The Majorana spin in magnetic atomic chain systems

Abstract

In this paper, we establish that Majorana zero modes emerging from a topological band structure of a chain of magnetic atoms embedded in a superconductor can be distinguished from trivial localized zero energy states that may accidentally form in this system using spin resolved measurements. To demonstrate this key Majorana diagnostics, we study the spin composition of magnetic impurity induced in-gap Shiba states in a superconductor using a quantum impurity model (at the mean-field level). By examining the spin and spectral densities in the context of the Bogoliubov-de Gennes (BdG) particle-hole symmetry, we derive a sum rule that relates the spin densities of localized Shiba states with those in the normal state without superconductivity. Extending our investigations to ferromagnetic chain of magnetic impurities, we identify key features of the spin properties of the extended Shiba state bands, as well as those associated with a localized Majorana end mode when the effect of spin-orbit interaction is included. We then formulate a phenomenological theory for the measurement of the local spin densities with spin-polarized scanning tunneling microscopy (STM) techniques. By combining the calculated spin densities and the measurement theory, we show that spin-polarized STM measurements can reveal a sharp contrast in spin polarization between an accidentally-zero-energy trivial Shiba state and a Majorana zero mode in a topological superconducting phase in atomic chains. We further confirm our results with numerical simulations that address generic parameter settings.

22 pages, 12 figures (references updated)

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Distinguishing a Majorana zero mode using spin resolved measurements
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Strong localization of Majorana end states in chains of magnetic adatoms
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• A road to reality with topological superconductors
• Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor
• Topological Phase Detection in Rashba Nanowires with a Quantum Dot
• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
• Conductance spectroscopy on Majorana wires and the inverse proximity effect
• Spin-polarized Andreev tunneling through the Rashba chain
• Fingerprints of Majorana fermions in current-correlations measurements from a superconducting tunnel microscope

Cited by in corpus (29)

• Distinguishing a Majorana zero mode using spin resolved measurements
• Observation of a Majorana zero mode in a topologically protected edge channel
• On controlling the bound states in quantum-dot hybrid-nanowire
• Spin-polarized Yu-Shiba-Rusinov states in an iron based superconductor
• Spin-dependent zero-bias peak in a hybrid nanowire-quantum dot system: Distinguishing isolated Majorana fermions from Andreev bound states
• Majorana Fermions in Magnetic Chains
• Kondo and Majorana signatures near the singlet-doublet quantum phase transition
• Topological superconductivity from magnetic impurities on monolayer NbSe${}_2$
• Photoinduced $\frac{1}{2}\frac{e^2}{h}$ and $\frac{3}{2}\frac{e^2}{h}$ conductance plateaus in topological insulator-superconductor heterostructures
• Spin-polarized Andreev tunneling through the Rashba chain
• Identification of topological superconductivity in magnetic impurity systems using bulk spin-polarization
• Universal two-time correlations, out-of-time-ordered correlators and Leggett-Garg inequality violation by edge Majorana fermion qubits
• Majorana quasiparticles in atomic spin chains on superconductors
• Volkov-Pankratov states in topological superconductors
• Leakage of Majorana mode into correlated quantum dot nearby its singlet-doublet crossover
• Probing Majorana zero modes by measuring transport through an interacting magnetic impurity
• Majorana phase-gate based on the geometric phase
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• Nonlocal correlations transmitted between quantum dots via short topological superconductor
• Study of Yu-Shiba-Rusinov bound states by tuning the electron density at the Fermi energy
• RKKY interaction at helical edges of topological superconductors
• Moiré dispersion of edge states in spin chains on superconductors
• Detecting Topological Superconductivity via Berry Curvature Effects in Spectral Functions
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Embedded Majorana Islands
• Anomalous Shiba spectrum and superconductivity induced magnetic interactions in materials with topological band inversion
• Spin-polarized zero-bias peak from a single magnetic impurity at an s-wave superconductor: first-principles study
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope