[Show abstract][Hide abstract] ABSTRACT: Recently it has been proposed that a unitary topological mirror symmetry can
stabilize multiple zero energy Majorana fermion modes in one dimensional (1D)
time reversal (TR) invariant topological superconductors. Here we establish an
exact equivalence between 1D "topological mirror superconductivity" and chiral
topological superconductivity in BDI class which can also stabilize multiple
Majorana-Kramers pairs in 1D TR-invariant topological superconductors. The
equivalence proves that topological mirror superconductivity can be understood
as chiral superconductivity in the BDI symmetry class co-existing with
time-reversal symmetry. Furthermore, we show that the mirror Berry phase
coincides with the chiral winding invariant of the BDI symmetry class, which is
independent of the presence of the time-reversal symmetry. Thus, the
time-reversal invariant topological mirror superconducting state may be viewed
as a special case of the BDI symmetry class in the well-known Altland-Zirnbauer
periodic table of free fermionic phases. We illustrate the results with the
examples of 1D spin-orbit coupled quantum wires in the presence of nodeless
s_{\pm} superconductivity and the recently discussed experimental system of
ferromagnetic atom (Fe) chains embedded on a lead (Pb) superconductor.
Physical Review B 07/2015; 92(4):045421. DOI:10.1103/PhysRevB.92.045421 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Weyl semimetals (WSM) are topologically protected three dimensional materials
whose low energy excitations are linearly dispersing massless Dirac fermions,
possessing a non-trivial Berry curvature. Using semi-classical Boltzmann
dynamics in the relaxation time approximation for a lattice model of time
reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and
anomalous contributions to the Nernst coefficient. In addition to the magnetic
field dependent Nernst response, which is present in both Dirac and Weyl
semimetals, we show that, contrary to previous reports, the TR-broken WSM also
has an anomalous Nernst response due to a non-vanishing Berry curvature. We
also compute the thermal conductivities of a WSM in the Nernst (${\nabla T}
\perp \mathbf{B}$) and the longitudinal (${\nabla T} \parallel \mathbf{B}$)
set-up and confirm from our lattice model that in the parallel set-up, the
Wiedemann-Franz law is violated between the longitudinal thermal and electrical
conductivities due to chiral anomaly.
[Show abstract][Hide abstract] ABSTRACT: A mechanism is proposed for the tantalizing evidence of polar Kerr effect in
a class of high temperature superconductors--the signs of the Kerr angle from
two opposite faces of the same sample are identical and magnetic field training
is non-existent. The mechanism does not break global time reversal symmetry, as
in an antiferromagnet, and results in zero Faraday effect. It is best
understood in a phenomenological model of bilayer cuprates, such as YBCO, in
which intra-bilayer tunneling nucleates a chiral d-density wave such that the
individual layers have opposite chirality. Although specific to the chiral
d-density wave, the mechanism may be more general to any quasi-two-dimensional
orbital antiferromagnet in which time reversal symmetry is broken in each
plane, but not when averaged macroscopically.
[Show abstract][Hide abstract] ABSTRACT: Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a platform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled s-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, 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 2 ne(2)/h in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.
[Show abstract][Hide abstract] ABSTRACT: Multiple zero-energy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasi-one-dimensional (Q1D) time-reversal-invariant topological superconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze ${(\mathrm{Li}}_{0.9}{\mathrm{Mo}}_{6}{\mathrm{O}}_{17})$ and certain families of organic superconductors, multiple Majorana-Kramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductor-superconductor heterostructures (class D) with ${t}_{$\perp${}}$\ll${}t$, where ${t}_{$\perp${}}$ and $t$ are the transverse and longitudinal hoppings, respectively. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.
