89 research outputs found
Weyl points and Dirac lines protected by multiple screw rotations
In three-dimensional noncentrosymmetric materials two-fold screw rotation
symmetry forces electron's energy bands to have Weyl points at which two bands
touch. This is illustrated for space groups No. 19 () and No. 198
(), which have three orthogonal screw rotation axes. In the case of
space groups No. 61 () and No. 205 (a-3) that have extra inversion
symmetry, Weyl points are promoted to four-fold degenerate line nodes in
glide-invariant planes. The three-fold rotation symmetry present in the space
groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to
appear along its rotation axes in the Brillouin zone and generates four-fold
and six-fold degeneracy at the point and R point, respectively.Comment: 8 pages, v2 added references; v3 corrected typos, sec.IIB slightly
expande
Correlation effects on topological crystalline insulators
We study interaction effects on the topological crystalline insulators
protected by time-reversal () and reflection symmetry () in two and three
spatial dimensions. From the stability analysis of the edge states with
bosonization, we find that the classification of the two-dimensional SPT phases
protected by Z_2\times[\mbox{U(1)}\rtimes T] symmetry is reduced from
to by interactions, where the symmetry
denotes the reflection whose mirror plane is the two-dimensional plane itself.
By extending the approach recently proposed by Isobe and Fu, we show that the
classification of the three-dimensional SPT phases (i.e., topological
crystalline insulators) protected by R\times[\mbox{U(1)}\rtimes T] symmetry
is reduced from to by interactions.Comment: 9 pages, 1 figures, v2: typos correcte
Stability of surface states of weak topological insulators and superconductors
We study the stability against disorder of surface states of weak
topological insulators (superconductors) which are stacks of
strong topological insulators (superconductors), considering
representative Dirac Hamiltonians in the Altland-Zirnbauer symmetry classes in
various spatial dimensions. We show that, in the absence of disorder, surface
Dirac fermions of weak topological insulators (superconductors)
can be gapped out by a Dirac mass term which couples surface Dirac cones and
leads to breaking of a translation symmetry (dimerization). The dimerization
mass is a unique Dirac mass term in the surface Dirac Hamiltonian, and the two
dimerized gapped phases which differ in the sign of the Dirac mass are
distinguished by a index. In other words the dimerized surfaces
can be regarded as a strong topological insulator
(superconductor). We argue that the surface states are not localized by
disorder when the ensemble average of the Dirac mass term vanishes.Comment: 8 page
Topological classification with additional symmetries from Clifford algebras
We classify topological insulators and superconductors in the presence of
additional symmetries such as reflection or mirror symmetries. For each member
of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra
defined by operators of the generic (time-reversal, particle-hole, or chiral)
symmetries and additional symmetries, together with gamma matrices in Dirac
Hamiltonians representing topological insulators and superconductors. Following
Kitaev's approach, we classify gapped phases of non-interacting fermions under
additional symmetries by examining all possible distinct Dirac mass terms which
can be added to the set of generators of the Clifford algebra. We find that
imposing additional symmetries in effect changes symmetry classes and causes
shifts in the periodic table of topological insulators and superconductors. Our
results are in agreement with the classification under reflection symmetry
recently reported by Chiu et al. Several examples are discussed including a
topological crystalline insulator with mirror Chern numbers and mirror
superconductors.Comment: 18 page
Weyl and Dirac semimetals with Z_2 topological charge
We study the stability of gap-closing (Weyl or Dirac) points in the
three-dimensional Brillouin zone of semimetals using Clifford algebras and
their representation theory. We show that a pair of Weyl points with
topological charge are stable in a semimetal with time-reversal
and reflection symmetries when the square of the product of the two symmetry
transformations equals minus identity. We present toy models of
Weyl semimetals which have surface modes forming helical Fermi arcs. We also
show that Dirac points with topological charge are stable in a
semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries
when the square of the product of time-reversal and inversion equals plus
identity. Furthermore, we briefly discuss the topological stability of point
