Adatom Chains Research Articles

Controlling Majorana hybridization in magnetic chain-superconductor systems

We propose controlling the hybridization between Majorana zero modes at the ends of magnetic adatom chains on superconductors by an additional magnetic adatom deposited close by. By tuning the additional adatom's magnetization, position, and coupling to the superconductor, we can couple and decouple the Majorana modes, as well as control the ground-state parity. The scheme is independent of microscopic details in ferromagnetic and helical magnetic chains on superconductors, with and without spin-orbit coupling, which we show by studying their full microscopic models and their common low-energy description. Our results show that scanning tunneling microscopy and electron-spin-resonance techniques are promising tools for controlling the Majorana hybridization in magnetic adatoms-superconductor setups, providing a basis for Majorana parity measurements, fusion, and braiding techniques. Published by the American Physical Society 2024

Fractionalization of Majorana-Ising-type quasiparticle excitations

We theoretically investigate the spectral properties of a quantum impurity (QI) hosting the here proposed Majorana-Ising-type quasiparticle excitation. It arises from the coupling between a finite topological superconductor (TSC) based on a chain of magnetic adatoms--superconducting hybrid system and an integer large spin $S$ flanking the QI. It is noteworthy that the spin $S$ couples to the QI via the Ising-type exchange interaction. As the Majorana zero modes (MZMs) at the edges of the TSC chain are overlapped, we counterintuitively find a regime wherein the Ising term modulates the localization of a fractionalized and resonant MZM at the QI site. Interestingly enough, the fermionic nature of this state is revealed as purely of the electron tunneling type and, most astonishingly, it has the Andreev conductance completely null in its birth. Therefore, we find that a resonant edge state appears as a zero mode and discuss it in terms of a poor man's Majorana [Dvir et al., Nature 614, 445 (2023)].

Systematic study of Mn atoms, artificial dimers, and chains on superconducting Ta(110)

Magnetic adatoms coupled to an $s$-wave superconductor give rise to local bound states, so-called Yu-Shiba-Rusinov states. Focusing on the ultimate goal of tailoring chains of such adatoms into a topologically superconducting phase, we investigate basic building blocks - single Fe and Mn adatoms and Mn dimers on clean superconducting Ta(110) - using scanning tunneling microscopy and spectroscopy. We perform a systematic study of the hybridizations and splittings in dimers, and their dependence on the crystallographic directions and interatomic spacings, in order to identify potentially interesting chain geometries for this novel sample type. Subsequently, we study the spin structure as well as the length dependent Shiba band structure in Mn chains of those geometries using spin-resolved scanning tunneling spectroscopy. All results are compared to the according properties of structurally identical dimers and chains on the previously studied Nb(110), which has almost identical surface structure and electronic properties, but an about three times smaller spin-orbit interaction.

Gold Interlayer Promotes Superconductivity in Single and Double Atomic Pb Layers on Si(100).

Introducing an atomic Au monolayer between a Pb film and a Si(100) substrate allows us to fabricate Pb films with single- and double-atom thicknesses. The Pb films have a 2D square-lattice structure with the 1D atomic chains of Pb adatoms on their top, forming Si(100)1 × 7-(Pb, Au) and Si(100)5 × 1-(Pb, Au) superstructures for single and double atomic Pb layers, respectively. Their common characteristic feature is the occurrence of bundles of quasi-1D metallic bands. Transport measurements showed that samples with a Au interlayer demonstrate enhanced superconductor properties, as compared to Pb layers grown on the bare Si(100) surface. Toward improved superconductor properties, the (Pb, Au)/Si(100) system successively avoids risks associated with possible intermixing between adsorbate layers and substrate, as well as with possible Peierls transition into an insulator state, typical for the 1D systems. This finding opens new ways to control low-dimensional superconductivity at the atomic-scale limit.

Spin chain on a metallic surface: Dissipation-induced order versus Kondo entanglement

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, $J_k$, to a two-dimensional electron gas. At weak $J_k$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large $J_k$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a unique negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor

Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe2. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe2. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity.

