arXiv subjects

Matthias Bode

Publications and source records attributed to Matthias Bode.

At least 19 recordsLinked to original sources

arXiv2026

Facet-selective ballistic supercurrent in a weak topological insulator

Topological superconductivity is widely pursued by inducing superconducting correlations in topologically protected boundary states. In two dimensions, this strategy has been realized using one-dimensional topological edge modes, but in three-dimensional crystals, spatially separated surface supercurrents confined to selected facets have not yet been achieved. Here we demonstrate facet-selective ballistic supercurrent in Josephson junctions based on the weak topological insulator ZrTe 5 . Superconducting quantum interferometry reveals SQUID-like critical current oscillations with flux-quantum periodicity, establishing that the supercurrent is spatially concentrated on specific crystallographic facets that host gapless topological surface states. Rotating the magnetic field yields markedly distinct interference patterns, linking the supercurrent distribution to the underlying bulk topology. The exponential temperature dependence of the critical current and triangular interference lobes provide signatures of ballistic transport due to high-transmission topological channels. These results establish weak topological insulators as a platform for facet-resolved superconducting devices and higher-order topological superconductivity.

cond-mat.mes-hall↗

arXiv2025

Experimental Realization of the Topologically Nontrivial Phase in Monolayer Si$_2$Te$_2$

The free-standing monolayer Si$_2$Te$_2$ (ML-Si$_2$Te$_2$) has been theoretically predicted to host a room-temperature quantum spin Hall phase. However, its experimental realization remains challenge due to the absence of a three-dimensional counterpart. Here, we demonstrate that HfTe$_2$ serves as an ideal substrate for the epitaxial growth of ML-Si$_2$Te$_2$, preserving its topological phase. Scanning tunneling microscopy and spectroscopy confirm a strain-free ${(1 \times 1)}$ lattice of ML-Si$_2$Te$_2$, along with a sizable band gap, which is well captured by first-principles calculations. Moreover, distinct edge states, independent of step geometry and exhibiting a broad spatial distribution, are observed at ML-Si$_2$Te$_2$ step edges, underscoring its topological nature.

cond-mat.mtrl-sci↗

arXiv2025

Sizable superconducting gap and anisotropic chiral topological superconductivity in the Weyl semimetal PtBi$_2$

Topological superconductors offer a fertile ground for realizing Majorana zero modes -- topologically protected, zero-energy quasiparticles that are resilient to local perturbations and hold great promise for fault-tolerant quantum computing. Recent studies have presented encouraging evidence for intrinsic topological superconductivity in the Weyl semimetal trigonal PtBi$_2$, hinting at a robust surface phase potentially stable beyond the McMillan limit. However, due to substantial spatial variations in the observed superconducting (SC) gap $\Delta$ the nature of the underlying order parameter $\Delta$($k$) remained under debate. Here we report the realization of sizable surface SC gaps ($\Delta > 10\,\mathrm{meV}$) in PtBi$_2$, exhibiting remarkable spatial uniformity from hundreds of nanometers down to the atomic level, as revealed by scanning tunneling microscopy and spectroscopy. Building on this spatial homogeneity -- indicative of long-range phase coherence -- we uncover previously unobserved low-energy Andreev bound states (ABSs) that ubiquitously emerge within the SC gap across the surface. Theoretical simulations that closely reproduce the experimental spectra, reveal an anisotropic chiral pairing symmetry of $\Delta$($k$), and further suggest that the observed ABSs are of topological origin. The combination of a large, nontrivial pairing gap and accessible surface states establishes PtBi$_2$ as a compelling platform for investigating topological superconductivity and its associated Majorana modes.

cond-mat.supr-con↗

arXiv2025

Rare-earth atoms on Nb(110) as a platform to engineer topological superconductivity