Physical Review B 03/2015; 91(12). DOI:10.1103/PhysRevB.91.121413 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The role of charge order in the phase diagram of high temperature cuprate
superconductors has been recently re-emphasized by the experimental discovery
of an incipient bi-directional charge density wave (CDW) phase in a class of
underdoped cuprates. In a subset of the experiments, the CDW has been found to
be accompanied by a d-wave intra-unit-cell form factor, indicating modulation
of charge density on the oxygen orbitals sandwiched between neighboring Cu
atoms on the CuO planes (the so-called bond-density wave (BDW) phase). Here we
take a mean field Q_1=(2\pi/3,0) and Q_2=(0,2\pi/3) bi-directional BDW phase
with a d-wave form factor, which closely resembles the experimentally observed
charge ordered states in underdoped cuprates, and calculate the Fermi surface
topology and the resulting quasiparticle Nernst coefficient as a function of
temperature and doping. We establish that, in the appropriate doping ranges
where the low temperature phase (in the absence of superconductivity) is a BDW,
the Fermi surface consists of an electron and a hole pocket, resulting in a low
temperature negative Nernst coefficient as observed in experiments.
[Show abstract][Hide abstract] ABSTRACT: We show that certain singularities of the Hamiltonian in the complex wave
vector space can be used to identify topological quantum phase transitions for
$1D$ chiral topological superconductors/superfluids in the BDI class. These
singularities fall into the category of the so-called exceptional points
($EP$'s) studied in the context of non-Hermitian Hamiltonians describing open
quantum systems. We also propose a generic formula in terms of the properties
of the $EP$'s to quantify the exact number of Majorana zero modes in a
particular chiral topological superconducting phase, given the values of the
parameters appearing in the Hamiltonian. This formula serves as an alternative
to the familiar integer ($\mathbb{Z}$) winding number invariant characterizing
topological superconductor/superfluid phases in the chiral BDI class.
[Show abstract][Hide abstract] ABSTRACT: We study the magnetic field response of Majorana-Kramers pairs of one-dimensional time-reversal (TR)-invariant topological superconductors (class DIII) with or without a coexisting chirality symmetry. In addition to explaining the anomalous magnetic field response of all the DIII class topological superconducting systems proposed in the literature, we provide a realistic route to engineer a ``true'' TR-invariant topological superconductor, i.e., one whose pair of Majorana bound states at each end is split by an applied Zeeman field in arbitrary direction. We also prove that quite generally the splitting of the Majorana bound states in a time-reversal-invariant topological superconductor by time-reversal breaking fields is highly anisotropic in spin space.
Physical Review B 12/2014; 90(24). DOI:10.1103/PhysRevB.90.245438 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The recent discovery of an incipient charge-density wave (CDW) instability competing with superconductivity in a class of high-temperature cuprate superconductors has brought the role of charge order in the phase diagram of the cuprates under renewed focus. Here, we take a mean field ${Q}_{1}=(2$\pi${}/3,0)$ and ${Q}_{2}=(0,2$\pi${}/3)$ biaxial CDW state and calculate the Fermi-surface topology and the resulting Hall and Seebeck coefficients as a function of temperature and hole doping. We establish that, in the appropriate doping ranges where the low-temperature state (in the absence of superconductivity) is a CDW, the Fermi surface consists of electron pockets, resulting in the Hall and Seebeck coefficients becoming negative at low temperatures, as seen in experiments.
Physical Review B 11/2014; 90(17). DOI:10.1103/PhysRevB.90.174503 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Motivated by a recent experiment in which zero-bias peaks have been observed
in scanning tunneling microscopy (STM) experiments performed on chains of
magnetic atoms on a superconductor, we show, by generalizing earlier work, that
a multichannel ferromagnetic wire deposited on a spin-orbit coupled
superconducting substrate can realize a non-trivial chiral topological
superconducting state with Majorana bound states localized at the wire ends.
The non-trivial topological state occurs for generic parameters requiring no
fine tuning, at least for very large exchange spin splitting in the wire. We
theoretically obtain the signatures which appear in the presence of an
arbitrary number of Majorana modes in multi-wire systems incorporating the role
of finite temperature, finite potential barrier at the STM tip, and finite wire
length. These signatures are presented in terms of spatial profiles of STM
differential conductance which clearly reveal zero energy Majorana end modes
and the prediction of a multiple Majorana based fractional Josephson effect. A
critical comparison of our results with the experimental data shows a basic
inconsistency in the interpretation of the Fe nanowire STM experiment in terms
of Majorana zero modes-- in particular, the observation of the precise
localization of the Majorana zero modes at the wire ends cannot be reconciled
with the extremely small topological superconducting gap (and the associated
extremely weak Majorana tunneling peak) observed simultaneously. Other than
this rather disturbing basic incompatibility, for which we can offer no
resolution at this stage, most other aspects of the experimental phenomenology
are reasonably well explained by our theory.
