Author(s): S. Wolgast, Y. S. Eo, T. Öztürk, G. Li, Z. Xiang, C. Tinsman, T. Asaba, B. Lawson, F. Yu, J. W. Allen, K. Sun, L. Li, Ç. Kurdak, D.-J. Kim, and Z. Fisk

The recent conjecture of a topologically protected surface state in SmB 6 and the verification of robust surface conduction below 4 K have prompted a large effort to understand surface states. Conventional Hall transport measurements allow current to flow on all surfaces of a topological insulator, s…


[Phys. Rev. B 92, 115110] Published Fri Sep 04, 2015

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Author(s): P. Zhang and Franco Nori

We propose a hybrid system composed of a Majorana qubit and a nanomechanical resonator, implemented by a spin-orbit-coupled superconducting nanowire, using a set of static and oscillating ferromagnetic gates. The ferromagnetic gates induce Majorana bound states in the nanowire, which hybridize and c…


[Phys. Rev. B 92, 115303] Published Fri Sep 04, 2015

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Author(s): Pai Wang, Ling Lu, and Katia Bertoldi

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic an…


[Phys. Rev. Lett. 115, 104302] Published Fri Sep 04, 2015

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Author(s): Aaron Farrell and T. Pereg-Barnea

Here we provide a picture of transport in quantum well heterostructures with a periodic driving field in terms of a probabilistic occupation of the topologically protected edge states in the system. This is done by generalizing methods from the field of photon-assisted tunneling. We show that the ti…


[Phys. Rev. Lett. 115, 106403] Published Fri Sep 04, 2015

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Author(s):

Non-linear charge transport in SIS Josephson junctions has a unique signature
in the shuttled charge quantum between the two superconductors. In the
zero-bias limit Cooper pairs, each with twice the electron charge, carry the
Josephson current. An applied bias $V_{SD}$ leads to multiple Andreev
reflections (MAR), which in the limit of weak tunneling probability should lead
to integer multiples of the electron charge $ne$ traversing the junction, with
$n$ integer larger than $2{\Delta}/eV_{SD}$ and ${\Delta}$ the superconducting
order parameter. Exceptionally, just above the gap, $eV_{SD}>2{\Delta}$, with
Andreev reflections suppressed, one would expect the current to be carried by
partitioned quasiparticles; each with energy dependent charge, being a
superposition of an electron and a hole. Employing shot noise measurements in
an SIS junction induced in an InAs nanowire (with noise proportional to the
partitioned charge), we first observed quantization of the partitioned charge
$q=e^*/e$, with $n=1-4$; thus reaffirming the validity of our charge
interpretation. Concentrating next on the bias region
$eV_{SD}{\approx}2{\Delta}$, we found a reproducible and clear dip in the
extracted charge to $q{\approx}0.6$, which, after excluding other
possibilities, we attribute to the partitioned quasiparticle charge. Such dip
is supported by numerical simulations of our SIS structure. Applying similar
measurements to a p-wave Josephson junction may be useful in understanding
Majorana bound state excitations.

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Author(s):

We study a system of interacting spinless fermions in one dimension which, in
the absence of interactions, reduces to the Kitaev chain [A. Yu Kitaev,
Phys.-Usp. \textbf{44}, 131 (2001)]. In the non-interacting case, a signal of
topological order appears as zero-energy modes localized near the edges. We
show that the exact ground states can be obtained analytically even in the
presence of nearest-neighbor repulsive interactions when the on-site (chemical)
potential is tuned to a particular function of the other parameters. As with
the non-interacting case, the obtained ground states are two-fold degenerate
and differ in fermionic parity. We prove the uniqueness of the obtained ground
states and show that they can be continuously deformed to the ground states of
the non-interacting Kitaev chain without gap closing. We also demonstrate
explicitly that there exists a set of operators each of which maps one of the
ground states to the other with opposite fermionic parity. These operators can
be thought of as an interacting generalization of Majorana edge zero modes.

