Author(s):


Gizmodo
Beyond Graphene: 6 Supermaterials That Could Change Our World
Gizmodo
Stanene was first theorized in 2013 by Stanford professor Shoucheng Zhang, whose lab specializes in, along other things, predicting the electronic properties of materials like stanene. According to their models, stanene is a topological insulator

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Author(s): Sigurdur I. Erlingsson and J. Carlos Egues

We show that electrons in ordinary III–V semiconductor double wells with an in-plane modulating periodic potential and interwell spin-orbit interaction are tunable topological insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the sp…

[Phys. Rev. B 91, 035312] Published Fri Jan 30, 2015

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Author(s): Tobias Förster, Peter Krüger, and Michael Rohlfing

We investigate the influence of potassium adsorption and selenium vacancies in the surface layer on the electronic properties of the prototypical topological insulator Bi2Se3. These modifications of the surface give rise to oscillations in the charge density that extend deep into the crystal. They r…

[Phys. Rev. B 91, 035313] Published Fri Jan 30, 2015

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Author(s): Matteo Michiardi, Marco Bianchi, Maciej Dendzik, Jill A. Miwa, Moritz Hoesch, Timur K. Kim, Peter Matzen, Jianli Mi, Martin Bremholm, Bo Brummerstedt Iversen, and Philip Hofmann

Near-surface two-dimensional electron gases on the topological insulator Bi2Te2Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The k-dependent splitting is strongly anisotropic to a degree whe…

[Phys. Rev. B 91, 035445] Published Fri Jan 30, 2015

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Author(s): P. C. Klipstein

[Phys. Rev. B 91, 039909] Published Fri Jan 30, 2015

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Author(s): Hong-Yi Xie, Yang-Zhi Chou, and Matthew S. Foster

We argue that surface spin and thermal conductivities of three-dimensional topological superconductors are universal and topologically quantized at low temperature. For a bulk winding number ν, there are |ν| “colors” of surface Majorana fermions. Localization corrections to surface transport coeffic…

[Phys. Rev. B 91, 024203] Published Fri Jan 30, 2015

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Author(s):

We demonstrate that a Weyl point, widely examined in 3D Weyl semimetals and
superfluids, can develop a pair of non-degenerate gapless spheres. Such a {\em
bouquet of two spheres} is characterized by {\em three distinct} topological
invariants of manifolds with full energy gaps, i.e., the Chern number of a 0D
point inside one developed sphere, the winding number of a 1D loop around the
original Weyl point, and the Chern number of a 2D surface enclosing the whole
bouquet. We show that such structured Weyl points can be realized in the
Fulde-Ferrell superfluid quasiparticle spectrum of a 3D degenerate Fermi gas
subject to spin-orbit couplings and Zeeman fields.

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Author(s):

In this paper we demonstrate under what conditions a pseudo-spin degree of
freedom or character can be ascribed to the Majorana bound states (MBS) which
can be created at the end of one dimensional non-interacting systems,
corresponding to D, DIII and BDI in the usual classification scheme. We have
found that such a character is directly related to the class of the topological
superconductor and its description by a $\mathbb{Z}$, rather than a
$\mathbb{Z}_2$, invariant which corresponds to the BDI class. We have also
found that the DIII case with mirror symmetry, which supports multiple MBS, is
in fact equivalent to the BDI class with an additional time-reversal symmetry.
In all cases where a character can be given to the Majorana states we show how
to construct the appropriate operator explicitly in various examples. We also
examine the consequences of the Majorana character by considering possible
hybridization of MBS brought into proximity and find that two MBS with the same
character do not hybridize. Finally, we show that having this character or not
has no consequence on the braiding properties of MBS.

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Author(s):

We establish that Majorana fermions on the boundary of topological
superconductors have only spin-triplet superconducting correlations independent
of whether the bulk superconducting gap is spin singlet or triplet. This is
universal for all topological superconductors (TSCs) as long as they have on
the boundary an odd number of Majorana fermions for D class and an odd number
of pairs of Majorana fermions for DIII class. Consequently, the resonant
Andreev reflection induced by Majorana fermions only occurs in spin-triplet
channels and always injects spin-triplet Cooper pairs into the leads. This
spin-triplet condensate results in the spin-orbit coupling (SOC) controlled
oscillatory critical current without $0-\pi$ transition in the
TSC/SOC-semiconductor/TSC Josephson junction. The observation of this unique
current-phase relation can serve as the definitive signal for Majorana
fermions. Our study opens a new technique to manipulate Majorana fermions based
on their spin-triplet superconducting correlations.

