Author(s):Rui Wang

Anyons have recently received great attention due to their promising
application in topological quantum computation. The best validated system that
enjoys the anyonic excitations are the Laughlin states. The quasi-particles in
Laughlin states are neither fermions nor bosons but possess the discrete
statistical angle ? = ?=m, with m being an integer. Here we report a possible
realization of the universal Abelian anyons, whose statistical angle can be
tuned continuously by external parameters and can take any arbitrary values
interpolating ? = 0 and ? = ?. The proposed setup is the surface state of a
three dimensional topological insulator driven by an amplitude-modulated
circularly-polarized light. It is found that the external field leads to a
particular Floquet phase, which is a two-spatial-dimensional analogy of the
Weyl semimetal phase in the Floquet first Brillouin zone. The chiral anomaly of
this phase results in a U(1) Chern-Simons gauge theory with a tunable Floquet
Chern number. Owing to this underlying gauge field theory, the irradiated
surface of topological insulator constitutes a promising platform for the
observation of the universal anyons.

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Author(s):Rui Wang

We investigate the Kondo e?ect in the two-dimensional electron system with a
non-trivial quadratic energy band crossing point. We show that the Kondo e?ect
can induce a new hybrid topological insulator phase which is a coexistence
state of the quantum anomalous Hall e?ect and the TRSbroken quantum spin Hall
e?ect. This hybrid topological insulator exhibits not only a quantized charge
Hall current but also a net spin current, which are localized at the edge
boundaries. This peculiar topological state arises due to the interplay of two
marginally relevant operators, i.e., the Kondo-coupling between the electrons
and the local magnetic moment and the electron-electron interaction in the
two-dimensional system.

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Author(s):Björn Sbierski

Strong topological insulators may have nonzero weak indices. The nonzero weak
indices allow for the existence of topologically protected helical states along
line defects of the lattice. If the lattice admits line defects that connect
opposite surfaces of a slab of such a “weak-and-strong” topological insulator,
these states effectively connect the surface states at opposite surfaces.
Depending on the phases accumulated along the dislocation lines, this
connection results in a suppression of in-plane transport and the opening of a
spectral gap or in an enhanced density of states and an increased conductivity.

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Author(s):Sayonee Ray

Despite the realizations of spin-orbit coupling (SOC) and synthetic gauge
fields in optical lattices, the associated time-reversal breaking, and
one-dimensional nature of the observed SOC pose challenges to obtain $Z_2$
topological insulator in these lattices. We propose here a model device for
engineering intrinsic $Z_2$ topological insulator which can be easily set up
with the already realized tools. The proposed device consists of two quantum
mechanically connected one-dimensional SOC channels (dubbed SO wires) aligned
antiparallel to each other in such a way that time-reversal symmetry is
restored. Tuning a complex hopping integral between the adjacent SO wires, two
counter-helical `chiral orbits’ of atoms can be easily engineered, whose
localization in the bulk concurrently leads to $Z_2$ topological invariant with
protected edge states. We also propose a non-local current measurement setup to
detect the chiral edge state.

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Author(s):Stefan Rex

Topological insulators (TIs) represent a fascinating and novel state of
matter, namely a combined bulk insulator and surface metal with the additional
property that the gapless current-carrying surface states are protected from
scattering by particle number conservation and time-reversal symmetry. When TIs
coexist with magnetic order, the magnetization opens a gap in the surface Dirac
cone on the topological insulator. This leads to an anomalous quantum Hall
effect with a half integer quantized conductance of $\sigma^0_{xy}=e^2/(2h)$,
and a topological magnetoelectric effect (TME) whereby an electric field
induces a magnetic polarization in the same direction and vice versa. The
latter can be understood from a field theoretic description of the Dirac
fermions, which resembles axion electrodynamics, yielding a contribution
proportional to $\boldsymbol{E\cdot B}$ in the Lagrangian. This term is
protected by topology and involves not only externally applied fields, but also
the Coulomb field induced by {magnetic charges. The result is a long-range
effect that enables novel device architechtures for spintronics. Here, we
demonstrate theoretically how a non-local all-electric control of the magnetic
texture of a TI/ferromagnetic insulator (FMI) interface is possible, where a
voltage is applied at a different, electrically well-separated layer.

