762 research outputs found

### Classification of flat bands according to the band-crossing singularity of Bloch wave functions

We show that flat bands can be categorized into two distinct classes, that
is, singular and nonsingular flat bands, by exploiting the singular behavior of
their Bloch wave functions in momentum space. In the case of a singular flat
band, its Bloch wave function possesses immovable discontinuities generated by
the band-crossing with other bands, and thus the vector bundle associated with
the flat band cannot be defined. This singularity precludes the compact
localized states from forming a complete set spanning the flat band. Once the
degeneracy at the band crossing point is lifted, the singular flat band becomes
dispersive and can acquire a finite Chern number in general, suggesting a new
route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave
function of a nonsingular flat band has no singularity, and thus forms a vector
bundle. A nonsingular flat band can be completely isolated from other bands
while preserving the perfect flatness. All one-dimensional flat bands belong to
the nonsingular class. We show that a singular flat band displays a novel
bulk-boundary correspondence such that the presence of the robust boundary mode
is guaranteed by the singularity of the Bloch wave function. Moreover, we
develop a general scheme to construct a flat band model Hamiltonian in which
one can freely design its singular or nonsingular nature. Finally, we propose a
general formula for the compact localized state spanning the flat band, which
can be easily implemented in numerics and offer a basis set useful in analyzing
correlation effects in flat bands.Comment: 23 pages, 13 figure

### Searching for topological density wave insulators in multi-orbital square lattice systems

We study topological properties of density wave states with broken
translational symmetry in two-dimensional multi-orbital systems with a
particular focus on t$_{2g}$ orbitals in square lattice. Due to distinct
symmetry properties of d-orbitals, a nodal charge or spin density wave state
with Dirac points protected by lattice symmetries can be achieved. When an
additional order parameter with opposite reflection symmetry is introduced to a
nodal density wave state, the system can be fully gapped leading to a band
insulator. Among those, topological density wave (TDW) insulators can be
realized, when an effective staggered on-site potential generates a gap to a
pair of Dirac points connected by the inversion symmetry which have the same
topological winding numbers. We also present a mean-field phase diagram for
various density wave states, and discuss experimental implications of our
results.Comment: 15 pages, 10 figures, 7 table

### Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle

We show that the Wannier obstruction and the fragile topology of the nearly
flat bands in twisted bilayer graphene at magic angle are manifestations of the
nontrivial topology of two-dimensional real wave functions characterized by the
Euler class. To prove this, we examine the generic band topology of two
dimensional real fermions in systems with space-time inversion $I_{ST}$
symmetry. The Euler class is an integer topological invariant classifying real
two band systems. We show that a two-band system with a nonzero Euler class
cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band
system with the Euler class $e_{2}$ has band crossing points whose total
winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya
theorem fails in systems with a nonzero Euler class. We propose that the
topological phase transition between two insulators carrying distinct Euler
classes can be described in terms of the pair creation and annihilation of
vortices accompanied by winding number changes across Dirac strings. When the
number of bands is bigger than two, there is a $Z_{2}$ topological invariant
classifying the band topology, that is, the second Stiefel Whitney class
($w_2$). Two bands with an even (odd) Euler class turn into a system with
$w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the
nontrivial second Stiefel-Whitney class remains robust against adding trivial
bands, it does not impose a Wannier obstruction when the number of bands is
bigger than two. However, when the resulting multi-band system with the
nontrivial second Stiefel-Whitney class is supplemented by additional chiral
symmetry, a nontrivial second-order topology and the associated corner charges
are guaranteed.Comment: 23 pages, 13 figure

### Topological insulators and metal-insulator transition in the pyrochlore iridates

The possible existence of topological insulators in cubic pyrochlore iridates
A$_{2}$Ir$_{2}$O$_{7}$ (A = Y or rare-earth elements) is investigated by taking
into account the strong spin-orbit coupling and trigonal crystal field effect.
It is found that the trigonal crystal field effect, which is always present in
real systems, may destabilize the topological insulator proposed for the ideal
cubic crystal field, leading to a metallic ground state. Thus the trigonal
crystal field is an important control parameter for the metal-insulator
changeover. We propose that this could be one of the reasons why distinct low
temperature ground states may arise for the pyrochlore iridates with different
A-site ions. On the other hand, examining the electron-lattice coupling, we
find that softening of the $\textbf{q}$=0 modes corresponding to trigonal or
tetragonal distortions of the Ir pyrochlore lattice leads to the resurrection
of the strong topological insulator. Thus, in principle, a finite temperature
transition to a low-temperature topological insulator can occur via structural
changes. We also suggest that the application of the external pressure along
[111] or its equivalent directions would be the most efficient way of
generating strong topological insulators in pyrochlore iridates.Comment: 10 pages, 11 figures, 2 table

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