Author(s):

We show the existence of an inherent property of evanescent electromagnetic
waves: spin-momentum locking, where the direction of momentum fundamentally
locks the polarization of the wave. We trace the ultimate origin of this
phenomenon to complex dispersion and causality requirements on evanescent
waves. We demonstrate that every case of evanescent waves in total internal
reflection, surface states and optical fibers/waveguides possesses this
intrinsic spin-momentum locking. We derive the Stokes parameters for evanescent
waves which reveal an intriguing result – every fast decaying evanescent wave
is inherently circularly polarized with its handedness tied to the direction of
propagation. We also show the existence of a fundamental angle associated with
total internal reflection (TIR) such that propagating waves locally inherit
perfect circular polarized characteristics from the evanescent wave. This
circular TIR condition occurs if and only if the ratio of permittivities of the
two dielectric media exceeds the golden ratio. Our work leads to a unified
understanding of this spin-momentum locking in various nanophotonic structures
and sheds light on the electromagnetic analogy with the quantum spin hall state
for electrons.

link to article (opens in new tab)

 

Author(s):

Mechanical metamaterials are artificial structures with unusual properties,
such as negative Poisson ratio, bistability or tunable vibrational properties,
that originate in the geometry of their unit cell. At the heart of such unusual
behaviour is often a soft mode: a motion that does not significantly stretch or
compress the links between constituent elements. When activated by motors or
external fields, soft modes become the building blocks of robots and smart
materials. Here, we demonstrate the existence of topological soft modes that
can be positioned at desired locations in a metamaterial while being robust
against a wide range of structural deformations or changes in material
parameters. These protected modes, localized at dislocations, are the
mechanical analogue of topological states bound to defects in electronic
systems. We create physical realizations of the topological modes in prototypes
of kagome lattices built out of rigid triangular plates. We show mathematically
that they originate from the interplay between two Berry phases: the Burgers
vector of the dislocation and the topological polarization of the lattice. Our
work paves the way towards engineering topologically protected nano-mechanical
structures for molecular robotics or information storage and read-out.

link to article (opens in new tab)

 

Author(s):

Based on the Born-Oppemheimer approximation, we divide total electron
Hamiltonian in a spinorbit coupled system into slow orbital motion and fast
interband transition process. We find that the fast motion induces a gauge
field on slow orbital motion, perpendicular to electron momentum, inducing a
topological phase. From this general designing principle, we present a theory
for generating artificial gauge field and topological phase in a conventional
two-dimensional electron gas embedded in parabolically graded
GaAs/In$_{x}$Ga$_{1-x}$As/GaAs quantum wells with antidot lattices. By tuning
the etching depth and period of antidot lattices, the band folding caused by
superimposed potential leads to formation of minibands and band inversions
between the neighboring subbands. The intersubband spin-orbit interaction opens
considerably large nontrivial minigaps and leads to many pairs of helical edge
states in these gaps.

link to article (opens in new tab)

 

Author(s):

We develop a topological theory for disordered Weyl semimetals in the
framework of gauge invariance of replica formalism and boundary-bulk
correspondence of Chern insulators. An anisotropic topological ?term is
analytically derived for the effective non-linear sigma model. It is this
nontrivial topological term that ensures the bulk transverse transport of Weyl
semimetals to be robust against disorders. Moreover, we establish a general
diagram that reveals the intrinsic relations among topological terms in the
non-linear sigma models and gauge response theories respectively for $(2n +
2)$-dimensional topological insulators, $(2n+1)$-dimensional chiral fermions,
$(2n+1)$-dimensional chiral semimetals, and $(2n)$-dimensional topological
insulators with $n$ being a positive integer.

link to article (opens in new tab)

 

Author(s):