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Author(s):Juntao Song

Using non-equilibrium Green’s functions, we studied numerically the transport
properties of a Josephson junction, superconductor-topological
insulator-superconductor hybrid system. Our numerical calculation shows first
that proximity-induced superconductivity is indeed observed in the edge states
of a topological insulator adjoining two superconducting leads and second that
the special characteristics of topological insulators endow the edge states
with an enhanced proximity effect with a superconductor but do not forbid the
bulk states to do the same. In a size-dependent analysis of the local current,
it was found that a few residual bulk states can lead to measurable resistance,
whereas because these bulk states spread over the whole sample, their
contribution to the interference pattern is insignificant when the sample size
is in the micrometer range. Based on these numerical results, it is concluded
that the apparent disappearance of residual bulk states in the superconducting
interference process as described in Ref. [\onlinecite{HartNautrePhys2014f}] is
just due to the effects of size: the contribution of the topological edge
states outweighs that of the residual bulk states.

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Author(s):S. A. Owerre

We investigate an ultra-thin film of topological insulator (TI) multilayer as
a model for a three-dimensional (3D) Weyl semi-metallic phase. In addition to
tunneling parameters of a 2D ultra-thin film TI, say $t_S$ and $t_\perp$, we
introduce tunneling parameter $t_D$ which couples neighbouring thin film layers
along the $z$-direction. It is shown that this model realizes a 3D Weyl
semi-metallic phase as an intermediate state between a quantum anomalous Hall
state and a normal insulator. The Chern number is computed in each phase and we
find that for $t_S,t_D>0$, the tunneling parameter $t_\perp$ changes from
positive to negative as the system transits from Weyl semi-metallic phase to
insulating phases. Furthermore, we propose and study a 3D lattice model of
Porphyrin thin film, an organic material known to support topological Frenkel
exciton edge states. We show that this model exhibits a 3D Weyl semi-metallic
phase and also supports a 2D Weyl semi-metallic phase. We further show that
this model recovers that of 3D Weyl semimetal in topological insulator thin
film multilayer. Thus, paving the way for simulating a 3D Weyl semimetal in
topological insulator thin film multilayer. We obtain the surface states (Fermi
arcs) in the 3D model and the chiral edge states in the 2D model and analyze
their topological properties.

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Author(s):S. A. Owerre

We investigate an ultra-thin film of topological insulator (TI) multilayer as
a model for a three-dimensional (3D) Weyl semimetal. We introduce tunneling
parameters $t_S$, $t_\perp$, and $t_D$, where the former two parameters couple
layers of the same thin film at small and large momenta, and the latter
parameter couples neighbouring thin film layers along the $z$-direction. The
Chern number is computed in each topological phase of the system and we find
that for $t_S,t_D>0$, the tunneling parameter $t_\perp$ changes from positive
to negative as the system transits from Weyl semi-metallic phase to insulating
phases. We further study the chiral magnetic effect (CME) of the system in the
presence of a time dependent magnetic field. We compute the low-temperature
dependence of the chiral magnetic conductivity and show that it captures three
distinct phases of the system separated by plateaus. Furthermore, we propose
and study a 3D lattice model of Porphyrin thin film, an organic material known
to support topological Frenkel exciton edge states. We show that this model
exhibits a 3D Weyl semi-metallic phase and also supports a 2D Weyl
semi-metallic phase. We further show that this model recovers that of 3D Weyl
semimetal in topological insulator thin film multilayer. Thus, paving the way
for simulating a 3D Weyl semimetal in topological insulator thin film
multilayer. We obtain the surface states (Fermi arcs) in the 3D model and the
chiral edge states in the 2D model and analyze their topological properties.