Physical Review B 10/2014; 91(9). DOI:10.1103/PhysRevB.91.094505 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We identify the dynamic chiral magnetic effect and the optical gyrotropy as
the manifestations of the same physical phenomenon, namely the dynamic
magnetoelectric effect. Therefore, the measurement of optical gyrotropy through
Kerr effect is provides a confirmation of the existence of the dynamic chiral
magnetic effect. We derive a general formula for the gyrotropic conductivity of
a noncentrosymmetric metal in the high frequency limit, and apply our results
to the special cases of inversion symmetry breaking Weyl semimetals and
noncentrosymmetric cubic metals.
[Show abstract][Hide abstract] ABSTRACT: Multiple zero-energy Majorana fermions (MFs) with spatially overlapping wave
functions can survive only if their splitting is prevented by an underlying
symmetry. Here we show that, in quasi-one-dimensional (Q1D) time reversal
invariant topological superconductors (class DIII), a realistic model for
superconducting lithium molybdenum purple bronze and certain families of
organic superconductors, multiple Majorana-Kramers pairs with strongly
overlapping wave functions persist at zero energy even in the absence of an
easily identifiable symmetry. We find that similar results hold in the case of
Q1D semiconductor-superconductor heterostructures (class D) with transverse
hopping t_{perp} much smaller than longitudinal hopping t_x. Our results,
explained in terms of special properties of the Hamiltonian and wave functions,
underscore the importance of hidden accidental symmetries in topological
superconductors.
[Show abstract][Hide abstract] ABSTRACT: The recent discovery of an incipient charge density wave (CDW) instability
competing with superconductivity in a class of high temperature cuprate
superconductors has brought the role of charge order in the phase diagram of
the cuprates under renewed focus. Here we take a mean field (Q = 2pi/3,2pi/3)
CDW state and calculate the Fermi surface topology and the resulting Hall and
Seebeck coefficients as a function of temperature and hole doping. We show
that, in the appropriate doping ranges where the low temperature state (in the
absence of superconductivity) is a CDW, the Fermi surface consists of electron
pockets, resulting in the Hall and Seebeck coefficients becoming negative at
low temperatures, as seen in experiments.
[Show abstract][Hide abstract] ABSTRACT: We consider the quasi-one-dimensional (quasi-1D) system realized by an
array of weakly coupled parallel one-dimensional “tubes” in
a two-dimensional lattice which permits free motion of atoms in an axial
direction in the presence of a Zeeman field, Rashba type spin-orbit
coupling (SOC), and an s-wave attractive interaction, while the radial
motion is tightly confined. We solve the zero-temperature (T=0)
Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas
with the dispersion modified by tunneling between the tubes and show
that the T=0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small
values of the SOC while for larger values of the SOC and high Zeeman
fields the uniform superfluid phase with zero center-of-mass momentum
Cooper pairs has an instability towards the topological uniform
superfluid phase with Majorana fermions at the tube ends. Also, we show
that tuning the two-dimensional optical lattice strength in this model
allows one to explore the crossover behaviors of the phases during the
transition between the three-dimensional and 1D systems and in general
the FFLO (for small SOC) and the topological uniform superfluid phase
(for large SOC) are favored as the system becomes more one dimensional.
We also find evidence of the existence of a Zeeman-tuned topological
quantum phase transition (TQPT) within the FFLO phase itself and, for
large values of the Zeeman field and small SOC, the TQPT gives rise to a
topologically distinct FFLO phase.
Physical Review A 12/2013; 88(6):63601-. DOI:10.1103/PhysRevA.88.063601 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: From a direct calculation of the anomalous Hall conductivity and an
effective electromagnetic action obtained via Fujikawa's chiral rotation
technique, we conclude that an axionic field theory with a nonquantized
coefficient describes the electromagnetic response of the
(3+1)-dimensional Weyl semimetal. The coefficient is proportional to the
momentum space separation of the Weyl nodes. Akin to the Chern-Simons
field theory of quantum Hall effect, the axion field theory violates
gauge invariance in the presence of the boundary, which is cured by the
chiral anomaly of the surface states via the Callan-Harvey mechanism.