In many of the experimental systems that may host Majorana zero modes, a
so-called chiral symmetry exists that protects overlapping zero modes from
splitting up. This symmetry is operative in a superconducting nanowire that is
narrower than the spin-orbit scattering length, and at the Dirac point of a
superconductor/topological insulator heterostructure. Here we show that chiral
symmetry strongly modifies the dynamical and spectral properties of a chaotic
scatterer, even if it binds only a single zero mode. These properties are
quantified by the Wigner-Smith time-delay matrix $Q=-i\hbar S^\dagger dS/dE$,
the Hermitian energy derivative of the scattering matrix, related to the
density of states by $\rho=(2\pi\hbar)^{-1}\,{\rm Tr}\,Q$. We compute the
probability distribution of $Q$ and $\rho$, dependent on the number $\nu$ of
Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral
symmetry is essential for a significant $\nu$-dependence.

link to article (opens in new tab)

 

Author(s):

Authors: Todd Van Mechelen, Zubin Jacob

We show the existence of an inherent property of evanescent electromagnetic
waves: spin-momentum locking, where the direction of momentum fundamentally
locks the polarization of the wave. We trace the ultimate origin of this
phenomenon to complex dispersion and causality requirements on evanescent
waves. We demonstrate that every case of evanescent waves in total internal
reflection, surface states and optical fibers/waveguides possesses this
intrinsic spin-momentum locking. We derive the Stokes parameters for evanescent
waves which reveal an intriguing result – every fast decaying evanescent wave
is inherently circularly polarized with its handedness tied to the direction of
propagation. We also show the existence of a fundamental angle associated with
total internal reflection (TIR) such that propagating waves locally inherit
perfect circular polarized characteristics from the evanescent wave. This
circular TIR condition occurs if and only if the ratio of permittivities of the
two dielectric media exceeds the golden ratio. Our work leads to a unified
understanding of this spin-momentum locking in various nanophotonic structures
and sheds light on the electromagnetic analogy with the quantum spin hall state
for electrons.

link to article (opens in new tab)

 

Author(s):

Authors: Jayson Paulose, Bryan Gin-ge Chen, Vincenzo Vitelli

Mechanical metamaterials are artificial structures with unusual properties,
such as negative Poisson ratio, bistability or tunable vibrational properties,
that originate in the geometry of their unit cell. At the heart of such unusual
behaviour is often a soft mode: a motion that does not significantly stretch or
compress the links between constituent elements. When activated by motors or
external fields, soft modes become the building blocks of robots and smart
materials. Here, we demonstrate the existence of topological soft modes that
can be positioned at desired locations in a metamaterial while being robust
against a wide range of structural deformations or changes in material
parameters. These protected modes, localized at dislocations, are the
mechanical analogue of topological states bound to defects in electronic
systems. We create physical realizations of the topological modes in prototypes
of kagome lattices built out of rigid triangular plates. We show mathematically
that they originate from the interplay between two Berry phases: the Burgers
vector of the dislocation and the topological polarization of the lattice. Our
work paves the way towards engineering topologically protected nano-mechanical
structures for molecular robotics or information storage and read-out.

link to article (opens in new tab)

 

Author(s):

Authors: Likun Shi, Wenkai Lou, F. Cheng, Y. L. Zou, Wen Yang, Kai Chang

Based on the Born-Oppemheimer approximation, we divide total electron
Hamiltonian in a spinorbit coupled system into slow orbital motion and fast
interband transition process. We find that the fast motion induces a gauge
field on slow orbital motion, perpendicular to electron momentum, inducing a
topological phase. From this general designing principle, we present a theory
for generating artificial gauge field and topological phase in a conventional
two-dimensional electron gas embedded in parabolically graded
GaAs/In$_{x}$Ga$_{1-x}$As/GaAs quantum wells with antidot lattices. By tuning
the etching depth and period of antidot lattices, the band folding caused by
superimposed potential leads to formation of minibands and band inversions
between the neighboring subbands. The intersubband spin-orbit interaction opens
considerably large nontrivial minigaps and leads to many pairs of helical edge
states in these gaps.

