One-dimensional 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:math>
-root topological insulators and superconductors

Marques, A. M.; Madail, L.; Dias, R. G.

doi:10.1103/physrevb.103.235425

Cited by 43 publications

(15 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A simple 2D example where the approach of this paper can be applied is that of a plane of parallel extended SSH chains with uniform or staggered hopping terms between them. An interesting ex-tension of these results should also be possible in the context of square-root topological insulators [29,30,36] or the recently proposed 2 n -root topological insulators [37][38][39]. We also expect that the introduction of longrange hopping terms in higher-order topological insulators [40][41][42] to raise similar concerns about the possibility of hidden symmetries as well as the existence of multiple localization lengths in the corners states.…”

Section: Discussionmentioning

confidence: 72%

Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexation must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

show abstract

Section: Discussionmentioning

confidence: 72%

Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…( 22) is not very convenient. We can transform it into block diagonal form, which is always possible because the original stub model lives on a bipartite lattice [61]. This is simply achieved by a reordering of the basis to…”

Section: Parent Hamiltonianmentioning

confidence: 99%

Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

Bartlett,

Hu,

Zhao

2021

Preprint

View full text Add to dashboard Cite

Topological characterization of non-Hermitian band structures demands more than a straightforward generalization of the Hermitian cases. Even for one-dimensional tight binding models with non-reciprocal hopping, the appearance of point gaps and the skin effect leads to the breakdown of the usual bulk-boundary correspondence. Luckily, the correspondence can be resurrected by introducing a winding number for the generalized Brillouin zone for systems with even number of bands and chiral symmetry. Here, we analyze the topological phases of a non-reciprocal hopping model on the stub lattice, where one of the three bands remains flat. Due to the lack of chiral symmetry, the bi-orthogonal Zak phase is no longer quantized, invalidating the winding number as a topological index. Instead, we show that a Z2 invariant can be defined from Majorana's stellar representation of the eigenstates on the Bloch sphere. The parity of the total azimuthal winding of the entire Majorana constellation correctly predicts the appearance of edge states between the bulk gaps. We further show that the system is not a square-root topological insulator, despite the fact that its parent Hamiltonian can be block diagonalized and related to a sawtooth lattice model. The analysis presented here may be generalized to understand other non-Hermitian systems with multiple bands.

show abstract

“…It is pertinent to mention here that in analysing the topological tight binding models, the use of nontrivial square-root technique yields an identical looking equation that is quadratic in energy 24 . In this context its pertinent to refer to a recent work on 2 n root topological insulators as well 25 .…”

Section: Ssh4 To Ssh: the Mapping And The Topological Issuesmentioning

confidence: 99%

Topological properties of a class of Su-Schrieffer-Heeger variants

Bid,

Chakrabarti

2021

Preprint

View full text Add to dashboard Cite

We investigate the edge states and the topological phase transitions in a class of tight binding lattices in one dimension where a Su-Schrieffer-Heeger (SSH) model exists in disguise. The unit cells of such lattices may have an arbitrarily intricate staggering pattern woven in the hopping integrals, that apparently masks the basic SSH structure. We unmask the SSH character in such lattices using a simple real space decimation of a subset of the degrees of freedom. The decimation not only allows us to recognize the familiar SSH geometry, but at the same time enables us to determine, in an analytically exact way, the precise energy eigenvalues at which the gaps open up (or close) at the Brillouin zone boundaries. It is argued that, a topological phase transition and the existence of the protected edge states can be observed in such lattices only under definite numerical correlations between the hopping integrals decorating the unit cell. Such a correlation, achievable in a variety of ways, brings different such models under a kind of a universality class.

show abstract

One-dimensional 2n -root topological insulators and superconductors

Cited by 43 publications

References 57 publications

Long-range hopping and indexing assumption in one-dimensional topological insulators

Long-range hopping and indexing assumption in one-dimensional topological insulators

Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

Topological properties of a class of Su-Schrieffer-Heeger variants

Contact Info

Product

Resources

About