This provides a unique solution for the radiatively induced CPT-odd term
in the electromagnetic polarization tensor of the Lorentz violating
spinor electrodynamics, where the source of the Lorentz violation is a
constant axial 4-vector term for the Dirac fermion. A direct linear
response calculation also establishes anomalous thermal Hall effect and
a Wiedemann-Franz law, but thermal Hall conductivity does not directly
follow from the well known formula for the gravitational chiral anomaly.
Physical Review B 12/2013; 88(24):245107-. DOI:10.1103/PhysRevB.88.245107 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: When the right and the left handed Weyl points are separated in energy, they
give rise to a non-dissipative charge current along the direction of a uniform
applied magnetic field, even in the absence of an external electric field. This
effect is known as the chiral magnetic effect and is a hallmark of the
underlying chiral anomaly of the Weyl fermions. According to the linearized
continuum theory of Weyl fermions, the induced current is proportional to the
magnetic field strength and the energy separation with a universal coefficient
$e^2/h^2$. By considering a generic tight binding model for the cubic
noncentrosymmetric metals, we show that such a system naturally supports a set
of Weyl points, which are separated in energies. We also show the existence of
the chiral magnetic effect for generic band parameters, and recover the
universal result of the continuum Weyl fermions for a restricted parameter
regime. Therefore, cubic noncentrosymmetric metals can serve as suitable
platforms for realizing Weyl fermions and the exotic chiral elctrodynamic
phenomena, which have promising technological applications.
[Show abstract][Hide abstract] ABSTRACT: We show that one-dimensional time reversal (TR) symmetric (class DIII)
topological superconductors (TS) frequently possess a coexisting chiral
symmetry allowing one to define an underlying integer chirality invariant. For
unbroken TR and chirality invariance the parameter regimes for nontrivial
values of the Z_2 DIII-invariant and the Z chiral invariant coincide. However,
broken TR may or may not be accompanied by broken chirality, and if chiral
symmetry is unbroken, the pair of Majorana fermions (MFs) at a given end
survives the loss of TR symmetry. Conversely, we show that broken chirality may
or may not be accompanied by broken TR, and if TR is unbroken, the pair of MFs
survives the loss of broken chirality. In addition to solving the outstanding
problem of the anomalous magnetic field response of all the DIII class
topological superconductors proposed in the literature so far, we also provide
a realistic route to engineer a "true" TR-invariant TS, whose Majorana Kramer's
pair at each end is split by an applied Zeeman field in arbitrary directions in
spin space.
[Show abstract][Hide abstract] ABSTRACT: The realization of spin-orbit coupling (SOC) in ultracold atomic gases has
opened the door for observing Majorana fermions (MFs) in cold atom systems. We
show that MFs exist in three dimensional (3D) fermionic optical lattices with
strictly one dimensional (1D) SOC which has already been realized in
experiments. The presence of an in-plane Zeeman field drives the system from a
Bardeen-Cooper-Schrieffer (BCS) superfluid to a Fulde-Ferrell (FF) superfluid
phase. We find that both phases support multiple MFs at each end of quasi-one
dimensional (quasi-1D) optical lattices with a weak transverse tunneling. In
the generalization to 3D, the multiple MFs form a zero energy flat band. Our
results are useful to guide the experimentalists on searching for MFs in the
context of ultracold fermionic atoms.
Physical Review A 10/2013; 92(2). DOI:10.1103/PhysRevA.92.023621 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that the topologically trivial zero bias peak (ZBP) emerging in
semiconductor Majorana wires due to soft confinement exhibits correlated
splitting oscillations as function of the applied Zeeman field, similar to the
correlated splitting of the Majorana ZBP. Also, we find that the presence of a
strong impurity can effectively cut the wire in two and destroy the correlated
splitting in both the trivial and the Majorana regimes. We identify a strong
non-local effect that operates only in the topologically trivial regime and
demonstrate that the dependence of the ZBP on the confining gate potential at
the opposite end in Majorana wires with two normal metal end-contacts
represents a powerful tool for discriminating between topologically trivial and
non-trivial ZBPs.
Physical Review B 10/2013; 89(22). DOI:10.1103/PhysRevB.89.220507 · 3.74 Impact Factor