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Author(s):

We address the question of whether individual nonmagnetic impurities can
induce zero-energy states in time reversal invariant topological
superconductors, and define a class of symmetries which guarantee the existence
of such states for a specific value of the impurity strength. These symmetries
allow the definition of a position space topological Z_2 invariant, which is
related to the standard bulk topological Z_2 invariant. Our general results are
applied to the time reversal invariant p-wave phase of the doped
Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can
drive a topologically trivial system into the non-trivial phase.

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Author(s):

We propose a method of measuring topological invariants of a photonic crystal
through phase spectroscopy. We show how the Chern numbers can be deduced from
the winding numbers of the reflection coefficient phase. An explicit proof of
existence of edge states in system with nonzero reflection phase winding number
is given. The method is illustrated for one- and two-dimensional photonic
crystals of nontrivial topology.

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Author(s):

Twisting symmetries provides an efficient method to diagnose
symmetry-protected topological (SPT) phases. In this paper, edge theories of
(2+1)-dimensional topological phases protected by reflection as well as other
symmetries are studied by twisting reflection symmetry, which effectively puts
the edge theories on an unoriented spacetime, such as the Klein bottle. A key
technical step taken in this paper is the use of the so-called cross-cap
states, which encode entirely the unoriented nature of spacetime, and can be
obtained by rearranging the spacetime geometry and exchanging the role of space
and time coordinates. When the system is in a non-trivial SPT phase, we find
that the corresponding cross-cap state is non-invariant under the action of the
symmetries of the SPT phase, but acquires an anomalous phase. This anomalous
phase, with a proper definition of a reference state, on which symmetry acts
trivially, reproduces the known classification of (2+1)-dimensional bosonic and
fermionic SPT phases protected by reflection symmetry, including in particular
the Z_8 classification of topological crystalline superconductors protected by
reflection and time-reversal symmetries.

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Author(s):

Experimental identification of three-dimensional (3D) Dirac semimetals in
solid state systems is critical for realizing exotic topological phenomena and
quantum transport such as the Weyl phases, high temperature linear quantum
magnetoresistance and topological magnetic phases. Using high resolution
angle-resolved photoemission spectroscopy, we performed systematic electronic
structure studies on well-known compound Cd3As2. For the first time, we observe
a highly linear bulk Dirac cone located at the Brillouin zone center projected
onto the (001) surface which is consistent with a 3D Dirac semimetal phase in
Cd3As2. Remarkably, an unusually high Dirac Fermion velocity up to 10.2
\textrm{\AA}{\cdot}$eV (1.5 \times 10^{6} ms^-1) is seen in samples where the
mobility far exceeds 40,000 cm^2/V.s suggesting that Cd3As2 can be a promising
candidate as a hypercone analog of graphene in many device-applications which
can also incorporate topological quantum phenomena in a large gap setting. Our
experimental identification of this novel topological 3D Dirac semimetal phase,
distinct from a 3D topological insulator phase discovered previously, paves the
way for exploring higher dimensional relativistic physics in bulk transport and
for realizing novel Fermionic matter such as a Fermi arc nodal metal.

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Author(s):

Authors: Yong Xu, Fan Zhang, Chuanwei Zhang

We demonstrate that a Weyl point, widely examined in 3D Weyl semimetals and
superfluids, can develop a pair of non-degenerate gapless spheres. Such a {\em
bouquet of two spheres} is characterized by {\em three distinct} topological
invariants of manifolds with full energy gaps, i.e., the Chern number of a 0D
point inside one developed sphere, the winding number of a 1D loop around the
original Weyl point, and the Chern number of a 2D surface enclosing the whole
bouquet. We show that such structured Weyl points can be realized in the
Fulde-Ferrell superfluid quasiparticle spectrum of a 3D degenerate Fermi gas
subject to spin-orbit couplings and Zeeman fields.

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Author(s):

Authors: N. Sedlmayr, M. Guigou, P. Simon, C. Bena

In this paper we demonstrate under what conditions a pseudo-spin degree of
freedom or character can be ascribed to the Majorana bound states (MBS) which
can be created at the end of one dimensional non-interacting systems,
corresponding to D, DIII and BDI in the usual classification scheme. We have
found that such a character is directly related to the class of the topological
superconductor and its description by a $\mathbb{Z}$, rather than a
$\mathbb{Z}_2$, invariant which corresponds to the BDI class. We have also
found that the DIII case with mirror symmetry, which supports multiple MBS, is
in fact equivalent to the BDI class with an additional time-reversal symmetry.
In all cases where a character can be given to the Majorana states we show how
to construct the appropriate operator explicitly in various examples. We also
examine the consequences of the Majorana character by considering possible
hybridization of MBS brought into proximity and find that two MBS with the same
character do not hybridize. Finally, we show that having this character or not
has no consequence on the braiding properties of MBS.

