Majoranas in condensed matter systems

Majorana fermions are quasiparticles that are the condensed matter analogs of exotic particles first proposed by Ettore Majorana as neutral free fermions that are their own antiparticle. Their emergence in a condensed matter setting, however, occurs with a key difference — they appear in pairs and obey non-abelian statistics — unlike ordinary fermions and bosons that we are familiar with today. A major goal of our program has been to create magnetic and superconducting hybrid structures that host Majorana zero modes (MZMs), which are Majorana fermions that appear at zero energy in one-dimensional systems that may be used to build a topological quantum bit. 

The first successful approach by our group to create a MZM platform was with chains of magnetic atoms on the surface of a superconductor. We proposed and implemented experiments to investigate whether chains of ferromagnetic atoms on the surface of a superconductor with strong spin orbit coupling can give rise to the formation of a topological superconducting phase that hosted MZMs at its ends (S. Nadj-Perge, et al. PRB 88, 2013S. Nadj-Perge, et al. Science 346, 2014). We carried out detailed scanning tunneling microscopy (STM) measurements to not only characterize the electronic properties of such chains, made up of Fe on a Pb surface, but also to utilize STM spectroscopic mapping techniques to directly visualize MZMs for the first time (S. Nadj-Perge, et al. Science 346, 2014, and B. E. Feldman, et al. Nature Physics 13, 2016). The topological phase in these chains emerges because of the interplay between ferromagnetism of the Fe chain together with strong spin-orbit coupling and superconductivity of the Pb surface.

Following this effort, we worked to develop methods that could uniquely identify MZMs and distinguish them from trivial zero modes that can accidentally form in a superconductor at zero energy (S. Jeon, et al, Science 358, 2017J. Li, et al. PRB 97, 2018). Our theoretical and experimental efforts showed that spin-polarized STM can be a powerful tool to uniquely identify MZMs, and applied this technique to unequivocally determine that the zero mode detected in Fe chains was indeed a MZM (S. Jeon, et al, Science 358, 2017J. Li, et al. PRB 97, 2018). We continue to work on developing the Majorana atomic chain platform further, by creating ways in which such chains can be assembled atom-by-atom.

More recently, we developed another platform for the creation of MZMs, which utilized edge modes of a topological insulator or hinge modes of higher order topological systems (B. Jack et. al. Science 364, 2019). It has long been recognized that the superconductivity that is induced by the proximity effect on such edge modes is topological in nature. Topological insulators provide a platform where topological superconductivity can be realized in channels that are protected by time-reversal symmetry, allowing for material imperfections, but without requiring the application of magnetic fields. Using a combination of proximity effect from a superconducting substrate and in situ growth of Bi (111) layers, and magnetic clusters, we were able to successfully create this platform. A variety of STM experiments, including spectroscopic mapping, spin-polarized measurements, and high-resolution experiments were carried out to demonstrate the presence of MZMs on the topological edge modes of Bi bilayers.

Collaboration between theory (with B. Andrei Bernevig’s group) and experiments has been critical to both guide and interpret the experimental measurements. We continue to explore methods to create MZMs, demonstrate their exotic properties, find way to manipulate them, and to ultimately demonstrate their non-Abelian properties.

Majorana fermions

A magnetized scanning tunneling microscope tip probes the spin property of the quantum wave function of the Majorana fermion at the end of a chain of iron atoms on the surface of a superconductor made of lead.

Highlight of Majorana fermions

High-resolution measurements of Majorana zero modes spatial distribution in Fe on Pb atomic chains