Author(s):

Authors: J. L. Lado, J. Fernandez-Rossier

Application of a perpendicular magnetic field to charge neutral graphene is
expected to result in a variety of broken symmetry phases, including
antiferromagnetic, canted and ferromagnetic. All these phases open a gap in
bulk but have very different edge states and non-collinear spin order, recently
confirmed experimentally. Here we provide an integrated description of both
edge and bulk for the various magnetic phases of graphene Hall bars making use
of a non-collinear mean field Hubbard model. Our calculations show that, at the
edges, the three types of magnetic order are either enhanced (zigzag) or
suppressed (armchair). Interestingly, we find that preformed local moments in
zigzag edges interact with the quantum Spin Hall like edge states of the
ferromagnetic phase and can induce back-scattering.

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Author(s):

Authors: Oleksandr V. Pylypovskyi, Volodymyr P. Kravchuk, Denis D. Sheka, Denys Makarov, Oliver G. Schmidt, Yuri Gaididei

We show that the interaction of the magnetic subsystem of a curved magnet
with the magnet curvature results in coupling of a topologically nontrivial
magnetization pattern and topology of the object. The mechanism of this
coupling is explored and illustrated by an example of ferromagnetic M\”obius
ring, where a topologically induced domain wall appears as a ground state in
case of strong easy-normal anisotropy. For the M\”obius geometry the
curvilinear form of the exchange interaction produces an additional effective
Dzyaloshinskii-like term which leads to the coupling of the magnetochirality of
the domain wall and chirality of the M\”obius ring. Two types of domain walls
are found, transversal and longitudinal, which are oriented across and along
the M\”obius ring, respectively. In both cases the effect of magnetochirality
symmetry breaking is established. The dependence of the ground state of the
M\”obius ring on its geometrical parameters and on the value of the easy-normal
anisotropy is explored numerically.

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Author(s):

Authors: Alex Westström, Kim Pöyhönen, Teemu Ojanen

Recent experiments announced an observation of topological superconductivity
and Majorana quasiparticles in Shiba chains, consisting of an array of magnetic
atoms deposited on top of a superconductor. In this work we study helical Shiba
chains and generalize the microscopic theory of subgap energy bands to a regime
where the decoupled magnetic impurity energy and the hybridization of different
impurity states can be significant compared to the superconducting gap of the
host material. From exact solutions of the Bogoliubov-de Gennes equation we
extract expressions for the topological phase boundaries for arbitrary values
of the superconducting coherence length. The subgap spectral problem can be
formulated as a nonlinear matrix eigenvalue problem from which we obtain an
analytical solution for energy bands in the long coherence length limit.
Physical consequences and departures from the previously obtained results in
the deep-dilute impurity limit are discussed in detail.

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Author(s):

Authors: Jutho Haegeman, Valentin Zauner, Norbert Schuch, Frank Verstraete

We study the eigenvalue structure of transfer matrices for topological phases
in the projected entangled pair formalism, and illustrate that those encode
essential information about the elementary anyonic excitations. We demonstrate
that topological quantum order requires a particular type of ‘symmetry
breaking’ for the fixed point subspace of the transfer matrix, while a phase
transition from the deconfined (topological) to the confined (trivial) phase
corresponds to a change in this subspace to either a larger or smaller
symmetry. In particular, we illustrate that physical anyonic excitations
correspond to domain wall excitations on the virtual level, and that a phase
transition to a confined phase is reflected by the fact that those domain wall
excitations get exterminated. Our formalism allows to determine the nature of
the elementary anyonic excitations in two-dimensional gapped phases very
efficiently, therefore opening novel avenues for studying fundamental open
questions related to anyon condensation in the tensor network formalism.