Si epitaxy on Cl-Si(100)

Current atomically-precise fabrication methods in Si utilize a scanning tunneling microscope (STM) to pattern a monatomic resist adsorbed on Si(100). Recent interest in the use of Cl-based resists has necessitated further investigations on the impact of the tightly bound Cl to the overall device fabrication process. In particular, impacts to the crystallinity of the Si capping layer used to encapsulate the active device region can have dramatic effects on the functionality of atomic-scale quantum devices. Here, the epitaxial growth of Si films on Cl-Si(100) was studied to identify and characterize the Si thin film growth process. Adatoms diffusion on the surface was simulated based on the experimental results of the number density and distribution of Si adatom chains after <0.10 ML of Si deposition at temperatures ranging from 300–850 K. A diffusion barrier within 0.66–0.88 eV for Si adatoms on Cl-Si(100) was found. SIMS depth profiling of ∼25 nm thick Si films verified that Cl segregated towards the growth surface during Si deposition and was effectively removed below SIMS detection limits from both the buried interface and Si film at 850 K. TEM imaging confirmed good film crystallinity was achieved at temperatures as low as 600 K.

Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains.

Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.

Tunable topological states hosted by unconventional superconductors with adatoms

Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic impurities induce in-gap states since scattering of Cooper pairs changes their momentum but not their phase. Here, we propose a path for creating topological superconductivity, which is based on an unconventional superconductor with a chain of non-magnetic adatoms on its surface. The topological phase can be reached by tuning the magnitude and direction of a Zeeman field, such that Majorana zero modes at its boundary can be generated, moved and fused. To demonstrate the feasibility of this platform, we develop a general mapping of films with adatom chains to one-dimensional lattice Hamiltonians. This allows us to study unconventional superconductors such as Sr$_2$RuO$_4$ exhibiting multiple bands and an anisotropic order parameter.

Exploring the Kondo Effect of an Extended Impurity with Chains of Co Adatoms in a Magnetic Field.

Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two-level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum MonteCarlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effective Kondo coupling dominates. Our modeling and numerical simulations provide a theoretical basis for the interpretation of the STM spectrum in terms of level crossings of the Co adatom chains.

Atomically thin oxide layer on the elemental superconductor Ta(001) surface

Recently the oxygen-reconstructed tantalum surface Ta(001)-p(3$\times$3)-O has experienced considerable attention due its use as a potential platform for Majorana physics in adatom chains. Experimental studies using scanning tunneling microscopy and spectroscopy found rich atomic and electronic structures already for the clean Ta(001)-O surface, which we combine here with $ab~initio$ methods. We discover two metastable superstructures at the root of the different topographic patterns, discuss its emergence during annealing, and identify the electronic properties. The latter is determined as the sole origin for the contrast reversal seen at positive bias. The observed effects are essentially connected to the two distinct oxygen states appearing on the surface in different geometries. The second superstructure was found in simulations by introducing oxygen vacancies, what was also observed in tantalum pentoxide systems. Additionally we study the charge distribution on the oxidized surface and underline its importance for the adsorption process of polarizable atoms and molecules.

Real space manifestations of coherent screening in atomic scale Kondo lattices

The interaction among magnetic moments screened by conduction electrons drives quantum phase transitions between magnetically ordered and heavy-fermion ground states. Here, starting from isolated magnetic impurities in the Kondo regime, we investigate the formation of the finite size analogue of a heavy Fermi liquid. We build regularly-spaced chains of Co adatoms on a metallic surface by atomic manipulation. Scanning tunneling spectroscopy is used to obtain maps of the Kondo resonance intensity with sub-atomic resolution. For sufficiently small interatomic separation, the spatial distribution of Kondo screening does not coincide with the position of the adatoms. It also develops enhancements at both edges of the chains. Since we can rule out any other interaction between Kondo impurities, this is explained in terms of the indirect hybridization of the Kondo orbitals mediated by a coherent electron gas, the mechanism that causes the emergence of heavy quasiparticles in the thermodynamic limit.

On the Decoration of Zigzag Edges of an Epitaxial Graphene Nanoribbon

A double-chain model of an epitaxial graphene nanoribbon, the zigzag edges of which are decorated with foreign adparticles, has been proposed. The substrate is assumed to be a metal. Analytical expressions for the Green’s functions of carbon adatoms and adparticles are obtained. The band spectrum for the free state is determined, and the approximation of the density of states is proposed. Analytical expressions for the occupation numbers in the mode of tight binding between the adsorption complex and the substrate are presented. A chain of carbon adatoms decorated with adparticles (epicarbyne) is considered.

О декорировании зигзагообразных краев наноленты эпитаксиального графена

AbstractA double-chain model of an epitaxial graphene nanoribbon, the zigzag edges of which are decorated with foreign adparticles, has been proposed. The substrate is assumed to be a metal. Analytical expressions for the Green’s functions of carbon adatoms and adparticles are obtained. The band spectrum for the free state is determined, and the approximation of the density of states is proposed. Analytical expressions for the occupation numbers in the mode of tight binding between the adsorption complex and the substrate are presented. A chain of carbon adatoms decorated with adparticles (epicarbyne) is considered.