Helical spin textures in one-dimensional magnetic chains on superconductors can enable topological superconductivity and host Majorana zero modes, independent of the presence of intrinsic spin-orbit coupling. Here, we show that gadolinium (Gd) adatoms, possessing large 4f magnetic moments when placed on a Nb(110) surface, establish indirect exchange interactions mediated by valence electrons, manifesting as Yu-Shiba-Rusinov states. By combining scanning tunneling microscopy and spectroscopy with density functional theory, we analyze the emergence of the Yu-Shiba-Rusinov states in single Gd atoms and Gd dimers and uncover the underlying magnetic interaction mechanisms, on the basis of which we predict by means of spin-dynamics simulations the formation of stable chiral N\'eel-type spin-spiral configurations in Gd chains. These findings highlight rare-earth magnets as a promising platform for precisely tuning spin-spiral ground states, an essential prerequisite for the realization of topological superconductivity.

cond-mat.supr-con↗

arXiv2024

Probing chiral symmetry with a topological domain wall sensor

Chiral symmetry is a fundamental property with profound implications for the properties of elementary particles, that implies a spectral symmetry (i.e. E => -E ) in their dispersion relation. In condensed matter physics, chiral symmetry is frequently associated with superconductors or materials hosting Dirac fermions such as graphene or topological insulators. There, chiral symmetry is an emergent low-energy property, accompanied by an emergent spectral symmetry. While the chiral symmetry can be broken by crystal distortion or external perturbations, the spectral symmetry frequently survives. As the presence of spectral symmetry does not necessarily imply chiral symmetry, the question arises how these two properties can be experimentally differentiated. Here, we demonstrate how a system with preserved spectral symmetry can reveal underlying broken chiral symmetry using topological defects. Our study shows that these defects induce a spectral imbalance in the Landau level spectrum, providing direct evidence of symmetry alteration at topological domain walls. Using high-resolution STM/STS we demonstrate the intricate interplay between chiral and translational symmetry which is broken at step edges in topological crystalline insulator Pb$_{1-x}$Sn$_x$Se. The chiral symmetry breaking leads to a shift in the guiding center coordinates of the Landau orbitals near the step edge, thus resulting in a distinct chiral flow of the spectral density of Landau levels. This study underscores the pivotal role of topological defects as sensitive probes for detecting hidden symmetries, offering profound insights into emergent phenomena with implications for fundamental physics.

cond-mat.str-el↗

arXiv2023

Observation of zero-energy modes in Gd atomic chains on superconducting Nb(110)

In this experimental study, we use scanning tunneling microscopy and spectroscopy to investigate Yu-Shiba-Rusinov states induced by 4f-shell rare-earth Gd adatoms on a superconducting Nb(110) surface. We engineer Gd atom chains along the substrate's $[1\overline{1}0]$ and $[001]$ directions, revealing distinct behaviors in differently oriented chains. $[1\overline{1}0]$-oriented Gd chains exhibit spectroscopic features at their ends, identifying them as trivial edge states, while $[001]$-oriented Gd chains display zero-energy edge states, suggesting non-trivial nature. Notably, Gd chains with four atoms--independent of their particular orientation--exhibit a uniform zero-energy mode along the entire chain. These findings call for further research and a theoretical framework to describe rare-earth-based structures on superconductors.

cond-mat.supr-con↗

arXiv2023

Evidence for a conical spin spiral state in the Mn triple-layer on W(001): spin-polarized scanning tunneling microscopy and first-principles calculations

The spin structure of a Mn triple layer grown pseudomorphically on surfaces is studied using spin-polarized scanning tunneling microscopy (SP-STM) and density functional theory (DFT). In SP-STM images a c$(4 \times 2)$ super structure is found. The magnetic origin of this contrast is verified by contrast reversal and using the c$(2 \times 2)$ AFM state of the Mn double layer as a reference. SP-STM simulations show that this contrast can be explained by a spin spiral propagating along the [110] direction with an angle close to $90^\circ$ between magnetic moments of adjacent Mn rows. To understand the origin of this spin structure, DFT calculations have been performed for a large number of competing collinear and non-collinear magnetic states including the effect of spin-orbit oupling (SOC). Surprisingly, a collinear state in which the magnetic moments of top and central Mn layer are aligned antiparallel and those of the bottom Mn layer are aligned parallel to the central layer is the energetically lowest state. We show that in this so-called "up-down-down" ($\uparrow \downarrow \downarrow$) state the magnetic moments in the Mn bottom layer are only induced by those of the central Mn layer. Flat spin spirals propagating either in one, two, or all Mn layers are shown to be energetically unfavorable to the collinear $\uparrow \downarrow \downarrow$ state even upon including the Dzyaloshinskii-Moriya interaction (DMI). However, conical spin spirals with a small opening angle of about $10^\circ$ are only slightly energetically unfavorable within DFT and could explain the experimental observations. Surprisingly, the DFT energy dispersion of conical spin spirals including SOC cannot be explained if only the DMI is taken into account. Therefore, higher-order interactions such as chiral biquadratic terms need to be considered which could explain the stabilization of a conical spin spiral state.

