Sangjun Jeon

Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

A possible sighting of Majorana states Nearly 80 years ago, the Italian physicist Ettore Majorana proposed the existence of an unusual type of particle that is its own antiparticle, the so-called Majorana fermion. The search for a free Majorana fermion has so far been unsuccessful, but bound Majorana-like collective excitations may exist in certain exotic superconductors. Nadj-Perge et al. created such a topological superconductor by depositing iron atoms onto the surface of superconducting lead, forming atomic chains (see the Perspective by Lee). They then used a scanning tunneling microscope to observe enhanced conductance at the ends of these chains at zero energy, where theory predicts Majorana states should appear. Science, this issue p. 602; see also p. 547 Scanning tunneling microscopy is used to observe signatures of Majorana states at the ends of iron atom chains. [Also see Perspective by Lee] Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero-energy end-states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

One-dimensional Topological Edge States of Bismuth Bilayers

The conducting surface states of 3D topological insulators are two-dimensional. In an analogous way, the edge states of 2D topological insulators are one-dimensional. Direct evidence of this one-dimensionality is now presented, by means of scanning tunnelling spectroscopy, for bismuth bilayers—one of the first theoretically predicted 2D topological insulators.

The Crystal and Electronic Structures of Cd3As2, the Three-Dimensional Electronic Analogue of Graphene

The structure of Cd3As2, a high-mobility semimetal reported to host electrons that act as Dirac particles, is reinvestigated by single-crystal X-ray diffraction. It is found to be centrosymmetric rather than noncentrosymmetric as previously reported. It has a distorted superstructure of the antifluorite (M2X) structure type with a tetragonal unit cell of a = 12.633(3) and c = 25.427(7) Å in the centrosymmetric I41/acd space group. The antifluorite superstructure can be envisioned as consisting of distorted Cd6□2 cubes (where □ = an empty cube vertex) in parallel columns, stacked with opposing chirality. Electronic structure calculations performed using the experimentally determined centrosymmetric structure are similar to those performed with the inversion symmetry absent but with the important implication that Cd3As2 is a three-dimensional (3D)-Dirac semimetal with no spin splitting; all bands are spin degenerate and there is a 4-fold degenerate bulk Dirac point at the Fermi energy along Γ-Z in the Brillouin zone. This makes Cd3As2 a 3D electronic analogue of graphene. Scanning tunneling microscopy experiments identify a 2 × 2 surface reconstruction in the (112) cleavage plane of single crystals; needle crystals grow with a [110] long axis direction.This is a revised version of a manuscript that was originally posted here in February of 2014. It has been accepted at the journal Inorganic Chemistry after reviews that included those of two crystallographers who made sure all the ts were crossed and the is were dotted. The old work (from 1968) that said that Cd3As2 was noncentrosymmetric was mistaken, with the authors of that study making a type of error that in the 1980s became infamous in crystallography. As a result of the increased scrutiny of the issue of centrosymmetricity of the 1980s, there are now much better analysis tools to resolve the issue fully, and its important to understand that not just our crystals are centrosymmetric, even the old guys crystals were centrosymmetric (and by implication everyones are). There is no shame in having made that error back in the day and those authors would not find the current centrosymmetric result controversial; their paper is excellent in all other aspects. This manuscript describes how the structure is determined, explains the structure schematically, calculates the electronic structure based on the correct centrosymmetric crystal structure, and gives the structural details that should be used for future analysis and modeling.

High-resolution studies of the Majorana atomic chain platform

High-resolution scanning tunnelling microscopy measurements show that chains of magnetic atoms on the surface of a superconductor provide a promising platform for realizing and manipulating Majorana fermion quasiparticles.

Distinguishing a Majorana zero mode using spin-resolved measurements

Topological or trivial? Evidence for Majorana bound states (MBS), which are expected to provide a platform for topological quantum computing, has been found in several material systems. Typically, the experimental signature is a peak in the spectrum at zero energy, but mechanisms other than MBS need to be carefully ruled out. Using spin-polarized scanning tunneling spectroscopy, Jeon et al. studied chains of iron atoms deposited on superconducting lead and found a more distinctive signature of the topological states. Unlike trivial zero-energy states, MBS exhibited a characteristic spin-polarization signal. Science, this issue p. 772 Scanning tunneling spectroscopy measurements suggest that Majorana bound states have a distinctive spin-polarization signature. One-dimensional topological superconductors host Majorana zero modes (MZMs), the nonlocal property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin-polarization measurements as a diagnostic tool to distinguish topological MZMs from trivial in-gap states of a superconductor.

Higher-order topology in bismuth

The mathematical field of topology has become a framework in which to describe the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk–boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principles calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunnelling spectroscopy, we probe the signatures of the rotational symmetry of the one-dimensional states located at the step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.The study of the band structure and crystal symmetry of the semimetal bismuth indicates that this material is a higher-order topological insulator hosting robust one-dimensional metallic states on the hinges of the crystal.

Imaging electronic states on topological semimetals using scanning tunneling microscopy

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference (QPI) and emerging Landau levels at high magnetic field in Dirac semimetals Cd3As2 and Na3Bi, we observed extended Dirac-like bulk electronic bands. QPI imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.