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Author(s):

We study $(d-1)$-dimensional excitations in the $d$-dimensional color code
that are created by transversal application of the $R_{d}$ phase operators on
connected subregions of qubits. We find that such excitations are
superpositions of electric charges and can be characterized by fixed-point
wavefunctions of $(d-1)$-dimensional bosonic SPT phases with
$(\mathbb{Z}_{2})^{\otimes d}$ symmetry. While these SPT excitations are
localized on $(d-1)$-dimensional boundaries, their creation requires operations
acting on all qubits inside the boundaries, reflecting the non-triviality of
emerging SPT wavefunctions. Moreover, these SPT-excitations can be physically
realized as transparent gapped domain walls which exchange excitations in the
color code. Namely, in the three-dimensional color code, the domain wall,
associated with the transversal $R_{3}$ operator, exchanges a magnetic flux and
a composite of a magnetic flux and loop-like SPT excitation, revealing rich
possibilities of boundaries in higher-dimensional TQFTs. We also find that
magnetic fluxes and loop-like SPT excitations exhibit non-trivial three-loop
braiding statistics in three dimensions as a result of the fact that the
$R_{3}$ phase operator belongs to the third-level of the Clifford hierarchy. We
believe that the connection between SPT excitations, fault-tolerant logical
gates and gapped domain walls, established in this paper, can be generalized to
a large class of topological quantum codes and TQFTs.

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Author(s):

Topological insulators and D-brane charges in string theory can both be
classified by the same family of groups. In this paper, we extend this
connection via a geometric transform, giving a novel duality of topological
insulators which can be viewed as a condensed matter analog of T-duality in
string theory. For 2D Chern insulators, this duality exchanges the rank and
Chern number of the valence bands.

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Author(s):

The spectrum of electronic current-current correlations in an
out-of-equilibrium conducting channel is known to exhibit a partition noise
form, proportional to $R\, T$, where $R$ and $T$ are the channel reflection and
transmission probabilities. Although edge channels of 2D topological systems
are protected from elastic reflection and are noiseless at low temperature,
noise and cross-correlations can be induced by allowing electron waves to be
partly transmitted to the opposite edge via tunneling through a constriction.
In a quantum spin Hall (QSH) system tunneling occurs via both spin-preserving
($p$) and spin-flipping ($f$) processes, characterized by reflection
probabilities $R_{p}$ and $R_{f}$, respectively, which are both time-reversal
symmetric and do not commute.

We investigate the current-current correlations of a four-terminal QSH setup
in the presence of a tunneling region, both at equilibrium and
out-of-equilibrium. We find that, although the generic current-current
correlation depends on both $p$ and $f$ processes, under appropriate conditions
a direct detection of two types of partitioning $T_{p} R_{p}$ and $T_{f}R_{f}$
is possible. In particular, while the spin-preserving partitioning can be
probed for any arbitrary tunnel junction with a specific configuration of
terminal biases, the spin-flipping partitioning can be directly detected only
under suitably designed setups and conditions. We describe two setups where
these conditions can be fulfilled, and both types of partitioning can be
detected and controlled.

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Author(s):

Spins on the edge
Nanowerk
Naoto Nagaosa of the RIKEN Center for Emergent Matter Science and his colleagues from the RIKEN Condensed Matter Theory Laboratory have been studying how electron spins behave in an unusual class of materials known as topological insulators.

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Author(s):

Authors: Yuval Ronen, Yonatan Cohen, Jung-Hyun Kang, Arbel Haim, Maria-Theresa Rieder, Moty Heiblum, Diana Mahalu, Hadas Shtrikman

Non-linear charge transport in SIS Josephson junctions has a unique signature
in the shuttled charge quantum between the two superconductors. In the
zero-bias limit Cooper pairs, each with twice the electron charge, carry the
Josephson current. An applied bias $V_{SD}$ leads to multiple Andreev
reflections (MAR), which in the limit of weak tunneling probability should lead
to integer multiples of the electron charge $ne$ traversing the junction, with
$n$ integer larger than $2{\Delta}/eV_{SD}$ and ${\Delta}$ the superconducting
order parameter. Exceptionally, just above the gap, $eV_{SD}>2{\Delta}$, with
Andreev reflections suppressed, one would expect the current to be carried by
partitioned quasiparticles; each with energy dependent charge, being a
superposition of an electron and a hole. Employing shot noise measurements in
an SIS junction induced in an InAs nanowire (with noise proportional to the
partitioned charge), we first observed quantization of the partitioned charge
$q=e^*/e$, with $n=1-4$; thus reaffirming the validity of our charge
interpretation. Concentrating next on the bias region
$eV_{SD}{\approx}2{\Delta}$, we found a reproducible and clear dip in the
extracted charge to $q{\approx}0.6$, which, after excluding other
possibilities, we attribute to the partitioned quasiparticle charge. Such dip
is supported by numerical simulations of our SIS structure. Applying similar
measurements to a p-wave Josephson junction may be useful in understanding
Majorana bound state excitations.