link to article (opens in new tab)

 

Author(s):

Authors: Y. X. Zhao, Z. D. Wang

We develop a topological theory for disordered Weyl semimetals in the
framework of gauge invariance of replica formalism and boundary-bulk
correspondence of Chern insulators. An anisotropic topological ?term is
analytically derived for the effective non-linear sigma model. It is this
nontrivial topological term that ensures the bulk transverse transport of Weyl
semimetals to be robust against disorders. Moreover, we establish a general
diagram that reveals the intrinsic relations among topological terms in the
non-linear sigma models and gauge response theories respectively for $(2n +
2)$-dimensional topological insulators, $(2n+1)$-dimensional chiral fermions,
$(2n+1)$-dimensional chiral semimetals, and $(2n)$-dimensional topological
insulators with $n$ being a positive integer.

link to article (opens in new tab)

 

Author(s):

Authors: H. Schomerus, M. Marciani, C. W. J. Beenakker

In many of the experimental systems that may host Majorana zero modes, a
so-called chiral symmetry exists that protects overlapping zero modes from
splitting up. This symmetry is operative in a superconducting nanowire that is
narrower than the spin-orbit scattering length, and at the Dirac point of a
superconductor/topological insulator heterostructure. Here we show that chiral
symmetry strongly modifies the dynamical and spectral properties of a chaotic
scatterer, even if it binds only a single zero mode. These properties are
quantified by the Wigner-Smith time-delay matrix $Q=-i\hbar S^\dagger dS/dE$,
the Hermitian energy derivative of the scattering matrix, related to the
density of states by $\rho=(2\pi\hbar)^{-1}\,{\rm Tr}\,Q$. We compute the
probability distribution of $Q$ and $\rho$, dependent on the number $\nu$ of
Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral
symmetry is essential for a significant $\nu$-dependence.

link to article (opens in new tab)

 

Author(s):

We study theoretically the far-from-equilibrium relaxation dynamics of spin
spiral states in the three dimensional isotropic Heisenberg model. The
investigated problem serves as an archetype for understanding quantum dynamics
of isolated many-body systems in the vicinity of a spontaneously broken
continuous symmetry. We present a field-theoretical formalism that
systematically improves on mean-field for describing the real-time quantum
dynamics of generic spin-1/2 systems. This is achieved by mapping spins to
Majorana fermions followed by a 1/N expansion of the resulting two-particle
irreducible (2PI) effective action. Our analysis reveals rich
fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral
states. In particular, we find the sudden appearance of long-lived
prethermalized plateaus with diverging lifetimes as the spiral winding is tuned
toward the thermodynamically stable ferro- or antiferromagnetic phases. The
emerging prethermalized states are characterized by different bosonic modes
being thermally populated at different effective temperatures, and by a
hierarchical relaxation process reminiscent of glassy systems. Spin-spin
correlators found by solving the non-equilibrium Bethe-Salpeter equation
provide further insight into the dynamic formation of correlations, the fate of
unstable collective modes, and the emergence of fluctuation-dissipation
relations. Our predictions can be verified experimentally using recent
realizations of spin spiral states [S. Hild, et al. Phys. Rev. Lett. 113,
147205 (2014)].

link to article (opens in new tab)

 

Author(s):

Topological media are gapped or gapless fermionic systems, whose properties
are protected by topology, and thus are robust to deformations of parameters of
the system and generic. We discuss the class of gapless topological media,
which contains the quantum vacuum of Standard Model in its symmetric phase, and
condensed matter systems with zeroes in the energy spectrum, which form Fermi
surfaces, Weyl and Dirac points, Dirac lines, Khodel-Shaginyan flat bands, etc.
Some zeroes are topologically protected, being characterized by topological
invariants, expressed in terms of Green’s function. For stability of the others
the ${\bf p}$-space topology must be accompanied by symmetry.

