Author(s):

Authors: Gil Young Cho, Rodrigo Soto-Garrido, Eduardo Fradkin

We show that the pair-density-wave (PDW) superconducting state emergent in
extended Heisenberg-Hubbard models in two-leg ladders is topological in the
presence of an Ising spin symmetry and supports a Majorana fermion zero mode at
an open boundary. The state is similar to a conventional finite-momentum paired
state in that the order parameter is a charge-$2e$ field carrying finite
momentum. However, the order parameter here is a {\it quartic} electron
operator and conventional mean-field theory cannot be applied to study this
state. Beyond mean-field theory, we use bosonization to show that the
one-dimensional and quasi-one-dimensional pair-density-wave states have the
Majorana fermions zero modes at the boundary, and also at certain lattice
defects. Thus the superconducting states are exotic topological phases
supporting Majorana fermions with finite-momentum pairing fields and
charge-$4e$ superconductivity.

link to article (opens in new tab)

 

Author(s):

Authors: B. H. Wu, W. Yi, J. C. Cao, G.-C. Guo

We show that noncollinear Andreev reflections can be induced at interfaces of
semiconductor nanowires with spin-orbit coupling, Zeeman splitting and
proximity-induced superconductivity. In a noncollinear local Andreev
reflection, the spin polarizations of the injected and the retro-reflected
carriers are typically at an angle which is tunable via system parameters.
While in a nonlocal transport, this noncollinearity enables us to identify and
block, at different voltage configurations, the noncollinear cross Andreev
reflection and the direct charge transfer processes. We demonstrate that the
intriguing noncollinearity originates from the spin-dependent coupling between
carriers in the lead and the lowest discrete states in the wire, which, for a
topological superconducting nanowire, are related to the overlap-induced
hybridization of Majorana edge states in a finite system. These interesting
phenomena can be observed in semiconductor nanowires of experimentally relevant
lengths, and are potentially useful for spintronics.

link to article (opens in new tab)

 

Author(s):

Authors: Zheng-Cheng Gu, Hong-Chen Jiang, G. Baskaran

Searching for $p+ip$ superconducting(SC) state has become a fascinating
subject in condensed matter physics, as a dream application awaiting in
topological quantum computation. In this paper, we report a theoretical
discovery of a $p+ip$ SC ground state (coexisting with ferromagnetic order) in
honeycomb lattice Hubbard model with infinite repulsive interaction at low
doping($\delta< 0.2$), by using both the state-of-art Grassmann tensor product
state(GTPS) approach and a quantum field theory approach. Our discovery
suggests a new mechanism for $p+ip$ SC state in generic strongly correlated
systems and opens a new door towards experimental realization. The $p+ip$ SC
state has an instability towards a potential non-Fermi liquid with a large but
finite $U$. However, a small Zeeman field term stabilizes the $p+ip$ SC state.
Relevant realistic materials are also proposed.

link to article (opens in new tab)

 

Author(s):

Authors: Takeshi Mizushima

We here examine the relation between odd-frequency spin-triple even-parity
(OTE) Cooper pairs and anomalous surface magnetic response in time-reversal
invariant (TRI) spin-triplet superfluids and superconductors. The spin
susceptibility generally consists of two contributions: Even-frequency
odd-parity pair amplitudes and odd-frequency even-parity pair amplitudes. The
OTE pair amplitudes are absent in the bulk region, but ubiquitously exist in
the surface and interface region as Andreev bound states. We here clarify that
additional discrete symmetries, originating from the internal symmetry and
point group symmetry, impose strong constraint on the OTE pair amplitudes
emergent in the surface of TRI superfluids and superconductors. As a result of
the symmetry constraint, the magnetic response of the OTE pairs yields
Ising-like anisotropy. For the topological phase of the $^3$He-B in a
restricted geometry, the coupling of the OTE pair amplitudes to an applied
field is prohibited by an additional discrete symmetry. Once the discrete
symmetry is broken, however, the OTE pairs start to couple to the applied
field, which anomalously enhances surface spin susceptibility. Furthermore, we
extend this theory to TRI superconductors, where the corresponding discrete
symmetry is the mirror reflection symmetry.

link to article (opens in new tab)

 

Author(s):

Authors: Hoi-Yin Hui, Jay D. Sau, S. Das Sarma

Disorder is known to suppress the gap of a topological superconducting state
that would support non-Abelian Majorana zero modes. In this paper, we study
using the self-consistent Born approximation the robustness of the Majorana
modes to disorder within a suitably extended Eilenberger theory, in which the
spatial dependence of the localized Majorana wave functions is included. We
find that the Majorana mode becomes delocalized with increasing disorder
strength as the topological superconducting gap is suppressed. However,
surprisingly, the zero bias peak seems to survive even for disorder strength
exceeding the critical value necessary for closing the superconducting gap
within the Born approximation.

