quantum Hall
states in the lowest Landau level. We show that electrons bind to quantized
vortices to form composite fermions, interacting through an exact instantaneous
interaction that favors chiral p-wave pairing. Two canonically dual pairing gap
functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due
to the correlation holes. We find that the ground state is the Moore-Read
pfaffian in the long wavelength limit for weak Coulomb interactions, a new
pfaffian of an oscillatory pairing function for intermediate interactions, and
a Read-Rezayi composite Fermi liquid beyond a critical interaction strength.
Our findings are consistent with recent experimental observations of the 1/2
and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.Comment: 4 pages, 2 figures; published versio
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