1D Topological Superconductors Research Articles

High-resolution studies of the Majorana atomic chain platform

Ordered assemblies of magnetic atoms on the surface of conventional superconductors can be used to engineer topological superconducting phases and realize Majorana fermion quasiparticles (MQPs) in a condensed matter setting. Recent experiments have shown that chains of Fe atoms on Pb generically have the required electronic characteristics to form a 1D topological superconductor and have revealed spatially resolved signatures of localized MQPs at the ends of such chains. Here we report higher resolution measurements of the same atomic chain system performed using a dilution refrigerator scanning tunneling microscope (STM). With significantly better energy resolution than previous studies, we show that the zero bias peak (ZBP) in Fe chains has no detectable splitting from hybridization with other states. The measurements also reveal that the ZBP exhibits a distinctive 'double eye' spatial pattern on nanometer length scales. Theoretically we show that this is a general consequence of STM measurements of MQPs with substantial spectral weight in the superconducting substrate, a conclusion further supported by measurements of Pb overlayers deposited on top of the Fe chains. Finally, we report experiments performed with superconducting tips in search of the particle-hole symmetric MQP signature expected in such measurements.

CaFeAs2: A staggered intercalation of quantum spin Hall and high-temperature superconductivity

We predict that CaFeAs$_2$, a newly discovered iron-based high temperature (T$_c$) superconductor, is a staggered intercalation compound that integrates topological quantum spin hall (QSH) and superconductivity (SC). CaFeAs$_2$ has a structure with staggered CaAs and FeAs layers. While the FeAs layers are known to be responsible for high T$_c$ superconductivity, we show that with spin orbital coupling each CaAs layer is a $Z_{2}$ topologically nontrivial two-dimensional QSH insulator and the bulk is a 3-dimensional weak topological insulator. In the superconducting state, the edge states in the CaAs layer are natural 1D topological superconductors. The staggered intercalation of QSH and SC provides us an unique opportunity to realize and explore novel physics, such as Majorana modes and Majorana Fermions chains.

Longitudinal spin pumping and topological superconductivity: Search for Majorana edge states

We propose to study the absorption of the ac magnetic field polarized parallel to the dc field (longitudinal spin pumping), applied to a one-dimensional (1D) topological superconductor. Such a longitudinal pumping in 1D topological superconductors does not produce a parametric instability due to the fermionic character of eigenstates. It is shown that Majorana edge states can manifest themselves in the absorption of the longitudinal spin pumping.

Classification of engineered topological superconductors

I perform a complete classification of two-dimensional, quasi-one-dimensional (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, such 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.

Theoretical modeling and properties of class DIII topological superconductors

We theoretically study topological superconductors (TSCs) with time-reversal (TR) symmetry in one- and two-dimensions (1D and 2D). In 2D, we introduce bilayer system with Rashba spin–orbit interaction (SOI), and find that the interplay between SOI and degrees of freedom of layers induces unconventional pairing states, which are topologically nontrivial and have the helical Majorana edge channels. We also find that a usual quantum nanowire on unconventional superconductor becomes a 1D TSC by means of the proximity effect. Majorana fermions at the ends of the wire offer a unique opportunity to relate fermion parity and non-local spin correlations.

Unfrozen spin effect in a composite 1D topological superconductor

The spin of Majorana fermions (MF) is nearly frozen by the applied magnetic field in a composite 1D topological superconductor due to the weak spin-orbit coupling (SOC). In this work, we address theoretically the strong SOC limit and weak-magnetic-field effect, under which the spin degree of freedom of MFs is reactivated and dependent on the wire direction. The quantized zero-energy conductance peak in a bent N/S wire junction can be severely suppressed. The MF phase is significantly modified due to the spin noncollinearity and the fusion of MFs is independent of the wire direction, which is opposite to the strong-magnetic-field case. It is also found that the spatial distribution of an MF could be heavily affected by the wire direction. The findings are helpful to identify and braid MFs in the 1D wire network.

Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions

Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. While elementary particles of the Majorana type were not identified yet, quasi-particles with Majorana like properties, born from interacting electrons in the solid, were predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminum superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin-orbit coupling. An induced 1d topological superconductor - supporting Majorana fermions at both ends - is expected to form. We concentrate on the characteristics of a distinct zero bias conductance peak (ZBP), and its splitting in energy, both appearing only with a small magnetic field applied along the wire. The ZBP was found to be robustly tied to the Fermi energy over a wide range of system parameters. While not providing a definite proof of a Majorana state, the presented data and the simulations support strongly its existence.