link to article (opens in new tab)

 

Author(s):

Authors: J. K. Asboth, B. Tarasinski, P. Delplace

Over the past few years, topological insulators have taken center stage in
solid state physics. The desire to tune the topological invariants of the bulk
and thus control the number of edge states has steered theorists and
experimentalists towards periodically driving parameters of these systems. In
such periodically driven setups, by varying the drive sequence the effective
(Floquet) Hamiltonian can be engineered to be topological: then, the principle
of bulk–boundary correspondence guarantees the existence of robust edge
states. It has also been realized, however, that periodically driven systems
can host edge states not predicted by the Floquet Hamiltonian. The exploration
of such edge states, and the corresponding topological phases unique to
periodically driven systems, has only recently begun. We contribute to this
goal by identifying the bulk topological invariants of periodically driven
one-dimensional lattice Hamiltonians with chiral symmetry. We find simple
closed expressions for these invariants, as winding numbers of blocks of the
unitary operator corresponding to a part of the time evolution, and ways to
tune these invariants using sublattice shifts. We illustrate our ideas on the
periodically driven Su-Schrieffer-Heeger model, which we map to a discrete time
quantum walk, allowing theoretical results about either of these systems to be
applied to the other. Our work helps interpret the results of recent
simulations where a large number of Floquet Majorana fermions in periodically
driven superconductors have been found, and of recent experiments on discrete
time quantum walks.

link to article (opens in new tab)

 

Author(s):

Authors: Titus Neupert, Claudio Chamon, Christopher Mudry, Ronny Thomale

A scheme is proposed to construct integer and fractional topological quantum
states of fermions in two spatial dimensions. We devise models for such states
by coupling wires of non-chiral Luttinger liquids of electrons, that are
arranged in a periodic array. Which inter-wire couplings are allowed is
dictated by symmetry and the compatibility criterion that they can
simultaneously acquire a finite expectation value, opening a spectral gap
between the ground state(s) and all excited states in the bulk. First, with
these criteria at hand, we reproduce the tenfold classification table of
integer topological insulators, where their stability against interactions
becomes immediately transparent in the Luttinger liquid description. Second, we
construct an example of a strongly interacting fermionic topological phase of
matter with short-range entanglement that lies outside of the tenfold
classification. Third, we expand the table to long-range entangled topological
phases with intrinsic topological order and fractional excitations.

link to article (opens in new tab)

 

Author(s):

Authors: Yasaman Bahri, Andrew C. Potter

Direct coupling between a gapless boson and a Fermi surface results in the
destruction of Landau quasiparticles and a breakdown of Fermi liquid theory.
Such a non-Fermi liquid phase arises in spin-orbit coupled ferromagnets with
spontaneously broken continuous symmetries due to strong coupling between
rotational Goldstone modes and itinerant electrons. These systems provide an
experimentally accessible context for studying non-Fermi liquid physics.
Possible examples include low-density Rashba coupled electron gases, which have
a natural tendency towards spontaneous ferromagnetism, or topological insulator
surface states with proximity induced ferromagnetism. Crucially, unlike the
related case of a spontaneous nematic distortion of the Fermi surface where the
non-Fermi liquid regime is expected to be hidden beneath a superconducting
dome, we show that the non-Fermi liquid phase in spin-orbit coupled
ferromagnets is stable.

link to article (opens in new tab)

 

Author(s):

Authors: Jan P. Dahlhaus, Benjamin M. Fregoso, Joel E. Moore

Circularly polarised light opens a gap in the electronic Dirac spectrum of
graphene and topological insulator surfaces, thereby inducing a quantum Hall
like phase. We propose to detect the accompanying light-induced edge states and
their current by the magnetic field they produce. The topological nature of the
edge states is reflected in the mean orbital magnetization of the sample, which
shows a universal linear dependence as a function of a generalized chemical
potential – independent of the driving details and the properties of the
material. The proposed protocol overcomes several typically encountered
problems in the realization and measurement of Floquet phases, including the
destructive effects of phonons and coupled electron baths and provides a way to
occupy the induced edge states selectively. We estimate practical experimental
parameters and conclude that the magnetization signature of the Floquet
topological phase may be detectable with current techniques.

link to article (opens in new tab)

 

Author(s):

Authors: Song-Bo Zhang, Yan-Yang Zhang, Shun-Qing Shen

The edge states in the quantum spin Hall effect are expected to be protected
by time reversal symmetry. The experimental observation of the quantized
conductance was reported in the InAs/GaSb quantum well {[}Du et al,
arXiv:1306.1925{]}, up to a large magnetic field, which raises a question on
the robustness of the edge states in the quantum spin Hall effect under time
reversal symmetry breaking. Here we present a theoretical calculation on
topological invariants for the Benevig-Hughes-Zhang model in an external
magnetic field, and find that the quantum spin Hall effect retains robust up to
a large magnetic field. The critical value of the magnetic field breaking the
quantum spin Hall effect is dominantly determined by the band gap at the
$\Gamma$ point instead of the indirect band gap between the conduction and
valence bands. This illustrates that the quantum spin Hall effect could persist
even under time reversal symmetry breaking.

link to article (opens in new tab)

 

Author(s):

Authors: Ling Lu, John D. Joannopoulos, Marin Soljačić

Topology is revolutionizing photonics, bringing with it new theoretical
discoveries and a wealth of potential applications. This field was inspired by
the discovery of topological insulators, in which interfacial electrons
transport without dissipation even in the presence of impurities. Similarly,
new optical mirrors of di?fferent wave-vector space topologies have been
constructed to support new states of light propagating at their interfaces.
These novel waveguides allow light to flow around large imperfections without
back-reflection. The present review explains the underlying principles and
highlights the major findings in photonic crystals, coupled resonators,
metamaterials and quasicrystals.

link to article (opens in new tab)

 

Author(s):

We show that the pair-density-wave (PDW) superconducting state emergent in
extended Heisenberg-Hubbard models in two-leg ladders is topological in the
presence of an Ising spin symmetry and supports a Majorana fermion zero mode at
an open boundary. The state is similar to a conventional finite-momentum paired
state in that the order parameter is a charge-$2e$ field carrying finite
momentum. However, the order parameter here is a {\it quartic} electron
operator and conventional mean-field theory cannot be applied to study this
state. Beyond mean-field theory, we use bosonization to show that the
one-dimensional and quasi-one-dimensional pair-density-wave states have the
Majorana fermions zero modes at the boundary, and also at certain lattice
defects. Thus the superconducting states are exotic topological phases
supporting Majorana fermions with finite-momentum pairing fields and
charge-$4e$ superconductivity.

link to article (opens in new tab)

 

Author(s):

We show that noncollinear Andreev reflections can be induced at interfaces of
semiconductor nanowires with spin-orbit coupling, Zeeman splitting and
proximity-induced superconductivity. In a noncollinear local Andreev
reflection, the spin polarizations of the injected and the retro-reflected
carriers are typically at an angle which is tunable via system parameters.
While in a nonlocal transport, this noncollinearity enables us to identify and
block, at different voltage configurations, the noncollinear cross Andreev
reflection and the direct charge transfer processes. We demonstrate that the
intriguing noncollinearity originates from the spin-dependent coupling between
carriers in the lead and the lowest discrete states in the wire, which, for a
topological superconducting nanowire, are related to the overlap-induced
hybridization of Majorana edge states in a finite system. These interesting
phenomena can be observed in semiconductor nanowires of experimentally relevant
lengths, and are potentially useful for spintronics.

link to article (opens in new tab)

 

Author(s):

Searching for $p+ip$ superconducting(SC) state has become a fascinating
subject in condensed matter physics, as a dream application awaiting in
topological quantum computation. In this paper, we report a theoretical
discovery of a $p+ip$ SC ground state (coexisting with ferromagnetic order) in
honeycomb lattice Hubbard model with infinite repulsive interaction at low
doping($\delta< 0.2$), by using both the state-of-art Grassmann tensor product
state(GTPS) approach and a quantum field theory approach. Our discovery
suggests a new mechanism for $p+ip$ SC state in generic strongly correlated
systems and opens a new door towards experimental realization. The $p+ip$ SC
state has an instability towards a potential non-Fermi liquid with a large but
finite $U$. However, a small Zeeman field term stabilizes the $p+ip$ SC state.
Relevant realistic materials are also proposed.

link to article (opens in new tab)

 

Author(s):

We here examine the relation between odd-frequency spin-triple even-parity
(OTE) Cooper pairs and anomalous surface magnetic response in time-reversal
invariant (TRI) spin-triplet superfluids and superconductors. The spin
susceptibility generally consists of two contributions: Even-frequency
odd-parity pair amplitudes and odd-frequency even-parity pair amplitudes. The
OTE pair amplitudes are absent in the bulk region, but ubiquitously exist in
the surface and interface region as Andreev bound states. We here clarify that
additional discrete symmetries, originating from the internal symmetry and
point group symmetry, impose strong constraint on the OTE pair amplitudes
emergent in the surface of TRI superfluids and superconductors. As a result of
the symmetry constraint, the magnetic response of the OTE pairs yields
Ising-like anisotropy. For the topological phase of the $^3$He-B in a
restricted geometry, the coupling of the OTE pair amplitudes to an applied
field is prohibited by an additional discrete symmetry. Once the discrete
symmetry is broken, however, the OTE pairs start to couple to the applied
field, which anomalously enhances surface spin susceptibility. Furthermore, we
extend this theory to TRI superconductors, where the corresponding discrete
symmetry is the mirror reflection symmetry.

