Author(s):

Authors: Zhen Gao, Wei-Jiang Gong

We discuss the change of the Kondo effect in the Josephson junction formed by
the indirect coupling between a one-dimensional \emph{DIII}-class topological
and s-wave superconductors via a quantum dot. By performing the
Schrieffer-Wolff transformation, we find that the single-electron occupation in
the quantum dot induces various correlation modes, such as the Kondo and
singlet-triplet correlations between the quantum dot and the $s$-wave
superconductor and the spin exchange correlation between the dot and Majorana
doublet. Moreover, it plays a nontrivial role in modifying the Josephson
effect, leading to the occurrence of anisotropic and high-order Kondo
correlation. In addition, due to the quantum dot in the Kondo regime, extra
spin exchange correlations contribute to the Josephson effect as well.
Nevertheless, if the \emph{DIII}-class topological superconductor degenerates
into \emph{D}-class because of the destruction of time-reversal invariance, all
such terms will disappear completely. We believe that this work shows the
fundamental difference between the \emph{D}- and \emph{DIII}-class topological
superconductors.

link to article (opens in new tab)

 

Author(s):

Authors: Zihao Gao, Meng Hua, Haijun Zhang, Xiao Zhang

Three dimensional (3D) Dirac semimetal is a novel state of quantum matter,
characterized by the gapless bulk four-fold degeneracy near Fermi energy. Soon
after its discovery, the classification of stable 3D Dirac semimetals with
inversion and rotational symmetry have been studied. However, only ten out of
thirty-two point groups have both inversion and rotational symmetry, and we
need a more complete classification of stable 3D Dirac semimetals. Here we
classify stable 3D Dirac semimetals with reflection symmetry and rotational
symmetry in the presence of time reversal symmetry, which belong to seventeen
different point groups. These systems include the systems preserving inversion
symmetry expect $\mathrm{C_{3i}}$. They have two classes of reflection
symmetry, with the mirror plane parallel to rotation axis and the mirror plane
perpendicular to rotation axis. In both cases two types of Dirac semimetals are
determined by five different reflection symmetries. The first type of Dirac
semimetals will appear through accidental band crossing (ABC). The second type
of Dirac semimetals have a Dirac point at a time reversal invariant momentum
(TBC). We show that only in the mirror perpendicular case, $C_{2}$ symmetry can
protect stable Dirac points (TBC) and in both cases, systems with $C_{3}$
symmetry can only have TBC and with $C_{4,6}$ symmetry can have stable Dirac
points as ABC or TBC. We further discuss that Weyl line nodes and Dirac
semimetal can exist in Brillouin zone at the same time using $\mathrm{C_{4v}}$
symmetry as an example. Finally we classify Dirac line nodes and Weyl line
nodes to show in which types of mirror plane they can exist.

link to article (opens in new tab)

 

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 time-reversal broken (respected) topological superconductors
(TSCs) with an odd number of (pairs of) Majorana fermions on the boundary.
Consequently, 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 a spin-orbit coupling
(SOC) controlled oscillatory critical current without a $0$-$\pi$ 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 shows a technique for manipulating Majorana fermions based
on their spin-triplet superconducting correlations.

link to article (opens in new tab)

 

Author(s):

Authors: Soumya Bera, Jay D. Sau, Bitan Roy

We study the stability of three-dimensional incompressible Weyl semimetals in
the presence of random quenched charge impurities. Using numerical analysis and
scaling theory we show that in the presence of sufficiently weak randomness (i)
Weyl semimetal remains stable, while (ii) the double-Weyl semimetal gives rise
to compressible diffusive metal where the mean density of states at vanishing
energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum
phase transition and enter into a metallic phase. Mean density of states at
zero energy serves as the order parameter and displays single-parameter scaling
across such disorder driven phase transition. We numerically determine various
exponents at the critical point, which appear to be insensitive to the number
of Weyl pairs, and also extract the extent of the quantum critical regime at
finite energy.

link to article (opens in new tab)

 

Author(s):

Authors: Jing Wang, Biao Lian, Xiao-Liang Qi, Shou-Cheng Zhang

Topological magnetoelectric effect in a three-dimensional topological
insulator is a novel phenomenon, where an electric field induces a magnetic
field in the same direction, with a universal coefficient of proportionality
quantized in units of $e^2/2h$. Here we propose that the topological
magnetoelectric effect can be realized in the zero-plateau quantum anomalous
Hall state of magnetic topological insulators or ferromagnet-topological
insulator heterostructure. The finite-size effect is also studied numerically,
where the magnetoelectric coefficient is shown to converge to a quantized value
when the thickness of topological insulator film increases. We further propose
a device setup to eliminate the non-topological contributions from the side
surface.

