Author(s):

Authors: Yong Xu, Chuanwei Zhang

The experimental observation of traditional Zeeman-field induced
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by
various challenges, in particular, the requirement of low dimension systems. In
2D, it is well known that finite temperature phase fluctuations lead to
extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature,
raising serious concern regarding the observability of 2D FFLO superfluids.
Recently, it was shown that FFLO superfluids can be realized using a Rashba
spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support
topological excitations such as Majorana fermions in 2D. Here we address the
finite temperature BKT transition issue in this system, which may exhibits
gapped, gapless, topological, and gapless topological FF phases. We find a
large BKT transition temperature due to large effective superfluid densities,
making it possible to observe 2D FF superfluids at finite temperature. In
addition, we show that gapless FF superfluids can be stable due to their
positive superfluid densities. These findings pave the way for the experimental
observation of 2D gapped and gapless FF superfluids and their associated
topological excitations at finite temperature.

link to article (opens in new tab)

 

Author(s):

Authors: Sutirtha Mukherjee, J. K. Jain, Sudhansu S. Mandal

There is much interest in the realization of systems with p-wave pairing in
one dimension or chiral p-wave pairing in two dimensions, because these are
believed to support Majorana modes at the ends or inside vortices. We consider
a two component system of composite fermions and provide theoretical evidence
that, under appropriate conditions, the screened interaction between the
minority composite fermions is such as to produce an almost exact realization
of p-wave paired state described by the so-called anti-Pfaffian wave function.
This state is predicted to occur at filling $\nu=3/8$ or 13/8 in GaAs when the
Zeeman energy is sufficiently small, and at $\nu=\pm 3/8$ or $\pm 13/8$ in
single layer graphene when either the Zeeman or the valley splitting is
sufficiently small.

link to article (opens in new tab)

 

Author(s):

Authors: Qi-Feng Liang, Rui Yu, Jian Zhou, Xiao Hu

We demonstrate the possibility of topological states for non-Dirac electrons.
Specifically it is shown that, because of the $C_{\rm 3}$ crystal symmetry and
time reversal symmetry, $p_x$ and $p_y$ orbits accommodated on triangular
lattice exhibit a quadratic band touching at $\Gamma$ point at the Fermi level.
When the atomic spin-orbit coupling (SOC) is taken into account, a gap is
opened resulting in a quantum spin Hall effect state. As revealed explicitly by
a $k\cdot p$ model, the topology is associated with a meron structure in the
pseudo spin texture with vorticity two, a mechanism different from honeycomb
lattice and the band inversion. One possible realization of this scheme is the
1/3 coverage by Bi atom adapted on the Si[111] surface. First-principle
calculations are carried out, and a global gap of $\sim 0.15$eV is observed.
With the Si substrate taking part in realizing the nontrivial topology, the
present template is expected to make the integration of topological states into
existing electronics and photonics technologies promising.

link to article (opens in new tab)

 

Author(s):

Authors: Anna Novelli, Wolfgang Belzig, Abraham Nitzan

The time evolution and the asymptotic outcome of a
Landau-Zener-Stueckelberg-Majorana (LZ) process under continuous weak
non-selective measurement is analyzed. We compare two measurement protocols in
which the populations of either the adiabatic or the non-adiabatic levels are
(continuously and weakly) monitored. The weak measurement formalism, described
using a Gaussian Kraus operator, leads to a time evolution characterized by a
Markovian dephasing process, which, in the non-adiabatic measurement protocol
is similar to earlier studies of LZ dynamics in a dephasing environment.
Casting the problem in the language of measurement theory makes it possible for
us to compare diabatic and adiabatic measurement scenarios, to consider
engineered dephasing as a control device and to examine the manifestation of
the Zeno effect under the different measurement protocols. In particular, under
measurement of the non- adiabatic populations, the Zeno effect is manifested
not as a freezing of the measured system in its initial state, but rather as an
approach to equal asymptotic populations of the two diabatic states. This
behavior can be traced to the way by which the weak measurement formalism
behaves in the strong measurement limit, with a built-in relationship between
measurement time and strength.

link to article (opens in new tab)

 

Author(s):

