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Caroli-de Gennes-Matricon (CdGM) states are localized states with a discrete energy spectrum bound to the core of vortices in superconductors. In topological superconductors, CdGM states are predicted to coexist with zero-energy, chargeless…

We theoretically predict an exotic topological superfluid state with spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. This inhomogeneous topological superfluidity is induced by applying simultaneously a…

Quantum Gases · Physics 2016-10-07 Chun Chen

An antidot-pinned vortex in a three-dimensional topological insulator-superconductor platform hosts a Majorana zero mode (MZM). However, numerous Caroli-de Gennes-Matricon (CdGM) states coexist with it. We develop a general theory to study…

Superconductivity · Physics 2026-04-14 Zhibo Ren , Jukka I. Väyrynen

We show that standard impurities, magnetic or nonmagnetic, weak or strong, can cause topological phase transitions inside the vortex cores of a conventional s-wave superconductor. Because of the nonzero angular momentum of Cooper pairs in…

Superconductivity · Physics 2020-10-20 Shengshan Qin , Chen Fang , Fu-chun Zhang , Jiangping Hu

Interfaces between topological insulators and superconductors are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a…

Superconductivity · Physics 2026-04-22 Umesh Kumar , Rafal Rechcinski , Tatiana de Picoli , Jukka Vayrynen , Satoshi Okamoto

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in…

Quantum states induced by single-atomic-impurities are the current frontier of material and information science. Recently the spin-orbit coupled correlated kagome magnets are emerging as a new class of topological quantum materials,…

We study numerically Majorana fermions (MFs) induced by a charged impurity in topological superconductors. It is revealed from the relevant Bogoliubov-de Gennes equations that (i) for quasi-one dimensional systems, a pair of MFs are bounded…

Superconductivity · Physics 2015-01-28 Tao Zhou , Xiao-Jing Li , Yi Gao , Z. D. Wang

Motivated by recent experiments we consider transport across an interacting magnetic impurity coupled to the Majorana zero mode (MZM) observed at the boundary of a topological superconductor (SC). In the presence of a finite tunneling…

Mesoscale and Nanoscale Physics · Physics 2022-03-11 Daniele Guerci , Andrea Nava

We investigate theoretically non-magnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps, by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to…

Quantum Gases · Physics 2013-01-22 Xia-Ji Liu

Both impurity- and magnetic-field-induced quasiparticle states in chiral $p$-wave superconductors are investigated theoretically by solving the Bogoliubov--de Gennes equations self-consistently. At the strong scattering limit, we find that…

Superconductivity · Physics 2017-05-10 Yao-Wu Guo , Wei Li , Yan Chen

We study in-gap states of a single magnetic impurity embedded in a honeycomb monolayer which is deposited on superconducting substrate. The intrinsic spin-orbit coupling induces the quantum spin Hall insulating (QSHI) phase gapped around…

Superconductivity · Physics 2020-08-12 Szczepan Głodzik , Tadeusz Domański

We reveal that Majorana bound states inside the vortex core in an odd-parity topological superconductivity classified as "pseudo-scalar" type in the gap function are distinctly spin-polarized by solving the massive Dirac Bogoliubov-de…

Superconductivity · Physics 2014-05-14 Yuki Nagai , Hiroki Nakamura , Masahiko Machida

We predict a universal mid-gap bound state in topological superfluids, induced by either non-magnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon…

Quantum Gases · Physics 2013-02-04 Hui Hu , Lei Jiang , Han Pu , Yan Chen , Xia-Ji Liu

Although the appearance of vortex-localized states with zero energy in first-order topological superconductors is well known, their possibility to form in the higher-order topological phase of 2D systems has not been completely uncovered…

Superconductivity · Physics 2025-06-06 A. D. Fedoseev , A. O. Zlotnikov

We study the subgap spectrum of a 2D Abrikosov vortex in an s-wave superconductor in the absence and presence of a point impurity. By solving the Eilenberger equations without impurity for two models of the vortex (including a…

Superconductivity · Physics 2021-10-12 A. A. Bespalov , V. D. Plastovets

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new…

Mesoscale and Nanoscale Physics · Physics 2014-03-12 Chen Fang , Matthew J. Gilbert , B. Andrei Bernevig

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one, in which impurity disorder strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and the…

Mesoscale and Nanoscale Physics · Physics 2018-06-13 G. E. Simion , A. Kazakov , L. P. Rokhinson , T. Wojtowicz , Y. B. Lyanda-Geller

We study the vortex lattice in a two-dimensional s-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations self-consistently for the superconducting order parameter. We…

Superconductivity · Physics 2016-08-24 Evan D. B. Smith , K. Tanaka , Yuki Nagai

Coherence effects by the impurity scattering of Caroli--de Gennes--Matricon (CdGM) modes in a vortex for nodal topological superconductors have been studied. The coherence effects reflect a topological number defined on a particular…

Superconductivity · Physics 2016-04-15 Yasumasa Tsutsumi , Yusuke Kato
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