Majorana bound states with chiral magnetic textures

Abstract

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. This Tutorial is aimed at students at the graduate level.

Tunable Planar Josephson Junctions Driven by Time-Dependent Spin-Orbit Coupling

“…In the push to implement beyond-CMOS applications, Josephson junctions (JJs) have found their broad use due to their high-speed switching, low-power dissipation, and intrinsic nonlinearities [1,2]. In addition to the well-established role of JJs as the key elements for superconducting electronics and superconducting qubits [1][2][3][4][5][6], there is a growing interest to tailor their spin-dependent properties to enable dissipationless spin currents, cryogenic memory [7][8][9][10][11][12][13][14], and faulttolerant quantum computing [15][16][17][18][19][20][21][22]. The role of spinorbit coupling (SOC) has been extensively studied in the normal-state properties and recognized for its importance in spintronics [23][24][25].…”

Superconductor/Ferromagnet Heterostructures: A Platform for Superconducting Spintronics and Quantum Computation

“…This topic has been recently reviewed in ref. [127]. Despite an impressive materials progress and intensive experimental effort, a conclusive demonstration of Majorana states is still missing.…”

Repulsion of a Néel-Type Skyrmion from a Pearl Vortex in Thin Ferromagnet–Superconductor Heterostructures

“…Such topologically stable configurations can be stabilized by Dzyaloshinskii-Moriya interaction (DMI) in ferromagnetic films [9]. Skyrmions in SF heterostructures induce Yu-Shiba-Rusinov-type bound states [10,11], host Majorana modes [12][13][14][15][16][17][18][19][20], affect the Josephson effect [21], and change the superconducting critical temperature [22].…”