Authors: Gil Young Cho, Onkar Parrikar, Yizhi You, Robert G. Leigh, Taylor L. Hughes

Motivated by recent progress in understanding the interplay between lattice
and electronic topological phases, we consider quantum-melting transitions of
{\it weak} quantum liquid crystals, a crystal and a nematic phase, in which
electrons form a quantum Hall state. In certain classes of Chern band
insulators and quantum Hall phases, it has been previously demonstrated that
there are topological Chern-Simons terms such as a Hall viscosity term and a
gravitational Chern-Simons term for local lattice deformations. The
Chern-Simons terms can induce anyonic statistics for the topological lattice
defects and furthermore dress the defects with certain symmetry quantum
numbers. On the other hand, the melting transitions of such liquid-crystalline
orders are driven by the condensation of lattice defects. Based on these
observations, we show how the topological terms can change the nature of the
proximate disordered phases of the quantum liquid crystalline phases. We derive
and study the effective dual field theories for the liquid crystalline phases
with the geometric Chern-Simons terms, and carefully examine the symmetry
quantum numbers and statistics of defects. We show that a crystal may go
through a continuous phase transition into another crystal with the new
discrete translational symmetries because the dislocation, the topological
defect in the crystal, carries non-zero crystal momentum due to the Hall
viscosity term. For the nematic phase, the disclination will condense at the
phase transition to the isotropic phase, and we show that the isotropic phase
may support a deconfined fractionally charged excitation due to the Wen-Zee
term, and thus the isotropic phase and the nematic phase have different
electromagnetic Hall responses.

link to article (opens in new tab)

 

Author(s):

Authors: Hoi-Yin Hui, P. M. R. Brydon, Jay D. Sau, S. Tewari, S. Das Sarma

We establish theoretically that a ferromagnetic wire deposited on the surface
of a spin-orbit coupled $s$-wave superconductor generically supports
zero-energy topological Majorana fermion (MF) excitations near the two ends of
the wire. Depending on the strength of the ferromagnetic moment in the wire,
the number of MFs at each end, $n$, can be either one or two, and should be
revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning
tunneling microscopy (STM) measurements which would show strong (weak) signals
at the ends (middle) of the wire. The underlying physics of this system, which
is distinct from that of the well-studied spin-orbit-coupled
semiconductor-superconductor heterostructures in the presence of an applied
magnetic field, is discussed in terms of a topological chiral symmetry in BDI
class with an integer topological invariant. Our work introduces a new
platform, namely a magnetic metal-superconductor heterostructure, in the race
for finding a Majorana-carrying topological superconductor.

link to article (opens in new tab)

 

Author(s):

Authors: Lode Pollet, Anatoly Kuklov

The ground state of $^4$He confined in a system with the topology of a
cylinder can display properties of a solid, superfluid and liquid crystal. This
phase, which we call compactified supersolid (CSS), originates from wrapping
the basal planes of the bulk hcp solid into concentric cylindrical shells, with
several central shells exhibiting superfluidity along the axial direction. Its
main feature is the presence of a topological defect which can be viewed as a
disclination with Frank index $n=1$ observed in liquid crystals, and which, in
addition, has a superfluid core. The CSS as well as its transition to an
insulating compactified solid with a very wide hysteresis loop are found by ab
initio Monte Carlo simulations. A simple analytical model captures
qualitatively correctly the main property of the CSS — a gradual decrease of
the superfluid response with increasing pressure.

link to article (opens in new tab)

 

Author(s):

