Boundary-obstructed topological phases

@article{Khalaf2019BoundaryobstructedTP,
  title={Boundary-obstructed topological phases},
  author={Eslam Khalaf and Wladimir A. Benalcazar and Taylor L. Hughes and Raquel Queiroz},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2019}
}
Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here, we introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, we say two bulk Hamiltonians belong to distinct boundary obstructed topological `phases' (BOTPs) if they can be deformed to each other on a system with periodic… 
Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces
Higher-order topological insulators (HOTIs) are systems with topologically protected in-gap boundary states localized at their $(d-n)$-dimensional boundaries, with $d$ the system dimension and $n$
Acoustic Realization of Surface-Obstructed Topological Insulators
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the
Topological phases of the dimerized Hofstadter butterfly
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice’s hopping amplitudes can induce a
Bulk-boundary correspondence in disordered higher-order topological insulators
In this work, we study the disorder effects on the bulk-boundary correspondence of twodimensional higher-order topological insulators (HOTIs). We concentrate on two cases: (i) bulkcorner
Acoustic analogues of three-dimensional topological insulators
TLDR
This work experimentally demonstrates a three-dimensional topological acoustic crystal with pseudospins using bilayer chiral structures, in which multi-order topological bandgaps are generated step by step via elaborately manipulating the corresponding spatial symmetries.
Tenfold Topology of Crystals
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological
2n -root weak, Chern, and higher-order topological insulators, and 2n -root topological semimetals
Recently, we have introduced in [A. M. Marques et al., Phys. Rev. B 103, 235425 (2021)] the concept of 2-root topology and applied it to one-dimensional (1D) systems. These models require n squaring
Selective branching and converting of topological modes
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological
Square-root-like higher-order topological states in three-dimensional sonic crystals
TLDR
A three-dimensional (3D)square-root-like sonic crystal is presented by stacking the 2D square-root lattice in the normal (z) direction by introducing the staggered interlayer couplings on each square- root layer, which leads to a nontrivial bulk polarization in the z direction.
Subdimensional topologies, indicators, and higher order boundary effects
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a
...
1
2
3
4
...

References

SHOWING 1-10 OF 126 REFERENCES
Topological Phases Protected by Point Group Symmetry
We consider symmetry protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of
Higher-order topological insulators
TLDR
The notion of three-dimensional topological insulators is extended to systems that host no gapless surface states but exhibit topologically protected gapless hinge states and it is shown that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topology insulators.
Shift Insulators: Rotation-Protected Two-Dimensional Topological Crystalline Insulators
We study a two-dimensional (2D) tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite
Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators
The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in
Building crystalline topological phases from lower-dimensional states
We study the classification of symmetry protected topological (SPT) phases with crystalline symmetry (cSPT phases). Focusing on bosonic cSPT phases in two and three dimensions, we introduce a simple
Surfaces of axion insulators
Axion insulators are magnetic topological insulators in which the nontrivial ${\mathbb{Z}}_{2}$ index is protected by inversion symmetry instead of time-reversal symmetry. The naturally gapped
Acoustic higher-order topological insulator on a kagome lattice
TLDR
A second-order topological insulator in an acoustical metamaterial with a breathing kagome lattice, supporting one-dimensional edge states and zero-dimensional corner states is demonstrated, and shape dependence allows corner states to act as topologically protected but reconfigurable local resonances.
Inversion-symmetric topological insulators
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface
Wallpaper fermions and the nonsymmorphic Dirac insulator
TLDR
It is shown that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples.
Fragile topology protected by inversion symmetry: Diagnosis, bulk-boundary correspondence, and Wilson loop
We study the bulk and boundary properties of fragile topological insulators (TIs) protected by inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification. First, we
...
1
2
3
4
5
...