link to article (opens in new tab)

 

Author(s):

Authors: Hosho Katsura, Dirk Schuricht, Masahiro Takahashi

We study a system of interacting spinless fermions in one dimension which, in
the absence of interactions, reduces to the Kitaev chain [A. Yu Kitaev,
Phys.-Usp. \textbf{44}, 131 (2001)]. In the non-interacting case, a signal of
topological order appears as zero-energy modes localized near the edges. We
show that the exact ground states can be obtained analytically even in the
presence of nearest-neighbor repulsive interactions when the on-site (chemical)
potential is tuned to a particular function of the other parameters. As with
the non-interacting case, the obtained ground states are two-fold degenerate
and differ in fermionic parity. We prove the uniqueness of the obtained ground
states and show that they can be continuously deformed to the ground states of
the non-interacting Kitaev chain without gap closing. We also demonstrate
explicitly that there exists a set of operators each of which maps one of the
ground states to the other with opposite fermionic parity. These operators can
be thought of as an interacting generalization of Majorana edge zero modes.

link to article (opens in new tab)

 

Author(s):

Authors: Beni Yoshida

We study $(d-1)$-dimensional excitations in the $d$-dimensional color code
that are created by transversal application of the $R_{d}$ phase operators on
connected subregions of qubits. We find that such excitations are
superpositions of electric charges and can be characterized by fixed-point
wavefunctions of $(d-1)$-dimensional bosonic SPT phases with
$(\mathbb{Z}_{2})^{\otimes d}$ symmetry. While these SPT excitations are
localized on $(d-1)$-dimensional boundaries, their creation requires operations
acting on all qubits inside the boundaries, reflecting the non-triviality of
emerging SPT wavefunctions. Moreover, these SPT-excitations can be physically
realized as transparent gapped domain walls which exchange excitations in the
color code. Namely, in the three-dimensional color code, the domain wall,
associated with the transversal $R_{3}$ operator, exchanges a magnetic flux and
a composite of a magnetic flux and loop-like SPT excitation, revealing rich
possibilities of boundaries in higher-dimensional TQFTs. We also find that
magnetic fluxes and loop-like SPT excitations exhibit non-trivial three-loop
braiding statistics in three dimensions as a result of the fact that the
$R_{3}$ phase operator belongs to the third-level of the Clifford hierarchy. We
believe that the connection between SPT excitations, fault-tolerant logical
gates and gapped domain walls, established in this paper, can be generalized to
a large class of topological quantum codes and TQFTs.

link to article (opens in new tab)

 

Author(s):

Authors: Varghese Mathai, Guo Chuan Thiang

Topological insulators and D-brane charges in string theory can both be
classified by the same family of groups. In this paper, we extend this
connection via a geometric transform, giving a novel duality of topological
insulators which can be viewed as a condensed matter analog of T-duality in
string theory. For 2D Chern insulators, this duality exchanges the rank and
Chern number of the valence bands.

link to article (opens in new tab)

 

Author(s):

Authors: Fabrizio Dolcini

The spectrum of electronic current-current correlations in an
out-of-equilibrium conducting channel is known to exhibit a partition noise
form, proportional to $R\, T$, where $R$ and $T$ are the channel reflection and
transmission probabilities. Although edge channels of 2D topological systems
are protected from elastic reflection and are noiseless at low temperature,
noise and cross-correlations can be induced by allowing electron waves to be
partly transmitted to the opposite edge via tunneling through a constriction.
In a quantum spin Hall (QSH) system tunneling occurs via both spin-preserving
($p$) and spin-flipping ($f$) processes, characterized by reflection
probabilities $R_{p}$ and $R_{f}$, respectively, which are both time-reversal
symmetric and do not commute.