Vacua with Weyl points serve as a source of effective relativistic quantum
fields emerging at low energy: chiral fermions, effective gauge fields and
tetrad gravity emerge together in the vicinity of a Weyl point. The
accompanying effects, such as chiral anomaly, electroweak baryo-production and
chiral vortical effect, are expressed via the symmetry protected ${\bf
p}$-space invariants.

The gapless topological media exhibit the bulk-surface and bulk-vortex
correspondence: which in particular may lead to the flat band on the surface of
the system or in the core of topological defects. The materials with flat band
in bulk, on the surface or within the dislocations have singular density of
states, which crucially influences the critical temperature of the
superconducting transition in such media. While in all the known
superconductors the transition temperature is exponentially suppressed as a
function of the pairing interaction, in the flat band the transition
temperature is proportional to the pairing interaction, and can be essentially
higher. The ${\bf p}$-space topology may give us the general recipe for search
or artificial fabrication of the room-temperature superconductors.

link to article (opens in new tab)

 

Author(s):

Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic
gauge field have the potential of realizing many interesting states such as
rashbon condensates and topological phases. Here we develop a fluctuation
theory of such systems and demonstrate that beyond-Gaussian effects are
essential to capture the physics of such systems. We obtain their phase diagram
by constructing an approximate non-Gaussian theory. We conclusively establish
that spin-orbit coupling can enhance the exponentially small transition
temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi
temperature, paving a pathway towards high $T_c$ superfluids.

link to article (opens in new tab)

 

Author(s):

We study a one-dimensional $p$-wave superconductor capacitively coupled to a
microwave cavity. By probing the light exiting from the cavity, one can reveal
the electronic susceptibility of the $p$-wave superconductor. We demonstrate
that this susceptibility allows us to determine the topological phase
transition point, the emergence of the Majorana fermions, and the parity of the
ground state of the topological superconductor. All these effects, which are
absent in effective theories that take into account the coupling of light to
Majorana fermions only, are due to the interplay between the majoranas and the
bulk states in the superconductor.

link to article (opens in new tab)

 

Author(s):

We investigate the charge transport property of superconductor (S) /normal
metal (N) / ferromagnet insulator (FI) /(normal metal) N’ and S/N/FI/N’/S
Josephson junctions on a three-dimensional topological insulator surface. We
find asymmetric local density of states (LDOSs) in a S/N/FI/N’ junction and
show that the finite length of the N interlayer gives rise to subgap resonant
spikes in the differential conductance and LDOSs. In a S/N/FI/N’/S junction,
the Josephson current shows a non-sinusoidal current-phase relation and the N
(or N’) interlayer decreases the magnitude of the critical current
monotonically.

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Author(s):

The nontrivial evolution of Wannier functions (WF) for the occupied bands is
a good starting point to understand topological insulator. By modifying the
definition of WFs from the eigenstates of the projected position operator to
those of the projected modular position operator, we are able to extend the
usage of WFs to Weyl metal where the WFs in the old definition fails because of
the lack of band gap at the Fermi energy. This extension helps us to
universally understand topological insulator and topological semi-metal in a
same framework. Another advantage of using the modular position operators in
the definition is that the higher dimensional WFs for the occupied bands can be
easily obtained. We show one of their applications by schematically explaining
why the winding numbers $\nu_{3D}=\nu_{2D}$ for the 3D topological insulators
of DIII class presented in Phys. Rev. Lett. 114, 016801(2015).

link to article (opens in new tab)

 

Author(s):

