Topological invariants to characterize universality of boundary charge in one-dimensional insulators beyond symmetry constraints

@article{Pletyukhov2019TopologicalIT,
  title={Topological invariants to characterize universality of boundary charge in one-dimensional insulators beyond symmetry constraints},
  author={Mikhail Pletyukhov and Dante M. Kennes and Jelena Klinovaja and Daniel Loss and Herbert Schoeller},
  journal={Physical Review B},
  year={2019}
}
In the absence of any symmetry constraints we address universal properties of the boundary charge ${Q}_{B}$ for a wide class of nearest-neighbor tight-binding models in one dimension with one orbital per site but generic modulations of on-site potentials and hoppings. We provide a precise formulation of the bulk-boundary correspondence relating the boundary charge of a single band uniquely to the Zak phase evaluated in a particular gauge. We reveal the topological nature of ${Q}_{B}$ by proving… 

Figures from this paper

Rational boundary charge in one-dimensional systems with interaction and disorder

We study the boundary charge $Q_B$ of generic semi-infinite one-dimensional insulators with translational invariance and show that non-local symmetries (i.e., including translations) lead to rational

Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the hard-wall boundary and interface charges in one-dimensional single-channel continuum [S. Miles et al. , Phys. Rev. B 104 , 155409 (2021)] and multichannel

Topological and nontopological features of generalized Su-Schrieffer-Heeger models

The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longer-range hopping, is studied at half filling for an even number of sites. The ground-state phase

Theory of edge states based on the Hermiticity of tight-binding Hamiltonian operators

We develop a theory of edge states based on the hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which

Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model

A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. Although Zak’s phase remains quantized for the case of a mirror-symmetric chain, it is

Interacting Rice-Mele model: Bulk and boundaries

We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we firstly compute the single-particle spectral function,

Anomalous dielectric response in insulators with the π Zak phase

In various topological phases, nontrivial states appear at the boundaries of the system. In this paper, we investigate anomalous dielectric response caused by such states caused by the pi Zak phase.

Origin of band inversion in topological Bi2Se3

Topological materials and more so insulators have become ideal candidates for spintronics and other novel applications. These materials portray band inversion that is considered to be a key signature

Magnonic Quadrupole Topological Insulator in Antiskyrmion Crystals.

We uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic quadrupole topological insulator, whose hallmark signatures are robust magnonic corner

References

SHOWING 1-10 OF 91 REFERENCES

Topological mirror insulators in one dimension

We demonstrate the existence of topological insulators in one dimension (1D) protected by mirror and time-reversal symmetries. They are characterized by a nontrivial ${\mathbb{Z}}_{2}$ topological

Colloquium : Topological insulators

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to

Bott periodicity for the topological classification of gapped states of matter with reflection symmetry

Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two

Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function.

  • Hatsugai
  • Mathematics, Physics
    Physical review. B, Condensed matter
  • 1993
It is found that the energies of the edge states are given by the zero points of the Bloch function on some Riemann surface (RS) (complex energy surface) when the system size is commensurate with the flux.

Classification of topological insulators and superconductors in three spatial dimensions

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial

Classification of two-dimensional topological crystalline superconductors and Majorana bound states at disclinations

We classify discrete-rotation symmetric topological crystalline superconductors (TCS) in two dimensions and provide the criteria for a zero energy Majorana bound state (MBS) to be present at

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

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim

Topology of crystalline insulators and superconductors

We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by noninteracting

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,
...