link to article (opens in new tab)

 

Author(s):

Disorder is known to suppress the gap of a topological superconducting state
that would support non-Abelian Majorana zero modes. In this paper, we study
using the self-consistent Born approximation the robustness of the Majorana
modes to disorder within a suitably extended Eilenberger theory, in which the
spatial dependence of the localized Majorana wave functions is included. We
find that the Majorana mode becomes delocalized with increasing disorder
strength as the topological superconducting gap is suppressed. However,
surprisingly, the zero bias peak seems to survive even for disorder strength
exceeding the critical value necessary for closing the superconducting gap
within the Born approximation.

link to article (opens in new tab)

 

Author(s):

Over the past few years, topological insulators have taken center stage in
solid state physics. The desire to tune the topological invariants of the bulk
and thus control the number of edge states has steered theorists and
experimentalists towards periodically driving parameters of these systems. In
such periodically driven setups, by varying the drive sequence the effective
(Floquet) Hamiltonian can be engineered to be topological: then, the principle
of bulk–boundary correspondence guarantees the existence of robust edge
states. It has also been realized, however, that periodically driven systems
can host edge states not predicted by the Floquet Hamiltonian. The exploration
of such edge states, and the corresponding topological phases unique to
periodically driven systems, has only recently begun. We contribute to this
goal by identifying the bulk topological invariants of periodically driven
one-dimensional lattice Hamiltonians with chiral symmetry. We find simple
closed expressions for these invariants, as winding numbers of blocks of the
unitary operator corresponding to a part of the time evolution, and ways to
tune these invariants using sublattice shifts. We illustrate our ideas on the
periodically driven Su-Schrieffer-Heeger model, which we map to a discrete time
quantum walk, allowing theoretical results about either of these systems to be
applied to the other. Our work helps interpret the results of recent
simulations where a large number of Floquet Majorana fermions in periodically
driven superconductors have been found, and of recent experiments on discrete
time quantum walks.

link to article (opens in new tab)

 

Author(s):

A scheme is proposed to construct integer and fractional topological quantum
states of fermions in two spatial dimensions. We devise models for such states
by coupling wires of non-chiral Luttinger liquids of electrons, that are
arranged in a periodic array. Which inter-wire couplings are allowed is
dictated by symmetry and the compatibility criterion that they can
simultaneously acquire a finite expectation value, opening a spectral gap
between the ground state(s) and all excited states in the bulk. First, with
these criteria at hand, we reproduce the tenfold classification table of
integer topological insulators, where their stability against interactions
becomes immediately transparent in the Luttinger liquid description. Second, we
construct an example of a strongly interacting fermionic topological phase of
matter with short-range entanglement that lies outside of the tenfold
classification. Third, we expand the table to long-range entangled topological
phases with intrinsic topological order and fractional excitations.

link to article (opens in new tab)

 

Author(s):

Direct coupling between a gapless boson and a Fermi surface results in the
destruction of Landau quasiparticles and a breakdown of Fermi liquid theory.
Such a non-Fermi liquid phase arises in spin-orbit coupled ferromagnets with
spontaneously broken continuous symmetries due to strong coupling between
rotational Goldstone modes and itinerant electrons. These systems provide an
experimentally accessible context for studying non-Fermi liquid physics.
Possible examples include low-density Rashba coupled electron gases, which have
a natural tendency towards spontaneous ferromagnetism, or topological insulator
surface states with proximity induced ferromagnetism. Crucially, unlike the
related case of a spontaneous nematic distortion of the Fermi surface where the
non-Fermi liquid regime is expected to be hidden beneath a superconducting
dome, we show that the non-Fermi liquid phase in spin-orbit coupled
ferromagnets is stable.

link to article (opens in new tab)

 

Author(s):

Circularly polarised light opens a gap in the electronic Dirac spectrum of
graphene and topological insulator surfaces, thereby inducing a quantum Hall
like phase. We propose to detect the accompanying light-induced edge states and
their current by the magnetic field they produce. The topological nature of the
edge states is reflected in the mean orbital magnetization of the sample, which
shows a universal linear dependence as a function of a generalized chemical
potential – independent of the driving details and the properties of the
material. The proposed protocol overcomes several typically encountered
problems in the realization and measurement of Floquet phases, including the
destructive effects of phonons and coupled electron baths and provides a way to
occupy the induced edge states selectively. We estimate practical experimental
parameters and conclude that the magnetization signature of the Floquet
topological phase may be detectable with current techniques.

link to article (opens in new tab)

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