Authors: Yasaman Bahri, Ashvin Vishwanath

Topological phases which host Majorana fermions can not be identified via
local order parameters. We give simple nonlocal order parameters to distinguish
quasi-one-dimensional (1D) topological superconductors of spinless fermions,
for any interacting model in the absence of time reversal symmetry. These
string or “brane” order parameters are natural for measurements in cold atom
systems using quantum gas microscopy. We propose them as a way to identify
symmetry-protected topological phases of Majorana fermions in cold atom
experiments via bulk rather than edge degrees of freedom. Subsequently, we
study two-dimensional (2D) topological superconductors via the quasi-1D limit
of coupling $N$ identical chains on the cylinder. We classify the symmetric,
interacting topological phases protected by the additional $\mathbb{Z}_N$
translation symmetry. The phases include quasi-1D analogs of (i) the $p+ip$
chiral topological superconductor, which can be distinguished up to the 2D
Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise
general rules for constructing nonlocal order parameters which distinguish the
phases. These rules encode the signature of the fermionic topological phase in
the symmetry properties of the terminating operators of the nonlocal string or
brane. The nonlocal order parameters for some of these phases simply involve a
product of the string order parameters for the individual chains. Finally, we
give a physical picture of one of the topological phases as a condensate of
certain defects, which motivates the form of the nonlocal order parameter and
is reminiscent of higher dimensional constructions of topological phases.

link to article (opens in new tab)

 

Author(s):

Authors: Jun Hu, Zhenyue Zhu, Ruqian Wu

The search of new topological insulators that demonstrate the quantum
anomalous Hall effect (QAHE) is a cutting-edge research topic in condensed
matter physics and materials science. So far, the QAHE has been observed only
in Cr-doped (Bi,Sb)2Te3 at extremely low temperature. Therefore, it is
important to find new materials with large topological band gap and high
thermal stability for the realization of the QAHE. Based on first-principles
and tight-binding model calculations, we discovered a new class of topological
phase$-$Chern half metal which manifests the QAHE in one spin channel while is
metallic in the other spin channel$-$in Co or Rh deposited graphene. Meanwhile,
these systems have large perpendicular magnetic anisotropy energies of 5.3 and
11.5 meV, necessary for the observation of the QAHE at reasonably high
temperature.

link to article (opens in new tab)

 

Author(s):

Authors: Udit Khanna, Arijit Kundu, Saurabh Pradhan, Sumathi Rao

We introduce superconducting proximity effects in Weyl semi-metals (WSM) with
broken time reversal symmetry by tunnel coupling one of its surfaces to an
$s$-wave superconductor using the Green’s function approach. We find that the
band structure develops coherence peaks, but despite the presence of metallic
states in the bulk, the coherence peaks do not extend far into the bulk and
remain confined to a few layers close to the interface, similar to the
proximity effect in the topological insulators (TI) which are gapped in the
bulk. The Weyl nodes remain unaffected, and in that sense, no true gap
develops. We also study the various induced $p$ and $s$-wave pairing amplitudes
classified by their symmetries, as a function of the various relevant
parameters of the theory and note the exponential decay of the induced pairings
in the bulk both in the TI and the WSM, even at finite chemical potential.

link to article (opens in new tab)

 

Author(s):

Authors: Onkar Parrikar, Taylor L. Hughes, Robert G. Leigh

We study the response of a class of topological systems to electromagnetic
and gravitational sources, including torsion and curvature. By using the
technology of anomaly polynomials, we derive the parity-odd response of a
massive Dirac fermion in $d=2+1$ and $d=4+1$, which provides a simple model for
a topological insulator. We discuss the covariant anomalies of the
corresponding edge states, from a Callan-Harvey anomaly-inflow, as well as a
Hamiltonian spectral flow point of view. We also discuss the applicability of
our results to other systems such as Weyl semi-metals. Finally, using
dimensional reduction from $d=4+1$, we derive the effective action for a
$d=3+1$ time-reversal invariant topological insulator in the presence of
torsion and curvature, and discuss its various physical consequences.

link to article (opens in new tab)

 

Author(s):

The experimental observation of traditional Zeeman-field induced
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by
various challenges, in particular, the requirement of low dimension systems. In
2D, it is well known that finite temperature phase fluctuations lead to
extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature,
raising serious concern regarding the observability of 2D FFLO superfluids.
Recently, it was shown that FFLO superfluids can be realized using a Rashba
spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support
topological excitations such as Majorana fermions in 2D. Here we address the
finite temperature BKT transition issue in this system, which may exhibits
gapped, gapless, topological, and gapless topological FF phases. We find a
large BKT transition temperature due to large effective superfluid densities,
making it possible to observe 2D FF superfluids at finite temperature. In
addition, we show that gapless FF superfluids can be stable due to their
positive superfluid densities. These findings pave the way for the experimental
observation of 2D gapped and gapless FF superfluids and their associated
topological excitations at finite temperature.