cond-mat.mtrl-sci↗

arXiv2023

Spin-resolved spectroscopic evidence for spinarons in Co adatoms

Single cobalt atoms on the (111) surfaces of noble metals were for a long time considered prototypical systems for the Kondo effect in scanning tunneling microscopy experiments. Yet, recent first-principle calculations suggest that the experimentally observed spectroscopic zero-bias anomaly (ZBA) should be interpreted in terms of excitations of the Co atom's spin and the formation of a novel quasiparticle, the spinaron, a magnetic polaron resulting from the interaction of spin excitations with conduction electrons, rather than in terms of a Kondo resonance. Here we present state-of-the-art spin-averaged and spin-polarized scanning tunneling spectroscopy measurements on Co atoms on the Cu(111) surface in magnetic fields of up to 12 T, that allow us to discriminate between the different theoretical models and to invalidate the prevailing Kondo-based interpretation of the ZBA. Employing extended ab-initio calculations, we instead provide strong evidence for multiple spinaronic states in the system. Our work opens a new avenue of research to explore the characteristics and consequences of these intriguing hybrid many-body states as well as their design in man-made nanostructures.

cond-mat.str-el↗

arXiv2023

Boosting the STM's spatial and energy resolution with double-functionalized probe tips

Scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances, known as Yu-Shiba-Rusinov (YSR) bound states. Similarly to the interference of itinerant electrons scattered by defects in normal metals, these resonances reveal a periodic texture around the magnetic impurity. However, the wavelength of these resonances is often too short to be resolved even by methods capable of atomic resolution, like scanning tunneling microscopy (STM). Here, we combine a CO molecule with a superconducting cluster pre-attached to an STM tip to maximize both spatial and energy resolution. The superior properties of such a double-functionalized probe are demonstrated by imaging the spatial distribution of YSR states around magnetic Fe atoms on a Nb(110) surface. Our approach reveals rich interference patterns of the hybridized YSR state, previously inaccessible with conventional STM probes. This advancement extends the capabilities of STM techniques, providing insights into superconducting phenomena at the atomic scale.

cond-mat.supr-con↗

arXiv2023

Probing spin-dependent charge transport at single-nanometer length scales

The coherent transport of charge and spin is one key requirement of future devices for quantum computing and communication. Scattering at defects or impurities may seriously reduce the coherence of quantum-mechanical states, thereby affecting device functionality. While numerous methods exist to experimentally assess charge transport, the real-space detection of a material's spin transport properties with nanometer resolution remains a challenge. Here we report on a novel approach which utilizes a combination of spin-polarized scanning tunneling microscopy (SP-STM) and the recently introduced molecular nanoprobe (MONA) technique. It relies on the local injection of spin-polarized charge carriers from a magnetic STM tip and their detection by a single surface-deposited phthalocyanine molecule via reversible electron-induced tautomerization events. Based on the particular electronic structure of the Rashba alloy BiAg$_2$ which is governed by a spin-momentum-locked surface state, we proof that the current direction inverses as the tip magnetization is reversed by an external field. In a proof-of-principle experiment we apply SP-MONA to investigate how a single Gd cluster influences the spin-dependent charge transport of the Rashba surface alloy.