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Author(s):

Authors: Shih-Hao Ho, Sung-Po Chao, Chung-Hsien Chou, Feng-Li Lin

We investigate the decoherence patterns of topological qubits in contact with
the environment by a novel way of deriving the open system dynamics other than
the Feynman-Vernon. Each topological qubit is made of two Majorana modes of a
1D Kitaev’s chain. These two Majorana modes interact with the environment in an
incoherent way which yields peculiar decoherence patterns of the topological
qubit. More specifically, we consider the open system dynamics of the
topological qubits which are weakly coupled to the fermionic/bosonic Ohmic-like
environments. We find atypical patterns of quantum decoherence. In contrast to
the cases of non-topological qubits for which they always decohere completely
in all Ohmic-like environments, the topological qubits decohere completely in
the Ohmic and sub-Ohmic environments but not in the super-Ohmic ones. Moreover,
we find that the fermion parities of the topological qubits though cannot
prevent the qubit states from decoherence in the sub-Ohmic environments, can
prevent from thermalization turning into Gibbs state. We also study the cases
in which each Majorana mode can couple to different Ohmic-like environments and
the time dependence of concurrence for two topological qubits.

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Author(s):

Authors: Christoph Ohm, Fabian Hassler

Majorana qubits offer a promising way to store and manipulate quantum
information by encoding it into the state of Majorana zero modes. As the
information is stored in a topological property of the system, local noise
cannot lead to decoherence. Manipulation of the information is achieved by
braiding the zero modes. The measurement however is challenging as the
information is well hidden and thus inherently hard to access. Here, we discuss
a setup for measuring the state of a Majorana qubit by employing standard tools
of microwave engineering. The basic physical effect which we employ is the fact
that a voltage-biased Josephson junction hosting Majorana fermions allows
photons to be emitted and absorbed at half the Josephson frequency. We show
that in the dispersive regime our setup allows to perform a quantum
non-demolition measurement and to reach the quantum limit. An appealing feature
of our setup is that the interaction of the Majorana qubit with the measurement
device can be turned on and off at will by changing the dc bias of the
junction.

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Author(s):

Authors: Jie Shen, Judy J. Cha

Topological crystalline insulators are topological insulators whose surface
states are protected by the crystalline symmetry, instead of the time reversal
symmetry. Similar to the first generation of three-dimensional topological
insulators such as Bi2Se3 and Bi2Te3, topological crystalline insulators also
possess surface states with exotic electronic properties such as spin-momentum
locking and Dirac dispersion. Experimentally verified topological crystalline
insulators to date are SnTe, Pb1-xSnxSe, and Pb1-xSnxTe. Because topological
protection comes from the crystal symmetry, magnetic impurities or in-plane
magnetic fields are not expected to open a gap in the surface states in
topological crystalline insulators. Additionally, because they are cubic
structure instead of layered structure, branched structures or strong coupling
with other materials for large proximity effects are possible, which are
difficult with layered Bi2Se3 and Bi2Te3. Thus, additional fundamental
phenomena inaccessible in three-dimensional topological insulators can be
pursued. In this review, topological crystalline insulator SnTe nanostructures
will be discussed. For comparison, experimental results based on SnTe thin
films will be covered. Surface state properties of topological crystalline
insulators will be discussed briefly.

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Author(s):

Authors: R. Valdés Aguilar, J. Qi, M. Brahlek, N. Bansal, A. Azad, J. Bowlan, S. Oh, A.J. Taylor, R.P. Prasankumar, D.A. Yarotski

We use optical pump–THz probe spectroscopy at low temperatures to study the
hot carrier response in thin Bi$_2$Se$_3$ films of several thicknesses,
allowing us to separate the bulk from the surface transient response. We find
that for thinner films the photoexcitation changes the transport scattering
rate and reduces the THz conductivity, which relaxes within 10 picoseconds
(ps). For thicker films, the conductivity increases upon photoexcitation and
scales with increasing both the film thickness and the optical fluence, with a
decay time of approximately 5 ps as well as a much higher scattering rate.
These different dynamics are attributed to the surface and bulk electrons,
respectively, and demonstrate that long-lived mobile surface photo-carriers can
be accessed independently below certain film thicknesses for possible
optoelectronic applications.