link to article (opens in new tab)

 

Author(s):

There is much interest in the realization of systems with p-wave pairing in
one dimension or chiral p-wave pairing in two dimensions, because these are
believed to support Majorana modes at the ends or inside vortices. We consider
a two component system of composite fermions and provide theoretical evidence
that, under appropriate conditions, the screened interaction between the
minority composite fermions is such as to produce an almost exact realization
of p-wave paired state described by the so-called anti-Pfaffian wave function.
This state is predicted to occur at filling $\nu=3/8$ or 13/8 in GaAs when the
Zeeman energy is sufficiently small, and at $\nu=\pm 3/8$ or $\pm 13/8$ in
single layer graphene when either the Zeeman or the valley splitting is
sufficiently small.

link to article (opens in new tab)

 

Author(s):

We demonstrate the possibility of topological states for non-Dirac electrons.
Specifically it is shown that, because of the $C_{\rm 3}$ crystal symmetry and
time reversal symmetry, $p_x$ and $p_y$ orbits accommodated on triangular
lattice exhibit a quadratic band touching at $\Gamma$ point at the Fermi level.
When the atomic spin-orbit coupling (SOC) is taken into account, a gap is
opened resulting in a quantum spin Hall effect state. As revealed explicitly by
a $k\cdot p$ model, the topology is associated with a meron structure in the
pseudo spin texture with vorticity two, a mechanism different from honeycomb
lattice and the band inversion. One possible realization of this scheme is the
1/3 coverage by Bi atom adapted on the Si[111] surface. First-principle
calculations are carried out, and a global gap of $\sim 0.15$eV is observed.
With the Si substrate taking part in realizing the nontrivial topology, the
present template is expected to make the integration of topological states into
existing electronics and photonics technologies promising.

link to article (opens in new tab)

 

Author(s):

The time evolution and the asymptotic outcome of a
Landau-Zener-Stueckelberg-Majorana (LZ) process under continuous weak
non-selective measurement is analyzed. We compare two measurement protocols in
which the populations of either the adiabatic or the non-adiabatic levels are
(continuously and weakly) monitored. The weak measurement formalism, described
using a Gaussian Kraus operator, leads to a time evolution characterized by a
Markovian dephasing process, which, in the non-adiabatic measurement protocol
is similar to earlier studies of LZ dynamics in a dephasing environment.
Casting the problem in the language of measurement theory makes it possible for
us to compare diabatic and adiabatic measurement scenarios, to consider
engineered dephasing as a control device and to examine the manifestation of
the Zeno effect under the different measurement protocols. In particular, under
measurement of the non- adiabatic populations, the Zeno effect is manifested
not as a freezing of the measured system in its initial state, but rather as an
approach to equal asymptotic populations of the two diabatic states. This
behavior can be traced to the way by which the weak measurement formalism
behaves in the strong measurement limit, with a built-in relationship between
measurement time and strength.

link to article (opens in new tab)

 

Author(s):

Motivated by recent progress in understanding the interplay between lattice
and electronic topological phases, we consider quantum-melting transitions of
{\it weak} quantum liquid crystals, a crystal and a nematic phase, in which
electrons form a quantum Hall state. In certain classes of Chern band
insulators and quantum Hall phases, it has been previously demonstrated that
there are topological Chern-Simons terms such as a Hall viscosity term and a
gravitational Chern-Simons term for local lattice deformations. The
Chern-Simons terms can induce anyonic statistics for the topological lattice
defects and furthermore dress the defects with certain symmetry quantum
numbers. On the other hand, the melting transitions of such liquid-crystalline
orders are driven by the condensation of lattice defects. Based on these
observations, we show how the topological terms can change the nature of the
proximate disordered phases of the quantum liquid crystalline phases. We derive
and study the effective dual field theories for the liquid crystalline phases
with the geometric Chern-Simons terms, and carefully examine the symmetry
quantum numbers and statistics of defects. We show that a crystal may go
through a continuous phase transition into another crystal with the new
discrete translational symmetries because the dislocation, the topological
defect in the crystal, carries non-zero crystal momentum due to the Hall
viscosity term. For the nematic phase, the disclination will condense at the
phase transition to the isotropic phase, and we show that the isotropic phase
may support a deconfined fractionally charged excitation due to the Wen-Zee
term, and thus the isotropic phase and the nematic phase have different
electromagnetic Hall responses.

