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This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some details the simplest "toy model" in which Majoranas appear,…

Mesoscale and Nanoscale Physics · Physics 2013-01-09 Martin Leijnse , Karsten Flensberg

We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of {\Delta} = t, and by using…

Strongly Correlated Electrons · Physics 2018-03-15 Jian-Jian Miao , Hui-Ke Jin , Fu-Chun Zhang , Yi Zhou

The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic…

Strongly Correlated Electrons · Physics 2026-05-04 Will Holdhusen , Daniel Huerga , Gerardo Ortiz

We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the…

Quantum Physics · Physics 2018-06-22 Yu-Ran Zhang , Yu Zeng , Heng Fan , J. Q. You , Franco Nori

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as…

High Energy Physics - Theory · Physics 2023-02-08 Pawel Caputa , Nitin Gupta , S. Shajidul Haque , Sinong Liu , Jeff Murugan , Hendrik J. R. Van Zyl

We demonstrate topological characterization of $S=\frac{1}{2}$ Kitaev quantum spin liquids on a series of one-dimensional honeycomb nanoribbon lattices with zigzag and armchair terminated edges. We draw their Majorana spinon phase diagrams…

Strongly Correlated Electrons · Physics 2023-06-21 Ryuto Tadokoro , Shoji Yamamoto

We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana zero-modes at the…

Superconductivity · Physics 2021-09-03 L. S. Ricco , J. E. Sanches , Y. Marques , M. de Souza , M. S. Figueira , I. A. Shelykh , A. C. Seridonio

In this work, the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a…

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections…

Strongly Correlated Electrons · Physics 2015-05-27 Wade DeGottardi , Diptiman Sen , Smitha Vishveshwara

We investigate the robustness of topological superconductors under the perturbing influence of a finite charge current. To this aim, we introduce a modified Kitaev Hamiltonian parametrically dependent on the quasiparticle momentum induced…

Superconductivity · Physics 2023-02-22 Alfonso Maiellaro , Francesco Romeo , Fabrizio Illuminati , Roberta Citro

Topological superconductors in one spatial dimension exhibiting a single Majorana bound state at each end are distinguished from trivial gapped systems by a Z_2 topological invariant. Originally, this invariant was calculated by Kitaev in…

Mesoscale and Nanoscale Physics · Physics 2013-08-15 Jan Carl Budich , Eddy Ardonne

1D superconductor-semiconductor nanowires are the leading candidates for topological quantum computation due to their ability to host non-Abelian Majorana zero modes (MZMs). However, the standard methods for identifying MZMs are often…

Mesoscale and Nanoscale Physics · Physics 2025-04-09 Jacob R. Taylor , Sankar Das Sarma

Most studies of non-trivial topological systems are carried out in non-interacting models that admit an exact solution. This raises the question, to which extent the consideration of electronic correlations and disorder, present in real…

Strongly Correlated Electrons · Physics 2024-11-12 A. C. P. Lima , M. S. Figueira , Mucio A. Continentino

We elaborate on the topological order in the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Delta=t, and chemical potential mu=0. In particular, we write out the explicit eigenstates…

Strongly Correlated Electrons · Physics 2015-02-20 Martin Greiter , Vera Schnells , Ronny Thomale

Exploration of topology protected by a certain symmetry is central in condensed matter physics. A recent idea of sub-symmetry-protected (SSP) topology--remains of a broken symmetry can still protect specific topological boundary states--has…

Mesoscale and Nanoscale Physics · Physics 2025-03-19 Myungjun Kang , Mingyu Lee , Sangmo Cheon

We present a stochastic formulation of the Keldysh theory to calculate the conductance of a finite Kitaev chain coupled to two electron reservoirs. We study the dependence of the conductance on the number of sites in the chain and find that…

Mesoscale and Nanoscale Physics · Physics 2015-06-22 Ruben Doornenbal , Georgios Skantzaris , Henk Stoof

We study the Kitaev model on a finite-size square lattice with periodic boundary conditions in one direction and open boundary conditions in the other. Based on the fact that the Majorana representation of Kitaev model is equivalent to a…

Quantum Physics · Physics 2018-08-27 P. Wang , S. Lin , G. Zhang , Z. Song

We study analytically a modified dimerized Kitaev chain model under both periodic and open boundary conditions and determine its phase diagram by calculating the topological number and edge correlation functions of Majorana fermions. We…

Strongly Correlated Electrons · Physics 2017-11-29 Yucheng Wang , Jian-Jian Miao , Shu Chen

We analyze the topological properties of a chiral ${p}+i{p}$ superconductor for a two-dimensional metal/semimetal with four Dirac points. Such a system has been proposed to realize second-order topological superconductivity and host corner…

Mesoscale and Nanoscale Physics · Physics 2022-01-07 Apoorv Tiwari , Ammar Jahin , Yuxuan Wang

Recent years saw the complete classification of topological band structures, revealing an abundance of topological crystalline insulators. Here we theoretically demonstrate the existence of topological materials beyond this framework,…

Mesoscale and Nanoscale Physics · Physics 2019-11-13 Daniel Varjas , Alexander Lau , Kim Pöyhönen , Anton R. Akhmerov , Dmitry I. Pikulin , Ion Cosma Fulga
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