cond-mat.mes-hall↗

arXiv2023

Anisotropic Ballistic Transport Revealed by Molecular Nanoprobe Experiments

Atomic-scale charge transport properties are not only of significant fundamental interest but also highly relevant for numerous technical applications. However, experimental methods which are capable of detecting charge transport at the relevant single-digit nanometer length scales are scarce. Here we report on molecular nanoprobe (MONA) experiments on Pd(110) where we utilize the charge carrier-driven switching of a single cis-2-butene molecule to detect ballistic transport properties over length scales of a few nanometers. Our data demonstrate a striking angular dependence with a dip in charge transport along the [1-10]-oriented atomic rows and a peak in the transverse [001] direction. The narrow angular width of both features and distance-dependent measurements suggest that the nanometer-scale ballistic transport properties of metallic surfaces is significantly influenced by the atomic structure.

cond-mat.mes-hall↗

arXiv2023

Coupling of Yu-Shiba-Rusinov states in 1D chains of Fe atoms on Nb(110)

The hybridization of Yu-Shiba-Rusinov states in dimers of magnetic impurities leads to molecular-like bonding and antibonding modes. In many-impurity systems, the interaction gives rise to YSR bands and can even result in the formation of a topologically non-trivial superconducting state, characterized by Majorana fermions at the edges of the system. To obtain a more detailed understanding of these interactions, we investigate the coupling of YSR states in short one-dimensional Fe chains on clean Nb(110). We observe a splitting of the single-atom YSR peaks into multiple states with even or odd spatial symmetry and identify a peculiar dependence of the even and odd states' energy position on the chain length.

cond-mat.supr-con↗

arXiv2022

Interaction effects in a 1D flat band at a topological crystalline step edge

Step edges of topological crystalline insulators can be viewed as predecessors of higher-order topology, as they embody one-dimensional edge channels embedded in an effective three-dimensional electronic vacuum emanating from the topological crystalline insulator. Using scanning tunneling microscopy and spectroscopy we investigate the behaviour of such edge channels in Pb$_{1-x}$Sn$_{x}$Se under doping. Once the energy position of the step edge is brought close to the Fermi level, we observe the opening of a correlation gap. The experimental results are rationalized in terms of interaction effects which are enhanced since the electronic density is collapsed to a one-dimensional channel. This constitutes a unique system to study how topology and many-body electronic effects intertwine, which we model theoretically through a Hartree-Fock analysis.

cond-mat.mes-hall↗

arXiv2022

Reversible Tuning of Collinear versus Chiral Magnetic Order by Chemical Stimulus

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediates collinear magnetic interactions via the conduction electrons of a non-magnetic spacer, resulting in a ferro- or antiferromagnetic magnetization in magnetic multilayers. The resulting spin-polarized charge transport effects have found numerous applications. Recently it has been discovered that heavy non-magnetic spacers are able to mediate an indirect magnetic coupling that is non-collinear and chiral. This Dzyaloshinskii-Moriya-enhanced RKKY (DME-RKKY) interaction causes the emergence of a variety of interesting magnetic structures, such as skyrmions and spin spirals. Applications using these magnetic quasi-particles require a thorough understanding and fine-tuning of the balance between the Dzyaloshinskii-Moriya interaction and other magnetic interactions, e.g., the exchange interaction and magnetic anisotropy contributions. Here, we show by spin-polarized scanning tunneling microscopy that the spin structure of manganese oxide chains on Ir(001) can reproducibly be switched from chiral to collinear antiferromagnetic interchain interactions by increasing the oxidation state of MnO$_2$ while the reverse process can be induced by thermal reduction. The underlying structural change is revealed by low-energy electron diffraction intensity data (LEED-IV) analysis. Density functional theory calculations suggest that the magnetic transition may be caused by a significant increase of the Heisenberg exchange upon oxidation.

cond-mat.mtrl-sci↗

arXiv2022

Magnetic domain structure of epitaxial Gd films grown on W(110)