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Author(s):

Authors: Xingyue Peng, Yiming Yang, Rajiv R. P. Singh, Sergey Y. Savrasov, Dong Yu

To date, spin generation in three-dimensional topological insulators (3D TIs)
is primarily modeled as a single-surface phenomenon, happening independently on
top and bottom surfaces. Because this surface charge transport is
Boltzmann-like, the surface spin accumulation is expected to be proportional to
the momentum relaxation time or the inverse of the impurity density. Here we
propose a fundamentally new mechanism for spin generation based on the
topological nature of the band structure: an external electric field creates a
transverse pure spin current in the bulk of 3D TIs, which transports spins
between the top and bottom surfaces and leads to spin accumulation on both. The
surface spin density and charge current are then proportional to the spin
relaxation time, which can be extended by nonmagnetic scattering via the
Dyakonov-Perel spin relaxation mechanism. Therefore, this new spin generation
mechanism results in a distinct strategy for the enhancement of surface spin
polarization by extending the spin relaxation time through increasing the
impurity density. Since this efficient spin generation directly originates from
the unique band topology of the TIs, it does not exist in other two-dimensional
(2D) systems such as graphene and two-dimensional electron gas (2DEG). This
theory is supported by the experimental observation of high conductivity near
the Dirac point, which indicates large spin density at the TI surface under an
external electric field even when “free carriers” are depleted.

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Author(s):

To date, spin generation in three-dimensional topological insulators (3D TIs)
is primarily modeled as a single-surface phenomenon, happening independently on
top and bottom surfaces. Because this surface charge transport is
Boltzmann-like, the surface spin accumulation is expected to be proportional to
the momentum relaxation time or the inverse of the impurity density. Here we
propose a fundamentally new mechanism for spin generation based on the
topological nature of the band structure: an external electric field creates a
transverse pure spin current in the bulk of 3D TIs, which transports spins
between the top and bottom surfaces and leads to spin accumulation on both. The
surface spin density and charge current are then proportional to the spin
relaxation time, which can be extended by nonmagnetic scattering via the
Dyakonov-Perel spin relaxation mechanism. Therefore, this new spin generation
mechanism results in a distinct strategy for the enhancement of surface spin
polarization by extending the spin relaxation time through increasing the
impurity density. Since this efficient spin generation directly originates from
the unique band topology of the TIs, it does not exist in other two-dimensional
(2D) systems such as graphene and two-dimensional electron gas (2DEG). This
theory is supported by the experimental observation of high conductivity near
the Dirac point, which indicates large spin density at the TI surface under an
external electric field even when “free carriers” are depleted.

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Author(s):

Stony Brook Scientists Disprove Theory That Reconstructed Boron Surface is
Newswise (press release)
Newswise — STONY BROOK, N.Y., October 21, 2014 – Scientific inquiry is a hit and miss proposition, subject to constant checking and rechecking. Recently, a new class of materials was discovered called topological insulators—nonmetallic materials with

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Author(s):Hoefer, K., Becker, C., Rata, D., Swanson, J., Thalmeier, P., Tjeng, L. H.

Topological insulators represent a novel state of matter with surface charge carriers having a massless Dirac dispersion and locked helical spin polarization. Many exciting experiments have been proposed by theory, yet their execution has been hampered by the extrinsic conductivity associated with the unavoidable presence of defects in Bi2Te3 and…

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Author(s): Franziska Maier, Tobias Meng, and Daniel Loss

We consider holes confined to Ge/Si core/shell nanowires subject to strong Rashba spin-orbit interaction and screened Coulomb interaction. Such wires can, for instance, serve as host systems for Majorana bound states. Starting from a microscopic model, we find that the Coulomb interaction strongly i…

[Phys. Rev. B 90, 155437] Published Tue Oct 21, 2014

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Author(s):