nodes in superconductors using Clifford algebras.Comment: 14 pages, 2 figure
Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
We study theoretically a strongly type-II s-wave superconducting state of
two-dimensional Dirac fermions in proximity to a ferromagnet having in-plane
magnetization. It is shown that a magnetic domain wall can host a chain of
equally spaced vortices in the superconducting order parameter, each of which
binds a Majorana fermion state. The overlap integral of neighboring Majorana
states is sensitive to the position of the chemical potential of the Dirac
fermions. This leads to a characteristic V-shaped dependence of thermal
conductivity of Majorana fermions on the chemical potential.Comment: 4+ pages, 2 figure
Bosonic symmetry protected topological phases with reflection symmetry
We study two-dimensional bosonic symmetry protected topological (SPT) phases
which are protected by reflection symmetry and local symmetry [,
, U(1), or U(1)], in the search for
two-dimensional bosonic analogs of topological crystalline insulators in
integer- spin systems with reflection and spin-rotation symmetries. To
classify them, we employ a Chern-Simons approach and examine the stability of
edge states against perturbations that preserve the assumed symmetries. We find
that SPT phases protected by symmetry are classified as
for even and 0 (no SPT phase) for odd
while those protected by U(1) symmetry are . We point
out that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state of spins
on the square lattice is a SPT phase protected by reflection and
-rotation symmetries.Comment: 11+epsilon pages, 2 figures; v3: typos correcte
Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
The conditions for both the stability and the breakdown of the topological
classification of gapped ground states of noninteracting fermions, the tenfold
way, in the presence of quartic fermion-fermion interactions are given for any
dimension of space. This is achieved by encoding the effects of interactions on
the boundary gapless modes in terms of boundary dynamical masses. Breakdown of
the noninteracting topological classification occurs when the quantum nonlinear
sigma models for the boundary dynamical masses favor quantum disordered phases.
For the tenfold way, we find that (i) the noninteracting topological
classification is always stable, (ii) the noninteracting
topological classification in even dimensions is always stable,
(iii) the noninteracting topological classification in odd
dimensions is unstable and reduces to that can be
identified explicitly for any dimension and any defining symmetries. We also
apply our method to the three-dimensional topological crystalline insulator
SnTe from the symmetry class AII, for which we establish the reduction
of the noninteracting topological
classification.Comment: 29 page
Unconventional Neel and dimer orders in a spin-1/2 frustrated ferromagnetic chain with easy-plane anisotropy
We study the ground-state phase diagram of a one-dimensional spin-1/2
easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling
and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling in
the parameter range . When , the model
is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the
critical phase of the XXZ model of . On the basis of the effective
(sine-Gordon) theory and numerical analyses of low-lying energy levels of
finite-size systems, we show that the NNN coupling induces phase transitions
from the Tomonaga-Luttinger liquid to gapped phases with either Neel or dimer
order. Interestingly, these two types of ordered phases appear alternately as
the easy-plane anisotropy is changed towards the isotropic limit. The
appearance of the antiferromagnetic (Neel) order in this model is remarkable,
as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling
and antiferromagnetic NNN coupling in the classical-spin picture. We argue that
emergent trimer degrees of freedom play a crucial role in the formation of the
Neel order.Comment: 10 pages, 7 figures. To be published in Phys. Rev. B (Editor's
Suggestion
Quantum impurity spin in Majorana edge fermions
We show that Majorana edge modes of two-dimensional spin-triplet topological
superconductors have Ising-like spin density whose direction is determined by
the d-vector characterizing the spin-triplet pairing symmetry. Exchange
coupling between an impurity spin (S=1/2) and Majorana edge modes is thus
Ising-type. Under external magnetic field perpendicular to the Ising axis, the
system can be mapped to a two-level system with Ohmic dissipation, which is
equivalent to the anisotropic Kondo model. The magnetic response of the
impurity spin can serve as a local experimental probe for the order parameter.Comment: 4+ pages, 2 figure
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