Authors: Mehrtash Babadi, Eugene Demler, Michael Knap

We study theoretically the far-from-equilibrium relaxation dynamics of spin
spiral states in the three dimensional isotropic Heisenberg model. The
investigated problem serves as an archetype for understanding quantum dynamics
of isolated many-body systems in the vicinity of a spontaneously broken
continuous symmetry. We present a field-theoretical formalism that
systematically improves on mean-field for describing the real-time quantum
dynamics of generic spin-1/2 systems. This is achieved by mapping spins to
Majorana fermions followed by a 1/N expansion of the resulting two-particle
irreducible (2PI) effective action. Our analysis reveals rich
fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral
states. In particular, we find the sudden appearance of long-lived
prethermalized plateaus with diverging lifetimes as the spiral winding is tuned
toward the thermodynamically stable ferro- or antiferromagnetic phases. The
emerging prethermalized states are characterized by different bosonic modes
being thermally populated at different effective temperatures, and by a
hierarchical relaxation process reminiscent of glassy systems. Spin-spin
correlators found by solving the non-equilibrium Bethe-Salpeter equation
provide further insight into the dynamic formation of correlations, the fate of
unstable collective modes, and the emergence of fluctuation-dissipation
relations. Our predictions can be verified experimentally using recent
realizations of spin spiral states [S. Hild, et al. Phys. Rev. Lett. 113,
147205 (2014)].

link to article (opens in new tab)

 

Author(s):

Authors: G.E. Volovik

Topological media are gapped or gapless fermionic systems, whose properties
are protected by topology, and thus are robust to deformations of parameters of
the system and generic. We discuss the class of gapless topological media,
which contains the quantum vacuum of Standard Model in its symmetric phase, and
condensed matter systems with zeroes in the energy spectrum, which form Fermi
surfaces, Weyl and Dirac points, Dirac lines, Khodel-Shaginyan flat bands, etc.
Some zeroes are topologically protected, being characterized by topological
invariants, expressed in terms of Green’s function. For stability of the others
the ${\bf p}$-space topology must be accompanied by symmetry.

Vacua with Weyl points serve as a source of effective relativistic quantum
fields emerging at low energy: chiral fermions, effective gauge fields and
tetrad gravity emerge together in the vicinity of a Weyl point. The
accompanying effects, such as chiral anomaly, electroweak baryo-production and
chiral vortical effect, are expressed via the symmetry protected ${\bf
p}$-space invariants.

The gapless topological media exhibit the bulk-surface and bulk-vortex
correspondence: which in particular may lead to the flat band on the surface of
the system or in the core of topological defects. The materials with flat band
in bulk, on the surface or within the dislocations have singular density of
states, which crucially influences the critical temperature of the
superconducting transition in such media. While in all the known
superconductors the transition temperature is exponentially suppressed as a
function of the pairing interaction, in the flat band the transition
temperature is proportional to the pairing interaction, and can be essentially
higher. The ${\bf p}$-space topology may give us the general recipe for search
or artificial fabrication of the room-temperature superconductors.

link to article (opens in new tab)

 

Author(s):

Authors: Jayantha P. Vyasanakere, Vijay B. Shenoy

Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic
gauge field have the potential of realizing many interesting states such as
rashbon condensates and topological phases. Here we develop a fluctuation
theory of such systems and demonstrate that beyond-Gaussian effects are
essential to capture the physics of such systems. We obtain their phase diagram
by constructing an approximate non-Gaussian theory. We conclusively establish
that spin-orbit coupling can enhance the exponentially small transition
temperature ($T_c$) of a weakly attracting superfluid to the order of Fermi
temperature, paving a pathway towards high $T_c$ superfluids.

link to article (opens in new tab)

 

Author(s):

Authors: Olesia Dmytruk, Mircea Trif, Pascal Simon

We study a one-dimensional $p$-wave superconductor capacitively coupled to a
microwave cavity. By probing the light exiting from the cavity, one can reveal
the electronic susceptibility of the $p$-wave superconductor. We demonstrate
that this susceptibility allows us to determine the topological phase
transition point, the emergence of the Majorana fermions, and the parity of the
ground state of the topological superconductor. All these effects, which are
absent in effective theories that take into account the coupling of light to
Majorana fermions only, are due to the interplay between the majoranas and the
bulk states in the superconductor.

link to article (opens in new tab)

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