link to article (opens in new tab)

 

Author(s):

Authors: Stefano Longhi, Davide Gatti, Giuseppe Della Valle

Unidirectional and robust transport is generally observed at the edge of two-
or three-dimensional quantum Hall and topological insulator systems. A hallmark
of these systems is topological protection, i.e. the existence of propagative
edge states that cannot be scattered by imperfections or disorder in the
system. A different and less explored form of robust transport arises in
non-Hermitian systems in the presence of an {\it imaginary} gauge field. As
compared to topologically-protected transport in quantum Hall and topological
insulator systems, robust non-Hermitian transport can be observed in {\it
lower} dimensional (i.e. one dimensional) systems. In this work the transport
properties of one-dimensional tight-binding lattices with an imaginary gauge
field are theoretically investigated, and the physical mechanism underlying
robust one-way transport is highlighted. Back scattering is here forbidden
because reflected waves are evanescent rather than propagative. Remarkably, the
spectral transmission of the non-Hermitian lattice is shown to be mapped into
the one of the corresponding Hermitian lattice, i.e. without the gauge field,
{\it but} computed in the complex plane. In particular, at large values of the
gauge field the spectral transmittance becomes equal to one, even in the
presence of disorder or lattice imperfections, a phenomenon that can be
referred to as {\it one-way non-Hermitian transparency}. Robust one-way
transport can be also realized in a more realistic setting, namely in
heterostructure systems, in which a non-Hermitian disordered lattice is
embedded between two homogeneous Hermitian lattices. Such a double
heterostructure realizes asymmetric (non-reciprocal) wave transmission.

link to article (opens in new tab)

 

Author(s):

We discuss the change of the Kondo effect in the Josephson junction formed by
the indirect coupling between a one-dimensional \emph{DIII}-class topological
and s-wave superconductors via a quantum dot. By performing the
Schrieffer-Wolff transformation, we find that the single-electron occupation in
the quantum dot induces various correlation modes, such as the Kondo and
singlet-triplet correlations between the quantum dot and the $s$-wave
superconductor and the spin exchange correlation between the dot and Majorana
doublet. Moreover, it plays a nontrivial role in modifying the Josephson
effect, leading to the occurrence of anisotropic and high-order Kondo
correlation. In addition, due to the quantum dot in the Kondo regime, extra
spin exchange correlations contribute to the Josephson effect as well.
Nevertheless, if the \emph{DIII}-class topological superconductor degenerates
into \emph{D}-class because of the destruction of time-reversal invariance, all
such terms will disappear completely. We believe that this work shows the
fundamental difference between the \emph{D}- and \emph{DIII}-class topological
superconductors.

link to article (opens in new tab)

 

Author(s):

Three dimensional (3D) Dirac semimetal is a novel state of quantum matter,
characterized by the gapless bulk four-fold degeneracy near Fermi energy. Soon
after its discovery, the classification of stable 3D Dirac semimetals with
inversion and rotational symmetry have been studied. However, only ten out of
thirty-two point groups have both inversion and rotational symmetry, and we
need a more complete classification of stable 3D Dirac semimetals. Here we
classify stable 3D Dirac semimetals with reflection symmetry and rotational
symmetry in the presence of time reversal symmetry, which belong to seventeen
different point groups. These systems include the systems preserving inversion
symmetry expect $\mathrm{C_{3i}}$. They have two classes of reflection
symmetry, with the mirror plane parallel to rotation axis and the mirror plane
perpendicular to rotation axis. In both cases two types of Dirac semimetals are
determined by five different reflection symmetries. The first type of Dirac
semimetals will appear through accidental band crossing (ABC). The second type
of Dirac semimetals have a Dirac point at a time reversal invariant momentum
(TBC). We show that only in the mirror perpendicular case, $C_{2}$ symmetry can
protect stable Dirac points (TBC) and in both cases, systems with $C_{3}$
symmetry can only have TBC and with $C_{4,6}$ symmetry can have stable Dirac
points as ABC or TBC. We further discuss that Weyl line nodes and Dirac
semimetal can exist in Brillouin zone at the same time using $\mathrm{C_{4v}}$
symmetry as an example. Finally we classify Dirac line nodes and Weyl line
nodes to show in which types of mirror plane they can exist.