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Author(s):Wei Chen

Quantum spin Hall insulator is characterized by the helical edge states, with
the spin polarization of electron being locked to its direction of motion.
Although the edge-state conduction has been observed, unambiguous evidence of
the helical spin texture is still lacking. Here, we investigate the coherent
edge-state transport in an interference loop pinched by two point contacts. Due
to the helical character, the forward inter-edge scattering enforces a $\pi$
spin rotation. Two successive processes can only produce a nontrivial $2\pi$ or
trivial $0$ spin rotation, which can be controlled by the Rashba spin-orbit
coupling. The nontrivial spin rotation results in a geometric $\pi$ Berry
phase, which can be detected by a $\pi$ phase shift of the conductance
oscillation relative to the trivial case. Our results provide a smoking gun
evidence for the helical spin texture of the edge states. Moreover, it also
provides the opportunity to all-electrically explore the trajectory-dependent
spin Berry phase in condensed matter.

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Author(s):Emil Prodan

Topological insulators are newly discovered materials with the defining
property that any boundary cut into such crystal supports spectrum which is
immune to the Anderson localization. The present paper summarizes our efforts
on the rigorous characterization of these materials in the regime of weak and
strong disorder. In particular, the defining property is rigorously proven
under certain relevant conditions, for more than half of the classification
table of topological insulators.

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Author(s):Erwann Bocquillon

In recent years, Majorana physics has attracted considerable attention in
both theoretical and experimental studies due to exotic new phenomena and its
prospects for fault-tolerant topological quantum computation. To this end, one
needs to engineer the interplay between superconductivity and electronic
properties in a topological insulator, but experimental work remains scarce and
ambiguous. Here we report experimental evidence for topological
superconductivity induced in a HgTe quantum well, a two-dimensional topological
insulator that exhibits the quantum spin Hall effect. The ac Josephson effect
demonstrates that the supercurrent has a $4\pi$-periodicity with the
superconducting phase difference as indicated by a doubling of the voltage step
for multiple Shapiro steps. In addition, an anomalous SQUID-like response to a
perpendicular magnetic field shows that this $4\pi$-periodic supercurrent
originates from states located on the edges of the junction. Both features
appear strongest when the sample is gated towards the quantum spin Hall regime,
thus providing evidence for induced topological superconductivity in the
quantum spin Hall edge states.

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Author(s):R. S. Akzyanov

We investigate a topological insulator — superconductor heterostructure with
an Abrikosov vortex in a magnetic field. Large Zeeman field causes a
topological phase transition in the system. We found that a Majorana fermion
exists at the vortex core in the phase with zero first Chern number and does
not exist at the phase with non-trivial first Chern number. This result is
supported by the index theorem. This system provides an example in which a
Majorana fermion emerges in a system with zero first Chern number.

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Author(s):Yury Deshko

The propagation of surface plasmon polaritons in thin films of topological
insulators is studied. The materials considered are second generation three
dimensional topological insulators Bi$_2$Se$_3$, Bi$_2$Te$_3$, and
Sb$_2$Te$_3$. Dispersion relations and propagation lengths are estimated
numerically, taking into account the variation of bulk dielectric functions of
topological insulators as well as substrate using the Drude-Lorentz model. Key
factors affecting propagation length are identified and ways to modify the
dispersion relations are suggested. The explanation of the apparent discrepancy
between the experimental data for Bi$_2$Se$_3$ and theory is proposed.

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Author(s):Yury Deshko

The propagation of surface plasmon polaritons in thin films of topological
insulators is studied. The materials considered are second generation three
dimensional topological insulators Bi$_2$Se$_3$, Bi$_2$Te$_3$, and
Sb$_2$Te$_3$. Dispersion relations and propagation lengths are estimated
numerically, taking into account the variation of bulk dielectric functions of
topological insulators as well as substrate using the Drude-Lorentz model. Key
factors affecting propagation length are identified and ways to modify the
dispersion relations are suggested. The explanation of the apparent discrepancy
between the experimental data for Bi$_2$Se$_3$ and theory is proposed.

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Author(s):SK Firoz Islam

Quantum spin Hall effect was first predicted in graphene. However, the weak
spin orbit interaction in graphene meant that the search for quantum spin Hall
effect in graphene never fructified. In this work we show how to generate the
quantum spin-valley Hall effect in graphene via quantum pumping by
adiabatically modulating a magnetic impurity and an electrostatic potential in
a monolayer of strained graphene. We see that not only exclusive spin polarized
currents can be pumped in the two valleys in exactly opposite directions but
one can have pure spin currents flowing in opposite directions in the two
valleys, we call this novel phenomena the quantum spin-valley Hall effect. This
means that the twin effects of quantum valley Hall and quantum spin Hall can
both be probed simultaneously in the proposed device.

