# Edge states of the long-range Kitaev chain: An analytical study

@article{Jger2020EdgeSO, title={Edge states of the long-range Kitaev chain: An analytical study}, author={Simon B. J{\"a}ger and Luca Dell'Anna and Giovanna Morigi}, journal={Physical Review B}, year={2020}, volume={102}, pages={035152} }

We analyze the properties of the edge states of the one-dimensional Kitaev model with long-range anisotropic pairing and tunneling. Tunneling and pairing are assumed to decay algebraically with exponents $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, respectively, and $\ensuremath{\alpha},\ensuremath{\beta}g1$. We determine analytically the decay of the edge modes. We show that the decay is exponential for $\ensuremath{\alpha}=\ensuremath{\beta}$ and when the coefficients scaling tunneling and…

## 3 Citations

Topological bands in the continuum using Rydberg states

- Physics
- 2021

The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this…

Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

In this paper, we study the localized states of a generic quadratic fermionic chain with finite-range couplings and an inhomogeneity in the hopping (defect) that breaks translational invariance. When…

Gapless Topological Phases and Symmetry-Enriched Quantum Criticality

- PhysicsPhysical Review X
- 2021

We introduce topological invariants for critical bosonic and fermionic chains. More generally, the symmetry properties of operators in the low-energy conformal field theory (CFT) provide discrete…

## References

SHOWING 1-10 OF 51 REFERENCES

Long-range Ising and Kitaev models: phases, correlations and edge modes

- Physics
- 2015

We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field.…

Universal dynamical scaling of long-range topological superconductors

- Physics
- 2019

We study the out-of-equilibrium dynamics of $p$-wave superconducting quantum wires with long-range interactions, when the chemical potential is linearly ramped across the topological phase…

Kitaev chains with long-range pairing.

- Physics, MedicinePhysical review letters
- 2014

A generalization of the Kitaev chain for fermions with long-range p-wave pairing is proposed, which decays with distance as a power law with exponent α, and the existence of two types of gapped regimes is demonstrated.

Extended Kitaev chain with longer-range hopping and pairing

- Physics
- 2017

We consider the Kitaev chain model with finite and infinite range in the hopping and pairing parameters, looking in particular at the appearance of Majorana zero energy modes and massive edge modes.…

Colloquium : Topological insulators

- Physics
- 2010

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…

Chiral Topological Superconductors Enhanced by Long-Range Interactions.

- Physics, MedicinePhysical review letters
- 2018

New topological phases and quasiparticles different from the usual short-range model are obtained when both hopping and pairing terms decay with the same exponent, and one of the topological chiral phases with propagating Majorana edge states gets significantly enhanced by long-range couplings.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

- Physics
- 2016

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display…

The 1D Ising model and the topological phase of the Kitaev chain

- Physics
- 2014

Abstract It has been noted that the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Δ = t , and chemical potential μ = 0 , can be mapped into a…

Topological superconducting phase in helical Shiba chains

- Physics
- 2013

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the…

Exploring a Proximity-Coupled Co Chain on Pb(110) as a Possible Majorana Platform

- Physics, MedicineNano letters
- 2017

Despite the ferromagnetic coupling within the chains and the strong spin-orbit coupling in the superconductor, the study of iron (Fe) chains does not find clear evidence of Majorana modes.