Classification of engineered topological superconductors

Abstract

I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1d systems with Rashba spin-orbit coupling and time-reversal violating superconductivity, as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional "hidden" symmetries emerge, with a significant impact on the topological properties of the system. The latter, generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.

To appear in New Journal of Physics for the Focus on Majorana Fermions in Condensed Matter; Final version 19 pages, 6 figures: a new section was added concerning the appearance of MFs in two coupled Rasba semiconducting wires with proximity induced superconductivity and a finite supercurrent flow, without the application of a magnetic field. Generally improved discussion and references added

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Cited by in corpus (36)

• Classification of topological quantum matter with symmetries
• Topology of crystalline insulators and superconductors
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor
• Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Nodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
• Unravelling incommensurate magnetism and its emergence in iron-based superconductors
• Topological superconductivity in Rashba semiconductors without a Zeeman field
• Magnetic-Field-Induced Topological Reorganization of a P-wave Superconductor
• Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Majorana fermion fingerprints in spin-polarised scanning tunneling microscopy
• Superconducting diodes from magnetization gradients
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
• Magnetic manipulation of topological states in p-wave superconductors
• Geometric dependence of Nb-Bi${}_2$Te${}_3$-Nb topological Josephson junction transport parameters
• Phase Space Crystal Vibrations: Chiral Edge States with Preserved Time-reversal Symmetry
• Nodal S-wave Superconductivity in Antiferromagnetic Semimetals
• Trapping Majorana Zero Modes in Vortices of Magnetic Texture Crystals Coupled to Nodal Superconductors
• Spin-orbital polarization of Majorana edge states in oxides nanowires
• High orbital-moment Cooper pairs by crystalline symmetry breaking
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity
• Anatomy of Spin and Current Generation from Magnetization Gradients in Topological Insulators and Rashba Metals
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids
• Josephson and persistent currents in a quantum ring between topological superconductors
• Transport in extended Kitaev chain with time reversal symmetry breaking and long-range interaction
• New mechanisms to engineer magnetic skyrmions and topological superconductors
• Majorana bound states with chiral magnetic textures
• Exact solutions for topological surface states of three-dimensional lattice models