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Author(s):Liang Wu

In this work, we use charge extraction via organic overlayer deposition to
lower the chemical potential of topological insulator Bi2Se3 thin films into
the intrinsic (bulk-insulating) regime. We demonstrate the tuning and
stabilization of intrinsic topological insulators at high mobility with
low-cost organic films. With the protection of the organic charge extraction
layers tetrafluorotetracyanoquinodimethane(F4TCNQ) or
tris(acetylacetonato)cobalt(III) (Co(acac)3), the sample is stable in the
atmosphere with chemical potential ~135 meV above the Dirac point (85 meV below
the conduction band minimum, well within the topological insulator regime)
after four months, which is an extraordinary level of environmental stability.
The Co complex represents the first use of an organometallic for modulating TI
charge density. The mobility of surface state electrons is enhanced as high as
~2000 cm2/Vs. Even at room temperature, a true topologically insulating state
is realized and stabilized for months’ exposure to the atmosphere.

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Author(s):K. N. Okada

We achieve the enhancement of circular photogalvanic effect arising from the
photo-injection of spins in topological insulator thin films by tuning the
Fermi level ($E_{\rm F}$). A series of (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ thin films
were tailored so that the Fermi energy ranges above 0.34 eV to below 0.29 eV of
the Dirac point, i.e., from the bulk conduction band bottom to the valence band
top through the bulk in-gap surface-Dirac cone. The circular photogalvanic
current, indicating a flow of spin-polarized surface-Dirac electrons, shows a
pronounced peak when the $E_{\rm F}$ is set near the Dirac point and is also
correlated with the carrier mobility. Our observation reveals that there are
substantial scatterings between the surface-Dirac and bulkstate electrons in
the generation process of spin-polarized photocurrent, which can be avoided by
designing the electronic structure in topological insulators.

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Author(s):S. A. Owerre

In ultra-thin film of topological insulator, the hybridization between the
top and bottom surfaces opens an energy gap and forms two degenerate quantum
anomalous Hall states which give rise to a quantum spin Hall state. In this
paper, we demonstrate that a three-dimensional (3D) Dirac semimetal can be
realized in an ultra-thin film of topological insulator heterostructure. By
breaking both time reversal symmetry and inversion symmetry the system transits
into a Weyl semimetal phase whose nodes appear at the same energy, thus
preserving nodal semimetal. In addition to Dirac and Weyl semimetal phases, the
system also realizes both 3D quantum anomalous Hall phase and 3D quantum spin
Hall phase.

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Author(s):S. A. Owerre

In ultra-thin film of topological insulator, the hybridization between the
top and bottom surfaces opens an energy gap and forms two degenerate quantum
anomalous Hall states, which give rise to a quantum spin Hall state. In this
paper, we demonstrate that a Weyl semimetal can be realized in an ultra-thin
film of topological insulator heterostructure in a similar way to that of the
surface state of a strong three-dimensional (3D) topological insulator studied
by Burkov and Balents . We find that the system realizes both 3D quantum
anomalous Hall phase and 3D quantum spin Hall phase, and the Weyl nodes occur
at zero energy when both time-reversal symmetry and inversion symmetry are
explicitly broken by the magnetic field and the structure inversion asymmetry
of the thin film.

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Author(s):S. A. Owerre

In ultra-thin film of topological insulator, the hybridization between the
top and bottom surfaces opens an energy gap and forms two degenerate quantum
anomalous Hall states, which give rise to a quantum spin Hall state. In this
paper, we demonstrate that a Weyl semimetal can be realized in an ultra-thin
film of topological insulator heterostructure in a similar way to that of the
surface state of a strong three-dimensional (3D) topological insulator studied
by Burkov and Balents . We find that the system realizes both 3D quantum
anomalous Hall phase and 3D quantum spin Hall phase, and the Weyl nodes occur
at zero energy when both time-reversal symmetry and inversion symmetry are
explicitly broken by the magnetic field and the structure inversion asymmetry
of the thin film.

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