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We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and…

Superconductivity · Physics 2007-05-23 A. V. Balatsky , I. Vekhter , Jian-Xin Zhu

A field theoretic approach is developed to investigate the profile and spectrum of sub-gap states in a superconductor subject to a weak magnetic impurity potential. Such states are found to be associated with inhomogeneous supersymmetry…

Superconductivity · Physics 2009-10-31 A Lamacraft , B D Simons

Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates…

Superconductivity · Physics 2019-01-14 Mahdi Mashkoori , Kristofer Björnson , Annica M. Black-Schaffer

Magnetic orders characterized by multiple ordering vectors harbor noncollinear and noncoplanar spin textures and can be a source of unusual electronic properties through the spin Berry phase mechanism. We theoretically show that such…

Strongly Correlated Electrons · Physics 2016-07-22 Satoru Hayami , Ryo Ozawa , Yukitoshi Motome

Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry.…

Recently topological superconducting states has attracted a lot of interest. In this work, we consider a topo- logical superconductor with $Z_2$ topological mirror order [1] and s$\pm$-wave superconducting pairing symmetry, within a…

Superconductivity · Physics 2015-11-18 Yuan-Yen Tai , Hongchul Choi , Towfiq Ahmed , C. S. Ting , Jian-Xin Zhu

Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an s-wave superconductor and the magnetization direction is reversed. In this paper we address the…

Mesoscale and Nanoscale Physics · Physics 2020-01-29 Gaurav Chaudhary , Allan H. MacDonald

In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby.…

Strongly Correlated Electrons · Physics 2015-05-13 H. Alloul , J. Bobroff , M. Gabay , P. J. Hirschfeld

Unconventional features in superconductivity are revealed by responses to impurity scattering. We study non-magnetic impurity effects in a three-dimensional topological superconductor, focusing on an effective model (massive Dirac…

Superconductivity · Physics 2014-11-06 Yuki Nagai , Yukihiro Ota , Masahiko Machida

We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from s_{+-} state to s_{++} state induced by interband impurity scattering. Using a Ginzburg-Landau theory, derived…

Superconductivity · Physics 2014-04-14 Valentin Stanev , Alexei E. Koshelev

Shortly after the discovery of topological band insulators, topological Kondo insulators (TKIs) have also been theoretically predicted. The latter has ignited revival interest in the properties of Kondo insulators. Currently, the…

Strongly Correlated Electrons · Physics 2025-06-05 C. -C. Joseph Wang , Jean-Pierre Julien , A. V. Balatsky , Jian-Xin Zhu

Topological superconductivity is currently one of the prime interests, given the properties of its exotic nature of chiral edge states. A broken time-reversal symmetry (TRS) is an essential ingredient in the recipe of a chiral edge state.…

Superconductivity · Physics 2025-08-05 Sajid Sekh , Andrzej Ptok

Regular arrays of magnetic atoms on a superconductor provide a promising platform for topological superconductivity. In this work we study effects of disorder in these systems, focusing on vacancies realized by missing magnetic atoms. We…

Mesoscale and Nanoscale Physics · Physics 2016-09-28 Alex Westström , Kim Pöyhönen , Teemu Ojanen

We show that a two-dimensional $s$-wave superconductor may become topological in the presence of a magnetic field that leads to the formation of an Abrikosov vortex lattice. Below the upper critical field, a superconducting state with a…

Superconductivity · Physics 2025-11-18 Daniil S. Antonenko , Liang Fu , Leonid. I Glazman

In light of recent proposals to realize a topological superconductor on the surface of strong topological insulators, we study impurity and vortex scattering in two dimensional topological superconductivity. We develop a theory of…

Superconductivity · Physics 2015-04-21 Aaron Farrell , Maxime Beaudry , M. Franz , T. Pereg-Barnea

We consider the effects of magnetic impurities on the surface of superconducting Cu doped $Bi_{2}Se_{3}$ in the odd parity pairing phase which support topologically protected Majorana fermions surface states with linear spectrum. We show…

Superconductivity · Physics 2013-01-11 Ting-Pong Choy , K. T. Law , Tai-Kai Ng

We investigate the fate of topological states on fractal lattices. Focusing on a spinless chiral p-wave paired superconductor, we find that this model supports two qualitatively distinct phases when defined on a Sierpinski gasket. While the…

Mesoscale and Nanoscale Physics · Physics 2019-10-22 Shriya Pai , Abhinav Prem

We address the electronic structure of the surface states of topological insulator thin films with embedded local non-magnetic and magnetic impurities. Using the $T$-matrix expansion of the real space Green's function, we derive the local…

Mesoscale and Nanoscale Physics · Physics 2017-07-14 Mahroo Shiranzaei , Fariborz Parhizgar , Jonas Fransson , Hosein Cheraghchi

When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that…

Superconductivity · Physics 2009-11-07 Francesca M. Marchetti , B. D. Simons

It is shown that the Hamiltonian for a quantum magnetic impurity on the surface of a topological insulator can be mapped to the conventional pseudo-gap Anderson impurity model, albeit with the combinations of continuum states which…

Strongly Correlated Electrons · Physics 2011-02-07 Rok Zitko