link to article (opens in new tab)

 

Author(s):

We establish theoretically that a ferromagnetic wire deposited on the surface
of a spin-orbit coupled $s$-wave superconductor generically supports
zero-energy topological Majorana fermion (MF) excitations near the two ends of
the wire. Depending on the strength of the ferromagnetic moment in the wire,
the number of MFs at each end, $n$, can be either one or two, and should be
revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning
tunneling microscopy (STM) measurements which would show strong (weak) signals
at the ends (middle) of the wire. The underlying physics of this system, which
is distinct from that of the well-studied spin-orbit-coupled
semiconductor-superconductor heterostructures in the presence of an applied
magnetic field, is discussed in terms of a topological chiral symmetry in BDI
class with an integer topological invariant. Our work introduces a new
platform, namely a magnetic metal-superconductor heterostructure, in the race
for finding a Majorana-carrying topological superconductor.

link to article (opens in new tab)

 

Author(s):

The ground state of $^4$He confined in a system with the topology of a
cylinder can display properties of a solid, superfluid and liquid crystal. This
phase, which we call compactified supersolid (CSS), originates from wrapping
the basal planes of the bulk hcp solid into concentric cylindrical shells, with
several central shells exhibiting superfluidity along the axial direction. Its
main feature is the presence of a topological defect which can be viewed as a
disclination with Frank index $n=1$ observed in liquid crystals, and which, in
addition, has a superfluid core. The CSS as well as its transition to an
insulating compactified solid with a very wide hysteresis loop are found by ab
initio Monte Carlo simulations. A simple analytical model captures
qualitatively correctly the main property of the CSS — a gradual decrease of
the superfluid response with increasing pressure.

link to article (opens in new tab)

 

Author(s):

Topological phases which host Majorana fermions can not be identified via
local order parameters. We give simple nonlocal order parameters to distinguish
quasi-one-dimensional (1D) topological superconductors of spinless fermions,
for any interacting model in the absence of time reversal symmetry. These
string or “brane” order parameters are natural for measurements in cold atom
systems using quantum gas microscopy. We propose them as a way to identify
symmetry-protected topological phases of Majorana fermions in cold atom
experiments via bulk rather than edge degrees of freedom. Subsequently, we
study two-dimensional (2D) topological superconductors via the quasi-1D limit
of coupling $N$ identical chains on the cylinder. We classify the symmetric,
interacting topological phases protected by the additional $\mathbb{Z}_N$
translation symmetry. The phases include quasi-1D analogs of (i) the $p+ip$
chiral topological superconductor, which can be distinguished up to the 2D
Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise
general rules for constructing nonlocal order parameters which distinguish the
phases. These rules encode the signature of the fermionic topological phase in
the symmetry properties of the terminating operators of the nonlocal string or
brane. The nonlocal order parameters for some of these phases simply involve a
product of the string order parameters for the individual chains. Finally, we
give a physical picture of one of the topological phases as a condensate of
certain defects, which motivates the form of the nonlocal order parameter and
is reminiscent of higher dimensional constructions of topological phases.

link to article (opens in new tab)

 

Author(s):

The search of new topological insulators that demonstrate the quantum
anomalous Hall effect (QAHE) is a cutting-edge research topic in condensed
matter physics and materials science. So far, the QAHE has been observed only
in Cr-doped (Bi,Sb)2Te3 at extremely low temperature. Therefore, it is
important to find new materials with large topological band gap and high
thermal stability for the realization of the QAHE. Based on first-principles
and tight-binding model calculations, we discovered a new class of topological
phase$-$Chern half metal which manifests the QAHE in one spin channel while is
metallic in the other spin channel$-$in Co or Rh deposited graphene. Meanwhile,
these systems have large perpendicular magnetic anisotropy energies of 5.3 and
11.5 meV, necessary for the observation of the QAHE at reasonably high
temperature.

link to article (opens in new tab)

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