link to article (opens in new tab)

 

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 time-reversal broken (respected) topological superconductors
(TSCs) with an odd number of (pairs of) Majorana fermions on the boundary.
Consequently, 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 a spin-orbit coupling
(SOC) controlled oscillatory critical current without a $0$-$\pi$ 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 shows a technique for manipulating Majorana fermions based
on their spin-triplet superconducting correlations.

link to article (opens in new tab)

 

Author(s):

We study the stability of three-dimensional incompressible Weyl semimetals in
the presence of random quenched charge impurities. Using numerical analysis and
scaling theory we show that in the presence of sufficiently weak randomness (i)
Weyl semimetal remains stable, while (ii) the double-Weyl semimetal gives rise
to compressible diffusive metal where the mean density of states at vanishing
energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum
phase transition and enter into a metallic phase. Mean density of states at
zero energy serves as the order parameter and displays single-parameter scaling
across such disorder driven phase transition. We numerically determine various
exponents at the critical point, which appear to be insensitive to the number
of Weyl pairs, and also extract the extent of the quantum critical regime at
finite energy.

link to article (opens in new tab)

 

Author(s):

Topological magnetoelectric effect in a three-dimensional topological
insulator is a novel phenomenon, where an electric field induces a magnetic
field in the same direction, with a universal coefficient of proportionality
quantized in units of $e^2/2h$. Here we propose that the topological
magnetoelectric effect can be realized in the zero-plateau quantum anomalous
Hall state of magnetic topological insulators or ferromagnet-topological
insulator heterostructure. The finite-size effect is also studied numerically,
where the magnetoelectric coefficient is shown to converge to a quantized value
when the thickness of topological insulator film increases. We further propose
a device setup to eliminate the non-topological contributions from the side
surface.

link to article (opens in new tab)

 

Author(s):

Unidirectional and robust transport is generally observed at the edge of two-
or three-dimensional quantum Hall and topological insulator systems. A hallmark
of these systems is topological protection, i.e. the existence of propagative
edge states that cannot be scattered by imperfections or disorder in the
system. A different and less explored form of robust transport arises in
non-Hermitian systems in the presence of an {\it imaginary} gauge field. As
compared to topologically-protected transport in quantum Hall and topological
insulator systems, robust non-Hermitian transport can be observed in {\it
lower} dimensional (i.e. one dimensional) systems. In this work the transport
properties of one-dimensional tight-binding lattices with an imaginary gauge
field are theoretically investigated, and the physical mechanism underlying
robust one-way transport is highlighted. Back scattering is here forbidden
because reflected waves are evanescent rather than propagative. Remarkably, the
spectral transmission of the non-Hermitian lattice is shown to be mapped into
the one of the corresponding Hermitian lattice, i.e. without the gauge field,
{\it but} computed in the complex plane. In particular, at large values of the
gauge field the spectral transmittance becomes equal to one, even in the
presence of disorder or lattice imperfections, a phenomenon that can be
referred to as {\it one-way non-Hermitian transparency}. Robust one-way
transport can be also realized in a more realistic setting, namely in
heterostructure systems, in which a non-Hermitian disordered lattice is
embedded between two homogeneous Hermitian lattices. Such a double
heterostructure realizes asymmetric (non-reciprocal) wave transmission.

link to article (opens in new tab)

 

Author(s): Hai-Yao Deng and Katsunori Wakabayashi

Retardation effects (REs) are known to cause a crossover from linear to sublinear behaviors in the dispersion relation of two-dimensional (2D) plasma waves at long wavelengths. In the present work, we systematically analyze REs on plasma waves in both 2D and 1D electron gases, and we clarify the exp…


[Phys. Rev. B 92, 045434] Published Tue Jul 28, 2015

link to article (opens in new tab)

 

Author(s): Yuval Baum, Thore Posske, Ion Cosma Fulga, Björn Trauzettel, and Ady Stern

The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two-dimensional Hamiltonians that yield an unusual class D topological superconductor with a gapless bulk spectrum but well-localiz…


[Phys. Rev. B 92, 045128] Published Tue Jul 28, 2015

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Author(s): Joseph Weston, Benoit Gaury, and Xavier Waintal

