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.

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Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

A major challenge in developing topological superconductors for implementing topological quantum computing is their characterization and control. It has been proposed that a p-wave-gapped topological superconductor can be fabricated with single-atom precision by assembling chains of magnetic atoms on s-wave superconductors with spin–orbit coupling. Here we analyse Bogoliubov quasiparticle interference in Mn chains, constructed atom by atom on Nb(110), and reveal the formation of multi-orbital Shiba bands using momentum-resolved measurements. We find evidence that one band features a topologically non-trivial p-wave gap, as inferred from its shape and particle–hole asymmetric intensity. Our work is an important step towards a distinct experimental determination of topological phases in multi-orbital systems by bulk electron band structure properties only. Chains of magnetic atoms on the surface of a superconductor are shown to have topologically non-trivial bands that could host Majorana bound states.

Topological Shiba bands in artificial spin chains on superconductors

One of the most exciting areas of research in quantum condensed matter physics is the push to create topologically protected qubits using non-Abelian anyons. The focus of these efforts has been Majorana zero modes (MZMs), which are predicted to emerge as localized zero-energy states at the ends of 1D topological superconductors. A key role in the search for experimental signatures of these quasiparticles has been played by the scanning tunnelling microscope (STM). The power of high-resolution STM techniques is perhaps best illustrated by their application in identifying MZMs in 1D chains of magnetic atoms on the surface of a superconductor. In this platform, STM spectroscopic mapping has demonstrated the localized nature of MZM zero-energy excitations at the ends of such chains, and experiments with superconducting and magnetic STM tips have been used to uniquely distinguish them from trivial edge modes. Beyond the atomic chains, STM has also uncovered signatures of MZMs in 2D materials and topological surface and boundary states, when they are subjected to the superconducting proximity effect. Looking ahead, future STM experiments may be able to demonstrate the non-Abelian statistics of MZMs. Majorana zero modes are non-Abelian anyons that hold promise for realizing topologically protected quantum computation. This Review discusses how scanning tunnelling microscopy can identify Majorana zero modes and investigate their properties, and outlines future research direction of the field.

Detecting and distinguishing Majorana zero modes with the scanning tunnelling microscope

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms. 

https://www.nature.com/articles/s41565-022-01078-4.pdf

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification. The influence of spin-orbit coupling on the hybridization of Shiba states in dimers of magnetic atoms on superconducting surfaces remains unexplored. Here, the authors reveal a splitting of atomic Shiba orbitals due to spin-orbit coupling and broken inversion symmetry in antiferromagnetically coupled Mn dimers placed on a Nb(110) surface.

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Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

We have studied cleaning procedures of Nb(110) by verifying the surface quality with low-energy electron diffraction, Auger electron spectroscopy, and scanning tunneling microscopy and spectroscopy. Our results show that the formation of a surface-near impurity depletion zone is inhibited by the very high diffusivity of oxygen in the Nb host crystal which kicks in at annealing temperatures as low as a few hundred degree Celsius. Oxygen can be removed from the surface by heating the crystal up to $T=2400{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. Tunneling spectra measured on the clean Nb(110) surface exhibit a sharp conductance peak in the occupied states at an energy of about $\ensuremath{-}450$ meV. Density functional theory calculations show that this peak is caused by a ${d}_{{z}^{2}}$ surface resonance band at the $\overline{\mathrm{\ensuremath{\Gamma}}}$ point of the Brillouin zone which provides a large density of states above the sample surface. The clean Nb(110) surface is superconducting with a gap width and a critical magnetic field strength in good agreement to the bulk value. In an external magnetic field we observe the Abrikosov lattice of flux quanta (vortices). Spatially resolved spectra show a zero-bias anomaly in the vortex core.

Preparation and electronic properties of clean superconducting Nb(110) surfaces

Envisioned extremely scaled, high-performance memory devices request to conduct the step from thin semiconductor films to nanoscale structures and the use of promising high-k materials such as hafnium oxide (HfO2). HfO2 is well suited for use in resistive random-access memory (ReRAM) devices based on the valence change mechanism. Here, we provide a decidedly scaled system, namely, HfO2 nanoislands that are grown by van der Waals epitaxy on highly oriented pyrolytic graphite (HOPG). The electronic and structural properties of these well-separated, crystalline HfO2 nanoislands are investigated by scanning probe methods as well as ab initio methods. The topography reveals homogeneously formed HfO2 nanoislands with areas down to 7 nm2 and a thickness of one unit cell. They exhibit several acceptor- and donor-like in-gap states in addition to the bulk band gap, implying bulk properties. X-ray photoelectron spectroscopy indicates hafnium carbide formation as one possible origin for defect states. Going further to the crystal nucleation of HfO2, nanocrystals with a diameter of 2.7–4.5 Å are identified next to carbon vacancies in the topmost HOPG layer, indicating that carbon is incorporated into the islands at early nucleation stages. A precise description of these nuclei is accomplished by the simulation of small HfmOn(:C) clusters (m = 3 to 10; n = 3 to 22) with and without carbon incorporation using ab initio methods. The comparison of the theoretically determined lowest-energy clusters and electronic states with the experimental results allows us to identify the structure of the most relevant HfO2 sub-nanometer crystals formed during the first nucleation steps and the nature of the in-gap states found at the surfaces of HfO2 nanoislands. That way, a model system is derived that consists of distinct structural units, related to surface states or defect states, respectively, that will promote the tailoring of in-gap states of smallest HfO2 structures and thus the scalability of memory devices. 

https://pubs.acs.org/doi/pdf/10.1021/acsanm.2c04165

Niclas Schmidt

Papers

Preparation and electronic properties of clean superconducting Nb(110) surfaces

In-Gap States of HfO2 Nanoislands Driven by Crystal Nucleation: Implications for Resistive Random-Access Memory Devices

Moisture Effect on the Threshold Switching of TOPO-Stabilized Sub-10 nm HfO2 Nanocrystals in Nanoscale Devices