Engineering the spin couplings in atomically crafted spin chains on an elemental superconductor

Magnetic atoms on a superconductor give rise to Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap. A spin chain of magnetic adatoms on an s-wave superconductor may lead to topological superconductivity accompanied by the emergence of Majorana modes at the chain ends. For their usage in quantum computation, it is a prerequisite to artificially assemble the chains and control the exchange couplings between the spins in the chain and in the substrate. Here, using a scanning tunneling microscope tip, we demonstrate engineering of the energy levels of the YSR states by placing interstitial Fe atoms in close proximity to adsorbed Fe atoms on an oxidized Ta surface. Based on this prototype platform, we show that the interaction within a long chain can be strengthened by linking the adsorbed Fe atoms with the interstitial ones. Our work adds an important step towards the controlled design and manipulation of Majorana end states.

Supercurrent as a probe for topological superconductivity in magnetic adatom chains

A magnetic adatom chain, proximity coupled to a conventional superconductor with spin-orbit coupling, exhibits locally an odd-parity, spin-triplet pairing amplitude. We show that the singlet-triplet junction, thus formed, leads to a net spin accumulation in the near vicinity of the chain. The accumulated spins are polarized along the direction of the local $\mathbf{d}$ vector for triplet pairing and generate an enhanced persistent current flowing around the chain. The spin polarization and the ``supercurrent'' reverse their directions beyond a critical exchange coupling strength at which the singlet superconducting order changes its sign on the chain. The current is strongly enhanced in the topological superconducting regime where Majorana bound states appear at the chain ends. The current and the spin profile offer alternative routes to characterize the topological superconducting state in adatom chains and islands.

Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions

We study Majorana zero energy modes (MZEM) that occur in an s-wave superconducting surface, at the ends of a ferromagnetic (FM) chain of adatoms, in the presence of Rashba spin–orbit interaction (SOI) considering both non self-consistent and self-consistent superconducting order. We find that in the self-consistent solution, the average superconducting gap function over the adatom sites has a discontinuous drop with increasing exchange interaction at the same critical value where the topological phase transition occurs. We also study the MZEM for both treatments of superconducting order and find that the decay length is a linear function of the exchange coupling strength, chemical potential and superconducting order. For wider FM chains the MZEM occur at smaller exchange couplings and the slope of the decay length as a function of exchange coupling grows with chain width. Thus we suggest experimental detection of different delocalization of MZEM in chains of varying widths. We discuss similarities and differences between the MZEM for the two treatments of the superconducting order.

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor

We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized' 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.

Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

Regular arrays of magnetic atoms on a superconductor provide a promising platform for topological superconductivity. In this work, we study the effects of disorder in these systems, focusing on vacancies realized by missing magnetic atoms. We develop approaches that allow treatment of ferromagnetic dense chains as well as long-range hopping ferromagnetic and helical Shiba chains at arbitrary subgap energies. Vacancies in magnetic chains play an analogous role to magnetic impurities in a clean $s$-wave superconductor. A single vacancy in a topological chain gives rise to a low-lying ``anti-Shiba'' state below the band edge of a regular magnetic chain. Proliferation of the anti-Shiba band formed by a finite density of hybridized vacancy states leads to deterioration of the topological phase, which exhibits unusual fragility in a particular parameter region in dilute chains. We also consider local fluctuation in the Shiba coupling and discuss how vacancy states could contribute to experimental verification of topological superconductivity.

Formation of Sr adatom chains on SrTiO3 (1 1 0) surface determined by strain

The adsorption behavior of Sr adatoms on the SrTiO3 (1 1 0)-(4 × 1) reconstructed surface with Ti2O3 vacancies distributed in a superstructure is studied by scanning tunneling microscopy and density functional theory calculations. With the adsorption amount increasing, all the Sr adatoms between adjacent Ti2O3 vacancies are closely packed along the quasi-1D stripes on the surface with a uniform separation from each other. The formation of such adatom chains is determined by the surface strain relief—the local lattice relaxations in response to Sr adatoms and Ti2O3 vacancies are incompatible, leading to the strong repulsive interaction between them. Consequently the distribution of Sr chains follows the long-range order of the growth template with their length tunable in a certain range by evaporation amount.