Ilya Drozdov

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.

Spatial fluctuations of helical Dirac fermions on the surface of topological insulators

Helical Dirac fermion states in topological insulators could enable dissipation-free spintronics and robust quantum information processors. A study of the influence of disorder on these states shows that although they are resilient against backscattering by magnetic impurities, fluctuations caused by charge impurities could cause problems for such applications.

Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor

We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains can be easily tuned between trivial and topological ground states. In the latter, spatially resolved spectroscopy can be used to probe the Majorana fermion end states. Decoupled Majorana bound states can form even in short magnetic chains consisting of only tens of atoms. We propose scanning tunneling microscopy as the ideal technique to fabricate such systems and to probe their topological properties.

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.

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.

Topological superconductivity induced by ferromagnetic metal chains

Recent experiments have provided evidence that one-dimensional (1D) topological superconductivity can be realized experimentally by placing transition-metal atoms that form a ferromagnetic chain on a superconducting substrate. We address some properties of this type of system by using a Slater-Koster tight-binding model to account for important features of the electronic structure of the transition-metal chains on the superconducting substrate. We predict that topological superconductivity is nearly universal when ferromagnetic transition-metal chains form straight lines on superconducting substrates and that it is possible for more complex chain structures. When the chain is weakly coupled to the substrate and is longer than superconducting coherence lengths, its proximity-induced superconducting gap is ∼ Δ E SO / J where Δ is the s -wave pair potential on the chain, E SO is the spin-orbit splitting energy induced in the normal chain state bands by hybridization with the superconducting substrate, and J is the exchange splitting of the ferromagnetic chain d bands. Because of the topological character of the 1D superconducting state, Majorana end modes appear within the gaps of finite length chains. We find, in agreement with the experiment, that when the chain and substrate orbitals are strongly hybridized, Majorana end modes are substantially reduced in amplitude when separated from the chain end by less than the coherence length defined by the p -wave superconducting gap. We conclude that Pb is a particularly favorable substrate material for ferromagnetic chain topological superconductivity because it provides both strong s -wave pairing and strong Rashba spin-orbit coupling, but that there is an opportunity to optimize properties by varying the atomic composition and structure of the chain. Finally, we note that in the absence of disorder, a new chain magnetic symmetry, one that is also present in the crystalline topological insulators, can stabilize multiple Majorana modes at the end of a single chain.

Design and performance of an ultra-high vacuum scanning tunneling microscope operating at dilution refrigerator temperatures and high magnetic fields

We describe the construction and performance of a scanning tunneling microscope capable of taking maps of the tunneling density of states with sub-atomic spatial resolution at dilution refrigerator temperatures and high (14 T) magnetic fields. The fully ultra-high vacuum system features visual access to a two-sample microscope stage at the end of a bottom-loading dilution refrigerator, which facilitates the transfer of in situ prepared tips and samples. The two-sample stage enables location of the best area of the sample under study and extends the experiment lifetime. The successful thermal anchoring of the microscope, described in detail, is confirmed through a base temperature reading of 20 mK, along with a measured electron temperature of 250 mK. Atomically resolved images, along with complementary vibration measurements, are presented to confirm the effectiveness of the vibration isolation scheme in this instrument. Finally, we demonstrate that the microscope is capable of the same level of performance as typical machines with more modest refrigeration by measuring spectroscopic maps at base temperature both at zero field and in an applied magnetic field.

Quasiparticle Interference on the Surface of the Topological Crystalline Insulator Pb1-xSnxSe

Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of this phase, which undergoes a topological phase transition upon changing the lead content. We used scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES) to probe the surface states on (001) Pb_(1−x)Sn_xSe in the topologically nontrivial (x=0.23) and topologically trivial (x=0) phases. We observed quasiparticle interference with STM on the surface of the topological crystalline insulator and demonstrated that the measured interference can be understood from ARPES studies and a simple band structure model. Furthermore, our findings support the fact that Pb_(0.77)Sn_(0.23)Se and PbSe have different topological nature.

Scanning Josephson spectroscopy on the atomic scale

Unconventional superconductors, with order parameters that are predicted to have short range spatial modulations, have held long standing interest in the field. The Josephson effect, which directly probes the strength of the pairing potential is an ideal technique to study these materials, in contrast to a majority of probes which rely on deductions made from quasiparticle measurements. The authors combine the Josephson effect with the high spatial resolution afforded by scanning tunneling microscopy to study atomic scale variations of the order parameter in a model system consisting of magnetic adatoms on a BCS superconductor. The atomic resolution achieved establishes scanning Josephson spectroscopy as a promising tool for the study of novel superconducting materials.

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.