Authors: V. Gurucharan, Shiroman Prakash

Non-abelian Chern-Simons theories coupled to fermions are known to provide an
interesting class of non-supersymmetric conformal fixed points
\cite{Giombi:2011kc}. These theories, particularly those based on bifundamental
matter, are important because they may provide simple non-supersymmetric
examples of the AdS/CFT correspondence. For instance, it seems natural to
conjecture that $O(N)_{-k}\times O(N)_k$ Chern-Simons theory coupled to
Majorana fermions transforming in a bi-vector representation may be dual to
pure Einstein gravity with a small negative cosmological constant in the
“M-theory” limit where $k=1$ and $N$ is large. While it is extremely difficult
to directly study such bifundamental theories when $k=1$ or even at strong ‘t
Hooft coupling $\lambda=\frac{N}{k}$, it is possible to calculate physical
quantities to all orders in $\lambda$ in a $U(M)_{k_M} \times U(N)_{k_N}$
theory, in the limit $M \ll N$, in an $M/N$ expansion. To illustrate this, we
calculate the anomalous dimension of the primary operator $\bar{\psi}{\psi}$,
to first order in $M/N$, to all orders in $\lambda_M=\frac{N}{k_M}$, but with
$\lambda_N=\frac{N}{k_N}=0$. We also comment on possible bosonization dualities
for bifundamental Chern-Simons theories.

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Author(s):

Authors: Itamar Kimchi, James G. Analytis, Ashvin Vishwanath

Motivated by the recent synthesis of two insulating Li$_2$IrO$_3$ polymorphs,
where Ir$^{4+}$ $S_{eff}$=1/2 moments form 3D (“harmonic”) honeycomb structures
with threefold coordination, we study magnetic Hamiltonians on the resulting
$\beta$-Li$_2$IrO$_3$ hyperhoneycomb lattice and $\gamma$-Li$_2$IrO$_3$
stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities
suggest that Kitaev interactions, predicted for the ideal 90$^\circ$ Ir-O-Ir
bonds, are sizable in these materials. We first consider pure Kitaev
interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL)
with emergent Majorana fermions and Z$_2$ flux loops. Unlike 2D QSLs, the 3D
QSL is stable to finite temperature, with $T_c \approx |K|/100$. On including
Heisenberg couplings, exact solubility is lost. However, by noting that the
shortest closed loop $\ell$ is relatively large in these structures, we
construct an $\ell\rightarrow \infty$ approximation by defining the model on
the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this
lattice is obtained directly in the thermodynamic limit, using tensor network
states and the infinite-system time-evolving-block-decimation (iTEBD)
algorithm. Both magnetically ordered and gapped QSL phases are found, the
latter being identified by an entanglement fingerprint.

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Author(s):

Authors: Cristiano Nisoli, Alan. R. Bishop

The inverse square potential arises in a variety of different quantum
phenomena, yet notoriously it must be handled with care: it suffers from
pathologies rooted in the mathematical foundations of quantum mechanics. We
show that its recently studied conformality-breaking corresponds to an
infinitely smooth winding-unwinding topological transition for the {\it
classical} statistical mechanics of a one-dimensional system: this describes
the the tangling/untangling of floppy polymers under a biasing torque. When the
ratio between torque and temperature exceeds a critical value the polymer
undergoes tangled oscillations, with an extensive winding number. At lower
torque or higher temperature the winding number per unit length is zero.
Approaching criticality, the correlation length of the order parameter—the
extensive winding number—follows a Kosterlitz-Thouless type law. The model is
described by the Wilson line of a (0+1) $U(1)$ gauge theory, and applies to the
tangling/untangling of floppy polymers and to the winding/diffusing kinetics in
diffusion-convection-reactions.

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Author(s):

