100 research outputs found
The geometry of entanglement: metrics, connections and the geometric phase
Using the natural connection equivalent to the SU(2) Yang-Mills instanton on
the quaternionic Hopf fibration of over the quaternionic projective space
with an fiber the geometry of
entanglement for two qubits is investigated. The relationship between base and
fiber i.e. the twisting of the bundle corresponds to the entanglement of the
qubits. The measure of entanglement can be related to the length of the
shortest geodesic with respect to the Mannoury-Fubini-Study metric on between an arbitrary entangled state, and the separable state nearest to
it. Using this result an interpretation of the standard Schmidt decomposition
in geometric terms is given. Schmidt states are the nearest and furthest
separable ones lying on, or the ones obtained by parallel transport along the
geodesic passing through the entangled state. Some examples showing the
correspondence between the anolonomy of the connection and entanglement via the
geometric phase is shown. Connections with important notions like the
Bures-metric, Uhlmann's connection, the hyperbolic structure for density
matrices and anholonomic quantum computation are also pointed out.Comment: 42 page
Topological Lifshitz Transitions and Fermi Arc Manipulation in Weyl Semimetal NbAs
Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered
recently in topological Weyl semimetals (TWSs), are unlike closed FSs in
conventional materials and can give rise to many exotic phenomena, such as
anomalous SFA-mediated quantum oscillations, chiral magnetic effects,
three-dimensional quantum Hall effect, non-local voltage generation and
anomalous electromagnetic wave transmission. Here, by using in-situ surface
decoration, we demonstrate successful manipulation of the shape, size and even
the connections of SFAs in a model TWS, NbAs, and observe their evolution that
leads to an unusual topological Lifshitz transition not caused by the change of
the carrier concentration. The phase transition teleports the SFAs between
different parts of the surface Brillouin zone. Despite the dramatic surface
evolution, the existence of SFAs is robust and each SFA remains tied to a pair
of Weyl points of opposite chirality, as dictated by the bulk topology.Comment: 15 pages, 5 figure
Insulating behavior in ultra-thin bismuth selenide field effect transistors
Ultrathin (~3 quintuple layer) field-effect transistors (FETs) of topological
insulator Bi2Se3 are prepared by mechanical exfoliation on 300nm SiO2/Si
susbtrates. Temperature- and gate-voltage dependent conductance measurements
show that ultrathin Bi2Se3 FETs are n-type, and have a clear OFF state at
negative gate voltage, with activated temperature-dependent conductance and
energy barriers up to 250 meV
One-dimensional Topological Edge States of Bismuth Bilayers
The hallmark of a time-reversal symmetry protected topologically insulating
state of matter in two-dimensions (2D) is the existence of chiral edge modes
propagating along the perimeter of the system. To date, evidence for such
electronic modes has come from experiments on semiconducting heterostructures
in the topological phase which showed approximately quantized values of the
overall conductance as well as edge-dominated current flow. However, there have
not been any spectroscopic measurements to demonstrate the one-dimensional (1D)
nature of the edge modes. Among the first systems predicted to be a 2D
topological insulator are bilayers of bismuth (Bi) and there have been recent
experimental indications of possible topological boundary states at their
edges. However, the experiments on such bilayers suffered from irregular
structure of their edges or the coupling of the edge states to substrate's bulk
states. Here we report scanning tunneling microscopy (STM) experiments which
show that a subset of the predicted Bi-bilayers' edge states are decoupled from
states of Bi substrate and provide direct spectroscopic evidence of their 1D
nature. Moreover, by visualizing the quantum interference of edge mode
quasi-particles in confined geometries, we demonstrate their remarkable
coherent propagation along the edge with scattering properties that are
consistent with strong suppression of backscattering as predicted for the
propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia
Evidence of silicene in honeycomb structures of silicon on Ag(111)
In the search for evidence of silicene, a two-dimensional honeycomb lattice
of silicon, it is important to obtain a complete picture for the evolution of
Si structures on Ag(111), which is believed to be the most suitable substrate
for growth of silicene so far. In this work we report the finding and evolution
of several monolayer superstructures of silicon on Ag(111) depending on the
coverage and temperature. Combined with first-principles calculations, the
detailed structures of these phases have been illuminated. These structure were
found to share common building blocks of silicon rings, and they evolve from a
fragment of silicene to a complete monolayer silicene and multilayer silicene.