We present a detailed real-space spin-polarized scanning tunneling microscopy (SP-STM) study of the magnetic domain structure of Gd(0001) films epitaxially grown on W(110). To find optimal preparation conditions, the influence of the substrate temperature during deposition and of the post-growth annealing temperature was investigated. Our results show that the lowest density of surface defects, such as step edges as well as screw and edge dislocations, is obtained for room temperature deposition and subsequent annealing at 900\,K. SP-STM data reveal small-sized magnetic domains at lower annealing temperatures, evidently caused by pinning at grain boundaries and other crystalline defects. The coverage-dependent magnetic domain structure of optimally prepared Gd films was systematically investigated. For low coverage up to about 80 atomic layers (AL) we observe $\mu$m-sized domains separated by domain walls which are oriented approximately along the $[1{\bar 1}0]$ direction of the underlying W substrate. Above a critical film thicknesses $\Theta_{\text{crit}} \approx (100 \pm 20)$\,AL, we identify stripe domains, indicative for a spin reorientation transition from in-plane to out-of-plane. In agreement with existing models, the periodicity of the stripe domains increases the further the coverage exceeds $\Theta_{\text{crit}}$. While the orientation of the stripe domains is homogeneous over large distances just above $\Theta_{\text{crit}}$, we find a characteristic zig-zag pattern at $\Theta \gtrsim 200$\,AL and irregular stripe domains beyond 500\,AL. Intermediate minima and maxima of the magnetic signal indicate the nucleation of branching domains. The results are discussed in terms of various contributions to the total magnetic energy, such as the magneto-crystalline, the magneto-static, and the magneto-elastic energy density.

cond-mat.mtrl-sci↗

arXiv2020

Anisotropic vortices on superconducting Nb(110)

We investigate the electronic properties of type-II superconducting Nb(110) in an external magnetic field. Scanning tunneling spectroscopy reveals a complex vortex shape which develops from circular via coffee bean-shaped to elliptical when decreasing the energy from the edge of the superconducting gap to the Fermi level. This anisotropy is traced back to the local density of states of Caroli-de-Gennes-Matricon states which exhibits a direction-dependent splitting. Oxidizing the Nb(110) surface triggers the transition from the clean to the dirty limit, quenches the vortex bound states, and leads to an isotropic appearance of the vortices. Density functional theory shows that the Nb(110) Fermi surface is stadium-shaped near the \Gamma point. Calculations within the Bogoliubov-de-Gennes theory using these Fermi contours consistently reproduce the experimental results.

cond-mat.supr-con↗

arXiv2019

Indirect Chiral Magnetic Exchange through Dzyaloshinskii-Moriya--Enhanced RKKY Interactions in Manganese Oxide Chains on Ir(100)

Ruderman-Kittel-Kasuya-Yosida interaction even if their wave functions lack direct overlap. Theory predicts that spin-orbit scattering leads to a Dzyaloshinskii-Moriya type enhancement of this indirect exchange interaction, giving rise to chiral exchange terms. Here we present a combined spin-polarized scanning tunneling microscopy, angle-resolved photoemission, and density functional theory study of MnO$_2$ chains on Ir(100). Whereas we find antiferromagnetic Mn--Mn coupling along the chain, the inter-chain coupling across the non-magnetic Ir substrate turns out to be chiral with a $120^{\circ}$ rotation between adjacent MnO$_2$ chains. Calculations reveal that the Dzyaloshinskii-Moriya interaction results in spin spirals with a periodicity in agreement with experiment. Our findings confirm the existence of indirect chiral magnetic exchange, potentially giving rise to exotic phenomena, such as chiral spin-liquid states in spin ice systems or the emergence of new quasiparticles.

cond-mat.mtrl-sci↗

arXiv2019

On the preparation and electronic properties of clean superconducting Nb(110) surfaces

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 $T = 2400^\circ$C. Tunneling spectra measured on the clean Nb(110) surface exhibit a sharp conductance peak in the occupied states at an energy of about $-450$\,meV. Density functional theory calculations show that this peak is caused by a $d_{z^2}$ surface resonance band at the $\bar{\Gamma}$ point of the Brillouin zonewhich 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.

cond-mat.supr-con↗