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Author(s):

Authors: Xin Liu, Jay D. Sau, S. Das Sarma

We establish that Majorana fermions on the boundary of topological
superconductors have only spin-triplet superconducting correlations independent
of whether the bulk superconducting gap is spin singlet or triplet. This is
universal for all topological superconductors (TSCs) as long as they have on
the boundary an odd number of Majorana fermions for D class and an odd number
of pairs of Majorana fermions for DIII class. Consequently, the resonant
Andreev reflection induced by Majorana fermions only occurs in spin-triplet
channels and always injects spin-triplet Cooper pairs into the leads. This
spin-triplet condensate results in the spin-orbit coupling (SOC) controlled
oscillatory critical current without $0-\pi$ transition in the
TSC/SOC-semiconductor/TSC Josephson junction. The observation of this unique
current-phase relation can serve as the definitive signal for Majorana
fermions. Our study opens a new technique to manipulate Majorana fermions based
on their spin-triplet superconducting correlations.

link to article (opens in new tab)

 

Author(s):

Authors: Lukas Kimme, Timo Hyart, Bernd Rosenow

We address the question of whether individual nonmagnetic impurities can
induce zero-energy states in time reversal invariant topological
superconductors, and define a class of symmetries which guarantee the existence
of such states for a specific value of the impurity strength. These symmetries
allow the definition of a position space topological Z_2 invariant, which is
related to the standard bulk topological Z_2 invariant. Our general results are
applied to the time reversal invariant p-wave phase of the doped
Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can
drive a topologically trivial system into the non-trivial phase.

link to article (opens in new tab)

 

Author(s):

Authors: A. V. Poshakinskiy, A. N. Poddubny, M. Hafezi

We propose a method of measuring topological invariants of a photonic crystal
through phase spectroscopy. We show how the Chern numbers can be deduced from
the winding numbers of the reflection coefficient phase. An explicit proof of
existence of edge states in system with nonzero reflection phase winding number
is given. The method is illustrated for one- and two-dimensional photonic
crystals of nontrivial topology.

link to article (opens in new tab)

 

Author(s):

Authors: Gil Young Cho, Chang-Tse Hsieh, Takahiro Morimoto, Shinsei Ryu

Twisting symmetries provides an efficient method to diagnose
symmetry-protected topological (SPT) phases. In this paper, edge theories of
(2+1)-dimensional topological phases protected by reflection as well as other
symmetries are studied by twisting reflection symmetry, which effectively puts
the edge theories on an unoriented spacetime, such as the Klein bottle. A key
technical step taken in this paper is the use of the so-called cross-cap
states, which encode entirely the unoriented nature of spacetime, and can be
obtained by rearranging the spacetime geometry and exchanging the role of space
and time coordinates. When the system is in a non-trivial SPT phase, we find
that the corresponding cross-cap state is non-invariant under the action of the
symmetries of the SPT phase, but acquires an anomalous phase. This anomalous
phase, with a proper definition of a reference state, on which symmetry acts
trivially, reproduces the known classification of (2+1)-dimensional bosonic and
fermionic SPT phases protected by reflection symmetry, including in particular
the Z_8 classification of topological crystalline superconductors protected by
reflection and time-reversal symmetries.

link to article (opens in new tab)

 

Author(s):

Authors: Madhab Neupane, SuYang Xu, R. Sankar, N. Alidoust, G. Bian, Chang Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, Fangcheng Chou, M. Zahid Hasan

Experimental identification of three-dimensional (3D) Dirac semimetals in
solid state systems is critical for realizing exotic topological phenomena and
quantum transport such as the Weyl phases, high temperature linear quantum
magnetoresistance and topological magnetic phases. Using high resolution
angle-resolved photoemission spectroscopy, we performed systematic electronic
structure studies on well-known compound Cd3As2. For the first time, we observe
a highly linear bulk Dirac cone located at the Brillouin zone center projected
onto the (001) surface which is consistent with a 3D Dirac semimetal phase in
Cd3As2. Remarkably, an unusually high Dirac Fermion velocity up to 10.2
\textrm{\AA}{\cdot}$eV (1.5 \times 10^{6} ms^-1) is seen in samples where the
mobility far exceeds 40,000 cm^2/V.s suggesting that Cd3As2 can be a promising
candidate as a hypercone analog of graphene in many device-applications which
can also incorporate topological quantum phenomena in a large gap setting. Our
experimental identification of this novel topological 3D Dirac semimetal phase,
distinct from a 3D topological insulator phase discovered previously, paves the
way for exploring higher dimensional relativistic physics in bulk transport and
for realizing novel Fermionic matter such as a Fermi arc nodal metal.

link to article (opens in new tab)

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