Our results elucidate how silicene formes on Ag(111) surface and provide
methods to synthesize high-quality and large-scale silicene.Comment: 6 pages, 4 figure
The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
The spectrum and degeneracies of the Dirac operator are analysed on compact
coset spaces when there is a non-zero homogeneous background gauge field which
is compatible with the symmetries of the space, in particular when the gauge
field is derived from the spin-connection. It is shown how the degeneracy of
the lowest Landau level in the recently proposed higher dimensional quantum
Hall effect is related to the Atiyah-Singer index theorem for the Dirac
operator on a compact coset space.Comment: 25 pages, typeset in LaTeX, uses youngtab.st
Josephson supercurrent through a topological insulator surface state
Topological insulators are characterized by an insulating bulk with a finite
band gap and conducting edge or surface states, where charge carriers are
protected against backscattering. These states give rise to the quantum spin
Hall effect without an external magnetic field, where electrons with opposite
spins have opposite momentum at a given edge. The surface energy spectrum of a
threedimensional topological insulator is made up by an odd number of Dirac
cones with the spin locked to the momentum. The long-sought yet elusive
Majorana fermion is predicted to arise from a combination of a superconductor
and a topological insulator. An essential step in the hunt for this emergent
particle is the unequivocal observation of supercurrent in a topological phase.
Here, we present the first measurement of a Josephson supercurrent through a
topological insulator. Direct evidence for Josephson supercurrents in
superconductor (Nb) - topological insulator (Bi2Te3) - superconductor e-beam
fabricated junctions is provided by the observation of clear Shapiro steps
under microwave irradiation, and a Fraunhofer-type dependence of the critical
current on magnetic field. The dependence of the critical current on
temperature and length shows that the junctions are in the ballistic limit.
Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a
topologically non-trivial two-dimensional surface state. We argue that the
ballistic Josephson current is hosted by this surface state despite the fact
that the normal state transport is dominated by diffusive bulk conductivity.
The lateral Nb-Bi2Te3-Nb junctions hence provide prospects for the realization
of devices supporting Majorana fermions
Mott physics and band topology in materials with strong spin-orbit interaction
Recent theory and experiment have revealed that strong spin-orbit coupling
can have dramatic qualitative effects on the band structure of weakly
interacting solids. Indeed, it leads to a distinct phase of matter, the
topological band insulator. In this paper, we consider the combined effects of
spin-orbit coupling and strong electron correlation, and show that the former
has both quantitative and qualitative effects upon the correlation-driven Mott
transition. As a specific example we take Ir-based pyrochlores, where the
subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak
electron-electron interaction, we predict that Ir electrons are in a metallic
phase at weak spin-orbit interaction, and in a topological band insulator phase
at strong spin-orbit interaction. Very generally, we show that with increasing
strength of the electron-electron interaction, the effective spin-orbit
coupling is enhanced, increasing the domain of the topological band insulator.
Furthermore, in our model, we argue that with increasing interactions, the
topological band insulator is transformed into a "topological Mott insulator"
phase, which is characterized by gapless surface spin-only excitations. The
full phase diagram also includes a narrow region of gapless Mott insulator with
a spinon Fermi surface, and a magnetically ordered state at still larger
electron-electron interaction.Comment: 10+ pages including 3+ pages of Supplementary Informatio
Sensitivity of the superconducting state and magnetic susceptibility to key aspects of electronic structure in ferropnictides
Experiments on the iron-pnictide superconductors appear to show some
materials where the ground state is fully gapped, and others where low-energy
excitations dominate, possibly indicative of gap nodes. Within the framework of
a 5-orbital spin fluctuation theory for these systems, we discuss how changes
in the doping, the electronic structure or interaction parameters can tune the
system from a fully gapped to nodal sign-changing gap with s-wave ()
symmetry (). In particular we focus on the role of the hole pocket at
the point of the unfolded Brillouin zone identified as crucial to
the pairing by Kuroki {\it et al.}, and show that its presence leads to
additional nesting of hole and electron pockets which stabilizes the isotropic
state. The pocket's contribution to the pairing can be tuned by doping,
surface effects, and by changes in interaction parameters, which we examine.
Analytic expressions for orbital pairing vertices calculated within the RPA
fluctuation exchange approximation allow us to draw connections between aspects
of electronic structure, interaction parameters, and the form of the
superconducting gap
Magnetic order in orbital models of the iron pnictides
We examine the appearance of the experimentally-observed stripe
spin-density-wave magnetic order in five different orbital models of the iron
pnictide parent compounds. A restricted mean-field ansatz is used to determine
the magnetic phase diagram of each model. Using the random phase approximation,
we then check this phase diagram by evaluating the static spin susceptibility
in the paramagnetic state close to the mean-field phase boundaries. The momenta
for which the susceptibility is peaked indicate in an unbiased way the actual
ordering vector of the nearby mean-field state. The dominant orbitally resolved
contributions to the spin susceptibility are also examined to determine the
origin of the magnetic instability. We find that the observed stripe magnetic
order is possible in four of the models, but it is extremely sensitive to the
degree of the nesting between the electron and hole Fermi pockets. In the more
realistic five-orbital models, this order competes with a strong-coupling
incommensurate state which appears to be controlled by details of the
electronic structure below the Fermi energy. We conclude by discussing the
implications of our work for the origin of the magnetic order in the pnictides.Comment: 19 pages, 19 figures; published version, typos corrected, references
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