Authors: W. Zhu, S. S. Gong, D. N. Sheng

The topological quantum spin liquids (SL) and the nature of quantum phase
transitions between them have attracted intensive attentions for the past
twenty years. The extended kagome spin-1/2 antiferromagnet emerges as the
primary candidate for hosting both time reversal symmetry (TRS) preserving and
TRS breaking SLs based on density matrix renormalization group simulations. To
uncover the nature of the novel quantum phase transition between the SL states,
we study a minimum XY model with the nearest neighbor (NN) ($J_{xy}$), the
second and third NN couplings ($J_{2xy}=J_{3xy}=J’_{xy}$). We identify the TRS
broken chiral SL with the turn on of a small perturbation $J’_{xy}\sim 0.06
J_{xy}$, which is fully characterized by the fractionally quantized topological
Chern number and the conformal edge spectrum as the $\nu=1/2$ fractional
quantum Hall state. On the other hand, the NN XY model ($J’_{xy}=0$) is shown
to be a critical SL state adjacent to the CSL, characterized by the gapless
spin singlet excitations and also vanishing small spin triplet excitations. The
quantum phase transition from the CSL to the gapless critical SL is driven by
the collapsing of the neutral (spin singlet) excitation gap. By following the
evolution of the entanglement spectrum, we find that the transition takes place
through the coupling of the edge states with opposite chiralities, which merge
into the bulk and become gapless neutral excitations. The effect of the NN
spin-$z$ coupling $J_z$ is also studied, which leads to a quantum phase diagram
with an extended regime for the gapless SL.

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Author(s):

Authors: Satoshi Sasaki, Yoichi Ando

Recently, the search for Majorana fermions (MFs) has become one of the most
prominent subjects in condensed matter physics. If found, Majorana fermions
will deepen our understanding of quantum physics and foster innovations in
future quantum technologies. Theoretically, MFs may reside in various types of
topological superconductor materials, and superconducting Sn_{1-x}In_{x}Te,
which is a doped topological crystalline insulator, is one of the promising
candidates to harbor MFs. Here, we report the first successful growth of
superconducting Sn_{1-x}In_{x}Te nanoplates on Si substrates by a simple vapor
transport method without employing any catalyst. We observed robust
superconducting transitions in those nanoplates after device fabrication and
found that the relation between the critical temperature and the carrier
density is consistent with that of bulk single crystals, suggesting that the
superconducting properties of the nanoplate devices are essentially the same as
those of bulk crystals. With the help of nanofabrication, those nanoplates
offer promising opportunities to elucidate the potentially topological nature
of superconductivity in Sn_{1-x}In_{x}Te to harbor MFs and thereby contribute
to the future quantum technologies.

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Author(s):

Authors: Eugene Dumitrescu, Brenden Roberts, Sumanta Tewari, Jay D. Sau, S. Das Sarma

Motivated by a recent experiment in which zero-bias peaks have been observed
in scanning tunneling microscopy (STM) experiments performed on chains of
magnetic atoms on a superconductor, we show, by generalizing earlier work, that
a multichannel ferromagnetic wire deposited on a spin-orbit coupled
superconducting substrate can realize a non-trivial chiral topological
superconducting state with Majorana bound states localized at the wire ends.
The non-trivial topological state occurs for generic parameters requiring no
fine tuning, at least for very large exchange spin splitting in the wire. We
theoretically obtain the signatures which appear in the presence of an
arbitrary number of Majorana modes in multi-wire systems incorporating the role
of finite temperature, finite potential barrier at the STM tip, and finite wire
length. These signatures are presented in terms of spatial profiles of STM
differential conductance which clearly reveal zero energy Majorana end modes
and the prediction of a multiple Majorana based fractional Josephson effect. A
critical comparison of our results with the experimental data shows a basic
inconsistency in the interpretation of the Fe nanowire STM experiment in terms
of Majorana zero modes– in particular, the observation of the precise
localization of the Majorana zero modes at the wire ends cannot be reconciled
with the extremely small topological superconducting gap (and the associated
extremely weak Majorana tunneling peak) observed simultaneously. Other than
this rather disturbing basic incompatibility, for which we can offer no
resolution at this stage, most other aspects of the experimental phenomenology
are reasonably well explained by our theory.

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Author(s):

Authors: Xiaosen Yang

We propose a simple approach to realize two-dimensional Floquet topological
superfluid by periodically tuning the depth of square optical lattice
potentials. We show that the periodic driving can induce topological phase
transitions between trivial superfluid and Floquet topological superfluid. For
this systems we verify the anomalous bulk-boundary correspondence, namely that
the robust chiral Floquet edge states can appear even when the winding number
of all the bulk Floquet bands is zero. We establish the existence of two
Floquet Majorana zero modes separated in the quasienergy space, with
$\varepsilon_{0,\pi}=0,\pi/T$ at the topological defects.

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