We investigate the current-current correlations of a four-terminal QSH setup
in the presence of a tunneling region, both at equilibrium and
out-of-equilibrium. We find that, although the generic current-current
correlation depends on both $p$ and $f$ processes, under appropriate conditions
a direct detection of two types of partitioning $T_{p} R_{p}$ and $T_{f}R_{f}$
is possible. In particular, while the spin-preserving partitioning can be
probed for any arbitrary tunnel junction with a specific configuration of
terminal biases, the spin-flipping partitioning can be directly detected only
under suitably designed setups and conditions. We describe two setups where
these conditions can be fulfilled, and both types of partitioning can be
detected and controlled.

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Author(s):Jun Xiong

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Author(s):

Authors: J. Gonzalez

We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means
of a self-consistent resolution of the Schwinger-Dyson equations, aiming to
obtain the respective phase diagrams in terms of the relative strength of the
Coulomb interaction and the number N of Dirac fermions. In this framework, 2D
Dirac semimetals have just a strong-coupling instability characterized by
exciton condensation (and dynamical generation of mass) that we find at a
critical coupling well above previous theoretical estimates, thus explaining
the absence of that instability in free-standing graphene samples. On the other
hand, we show that 3D Dirac semimetals have a richer phase diagram, with a
strong-coupling instability leading to dynamical mass generation up to N = 4
and a line of critical points for larger values of N characterized by the
vanishing of the electron quasiparticle weight in the low-energy limit. Such a
critical behavior signals the transition to a strongly correlated liquid,
characterized by noninteger scaling dimensions that imply the absence of a pole
in the electron propagator and are the signature of non-Fermi liquid behavior
with no stable electron quasiparticles.

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Author(s):

Authors: Eduardo V. Castro, M. Pilar López-Sancho, María A. H. Vozmediano

We analyse the topological transition and localization evolution of
disordered two dimensional systems with non trivial topology based on bipartite
lattices. Chern insulators with broken time reversal symmetry show non standard
behavior for disorder realizations selectively distributed on only one of the
sublattices. The Chern number survives to a much stronger disorder strength
(one order of magnitude higher) than in the equally distributed disordered case
and the final state in the strongly disordered case is metallic.

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Author(s):

Authors: Katharina Höfer, Christoph Becker, Steffen Wirth, Liu Hao Tjeng

We have identified epitaxially grown elemental Te as a capping material that
is suited to protect the topological surface states of intrinsically insulating
Bi$_2$Te$_3$. By using angle-resolved photoemission, we were able to show that
the Te overlayer leaves the dispersive bands of the surface states intact and
that it does not alter the chemical potential of the Bi$_2$Te$_3$ thin film.
From in-situ four-point contact measurements, we observed that the conductivity
of the capped film is still mainly determined by the metallic surface states
and that the contribution of the capping layer is minor. Moreover, the Te
overlayer can be annealed away in vacuum to produce a clean Bi$_2$Te$_3$
surface in its pristine state even after the exposure of the capped film to
air. Our findings will facilitate well-defined and reliable ex-situ experiments
on the properties of Bi$_2$Te$_3$ surface states with nontrivial topology.

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Author(s):

Authors: Kiminori Hattori

We generalize the topological phase diagram of magnetic topological insulator
(TI) thin films in an extended parameter space comprising out-of-plane (OP) and
in-plane (IP) exchange fields in the presence of structural inversion asymmetry
(SIA) while taking a generic orbital-dependent spin coupling allowed for TIs
into consideration. The results show that an IP field substantially deforms
phase boundaries and generically induces the quantum anomalous Hall (QAH)
effect. For symmetric spin coupling, extremely weak OP and IP exchange fields
create the QAH state by tuning SIA with a gate bias. For antisymmetric
coupling, the QAH phase is absent without a strong enough IP field. These
findings demonstrate that in the thin-film regime, engineering the phase
boundary is a key process to efficiently realize and manipulate the QAH effect
for nondissipative electronic applications.

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