We study the interplay between Andreev (Majorana) bound states that form at the boundary of a (topological) superconductor and a train of microwave pulses. We find that the extra dynamical phase coming from the pulses can shift the phase of the Andreev reflection, resulting in the appearance of dyna…


[Phys. Rev. B 92, 020513(R)] Published Tue Jul 28, 2015

link to article (opens in new tab)

 

Author(s):

We study collective plasmon excitations and screening of disordered single-
and bilayer black phosphorus beyond the low energy continuum approximation. The
dynamical polarizability of phosphorene is computed using a tight-binding model
that properly accounts for the band structure in a wide energy range.
Electron-electron interaction is considered within the Random Phase
Approximation. Damping of the plasmon modes due to different kinds of disorder,
such as resonant scatterers and long-range disorder potentials, is analyzed. We
further show that an electric field applied perpendicular to bilayer
phosphorene can be used to tune the dispersion of the plasmon modes. For
sufficiently large electric field, the bilayer BP enters in a topological phase
with a characteristic plasmon spectrum, which is gaped in the armchair
direction.

link to article (opens in new tab)

 

Author(s):

Three dimensional (3D) Dirac semimetal is a novel state of quantum matter,
characterized by the gapless bulk four-fold degeneracy near Fermi energy. Soon
after its discovery, the classification of stable 3D Dirac semimetals with
inversion and rotational symmetry have been studied. However, only ten out of
thirty-two point groups have both inversion and rotational symmetry, and we
need a more complete classification of stable 3D Dirac semimetals. Here we
classify stable 3D Dirac semimetals with reflection symmetry and rotational
symmetry in the presence of time reversal symmetry, which belong to seventeen
different point groups. These systems include the systems preserving inversion
symmetry expect $\mathrm{C_{3i}}$. They have two classes of reflection
symmetry, with the mirror plane parallel to rotation axis and the mirror plane
perpendicular to rotation axis. In both cases two types of Dirac semimetals are
determined by five different reflection symmetries. The first type of Dirac
semimetals will appear through accidental band crossing (ABC). The second type
of Dirac semimetals have a Dirac point at a time reversal invariant momentum
(TBC). We show that only in the mirror perpendicular case, $C_{2}$ symmetry can
protect stable Dirac points (TBC) and in both cases, systems with $C_{3}$
symmetry can only have TBC and with $C_{4,6}$ symmetry can have stable Dirac
points as ABC or TBC. We further discuss that Weyl line nodes and Dirac
semimetal can exist in Brillouin zone at the same time using $\mathrm{C_{4v}}$
symmetry as an example. Finally we classify Dirac line nodes and Weyl line
nodes to show in which types of mirror plane they can exist.

link to article (opens in new tab)

 

Author(s):

We investigate the Josephson effect in one triple-terminal junction with
embedded parallel-coupled double quantum dots. It is found that the
inter-superconductor supercurrent has opportunities to oscillate in $4\pi$
period, with the adjustment of the phase differences among the superconductors.
What is notable is that such a result is robust and independent of fermion
parities, intradot Coulomb strength, and the dot-superconductor coupling
manner. By introducing the concept of spinful many-particle Majorana modes, we
present the analytical definition of the Majorana operator via superposing
electron and hole operators. It can be believed that this work provide a simple
but feasible proposal for the realization of Majorana modes in a nonmagnetic
system.

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Author(s):

Single crystals of $(Cd_{1-x} Zn_x)_3 As_2$ were synthesized from
high-temperature solutions and characterized in terms of their structural and
electrical properties. Based on the measurements of resistivity and Hall
signals, we revealed a chemical-doping-controlled transition from a three
dimensional Dirac semimetal to a semiconductor with a critical point $x_c/sim
0.38$. We observed structural transitions from a body-center tetragonal phase
to a primary tetragonal phase then back to a body-center tetragonal phase in
the solid solutions as well, which are irrelevant to the topological phase
transition. This continuously tunable system controlled by chemical doping
provides a platform for investigating the topological quantum phase transition
of 3D Dirac electrons.

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Author(s):

Recently we introduced T-duality in the study of topological insulators. In
this paper, we study the bulk-boundary correspondence for three phenomena in
condensed matter physics, namely, the quantum Hall effect, the Chern insulator,
and time reversal invariant topological insulators. In all of these cases, we
show that T-duality trivializes the bulk-boundary correspondence.

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