Type-II superconductors under magnetic fields remain in a quantum-coherent, non-dissipative state as long as vortices are pinned. Dissipation emerges when vortices depin, a process often driven by thermal fluctuations and commonly associated with a melting transition from a vortex solid to a vortex liquid. Macroscopic experiments almost always observe this transition close to the superconducting critical temperature T c . However, how the vortex solid responds to thermal fluctuations at the scale of individual vortices, far below the melting transition, remains largely unexplored. Here, we use scanning tunneling microscopy (STM) to directly visualize vortices in the iron-based superconductor CaKFe 4 As 4 ( T c ≈ 35 K ). We observe the formation of vortex liquid droplets-spatially localized regions where vortices exhibit strong thermal fluctuations-at temperatures as low as 0.5 T c . These results demonstrate that the onset of dissipation at the local scale occurs at temperatures significantly below T c in type-II superconductors, revealing a previously unrecognized regime of vortex dynamics.

Superconducting vortices have a normal core and are pinned at imperfections, facilitating large current flow. Applications such as high-field solenoids or superconducting motors rarely use pure materials, as these are brittle, and instead employ superconductors embedded in ductile matrices (e.g., Cu or Ag). Processing superconductors into grains and then embedding in wires can significantly affect their properties, which remain less explored than in pure materials. In particular, the superconducting gap, relevant for vortex pinning, has been little studied in wires. Here, we determine the gap as a function of temperature and magnetic field in NbTi and MgB _2 wires using scanning tunneling microscopy. We find strong gap inhomogeneity, with Δ _NbTi=0.9± 0.6 mV and Δ _MgB_2=1.8± 0.2 mV. The temperature dependence follows BCS theory. Under magnetic field, the gap decreases approximately linearly, deviating from the usual ( 1-H/H_c2) ^2 behavior. We attribute this deviation to gap inhomogeneity arising possibly due to processing the materials into a wire. Our work shows that gap structure studies could complement efforts to improve superconducting properties of wires.

Most superconducting materials exhibit a vanishing density of states at the Fermi level and Anderson's theorem posits that the superconducting gap is robust against nonmagnetic disorder. Although dilute magnetic impurities lead to localized in-gap states, these states typically have no bearing on the material's bulk superconducting properties. However, numerous experiments reveal a finite density of states at the Fermi level in systems with an apparently negligible number of magnetic impurities. Here, using scanning tunneling microscopy and self-consistent Bogoliubov-de Gennes calculations, we find that gapless superconductivity emerges in 2H-NbSe2-xSx at remarkably low magnetic impurity concentrations. Furthermore, our density functional theory calculations and in-gap quasiparticle interference measurements demonstrate that the Se-S substitution significantly modifies the band structure. This modification favours nesting and dictates the in-gap scattering for x>0, in stark contrast to the dominant charge density wave interactions in pure 2H-NbSe2. Our findings reveal an unusual superconducting response to disorder and highlight the importance of incorporating material-specific band structures in the understanding of a superconductor's response to even very low concentrations of magnetic impurities.

ABSTRACT Most superconducting materials exhibit a vanishing density of states at the Fermi level and Anderson's theorem posits that the superconducting gap is robust against nonmagnetic disorder. Although dilute magnetic impurities lead to localized in‐gap states, these states typically have no bearing on the material's bulk superconducting properties. However, numerous experiments reveal a finite density of states at the Fermi level in systems with an apparently negligible number of magnetic impurities. Here, using scanning tunneling microscopy and self‐consistent Bogoliubov‐de Gennes calculations, we find that gapless superconductivity emerges in 2H‐ at remarkably low magnetic impurity concentrations. Furthermore, our density functional theory calculations and in‐gap quasiparticle interference measurements demonstrate that the Se‐S substitution significantly modifies the band structure. This modification favours nesting and dictates the in‐gap scattering for , in stark contrast to the dominant charge density wave interactions in pure 2H‐. Our findings reveal an unusual superconducting response to disorder and highlight the importance of incorporating material‐specific band structures in the understanding of a superconductor's response to even very low concentrations of magnetic impurities.

Type-II superconductors under magnetic fields are in a quantum coherent non-dissipative state as long as vortices remain pinned. Dissipation appears when vortices depin, eventually driven by thermal fluctuations. This can be associated to a melting transition between a vortex solid and a vortex liquid. This transition is almost always observed very close to T$_c$ when probed by macroscopic experiments. However, it remains unclear how the vortex solid responds to thermal fluctuations at the scale of individual vortices far from the melting transition. Here we use scanning tunneling microscopy (STM) to visualize vortices in CaKAs$_4$Fe$_4$ (T$_c \approx$ 35 K). We find vortex liquid droplets-localized regions in space where vortices strongly fluctuate due to thermal exctiation-at temperatures as low as 0.5\,T$_c$. Our results show that the onset of dissipation at the local scale occurs at temperatures considerably below T$_c$ in type-II superconductors.

In 2025, the Year of Quantum Science and Technology ( https://quantum2025.org/ ), we celebrate a century of quantum mechanics, witnessing a surge in activities that illuminate its inherent strangeness and drive technological innovation. Superconductivity, discovered 114 years ago, stands as a prime example, offering direct and compelling evidence of macroscopic quantum phenomena. Beyond its ability to conduct immense currents without loss, superconductivity reveals the quantum realm operating on a scale we can directly observe and manipulate. The macroscopic quantum coherence, where an ensemble of particles is described by a single wave function, leads to remarkable consequences: dissipation-less current and flux quantization—the basic properties exploited in superconducting quantum circuit fabrication. This Roadmap has been inspired by intensive discussions and collaborations emerging from the European Cooperation in Science & Technology COST-Action CA21144 (SuperQuMap—Superconducting Nanodevices and Quantum Materials for Coherent Manipulation). The aim of the COST Action SuperQuMap is to establish a strong European network centered on macroscopic quantum behavior in superconductors, bringing together groups of different backgrounds and more than 30 countries. The roadmap outlines the network’s concrete activities, driving advancements in superconductor-based quantum technologies and charting future directions. Spanning fundamental research to practical applications, the roadmap incorporates insights from industry partners developing quantum computation. It begins by exploring quantum materials, highlighting how topology and electronic correlations could catalyze a quantum leap in technology. We then delve into manipulating the superconducting phase, leveraging advancements in magnetism, 3D fabrication, and tunable correlations. Further, we showcase the advanced microscopy techniques—such as angle-resolved photoemission spectroscopy and scanning probes—used to visualize quantum behavior. Finally, and crucially, we detail the quantum devices developed within the network, and their transformative impact on modern quantum computing approaches.

Electronic conduction at the atomic scale can be described by Landauer’s formalism. In single-atom point contacts of noble metals like Au and Ag, there is just one channel open between both electrodes and the conductance is very close to the quantum of conductance G≈G_{0}=2e^{2}/h, with the factor of two coming from spin degeneracy. The magnetoconductivity of atomic size contacts has been studied for numerous systems, unveiling local Kondo screening, magnetic order, and spin-polarized currents. However, these have been mostly performed in elements with multiple open conduction channels where G differs from G_{0}. The realization of a magnetically active conductor with a single-open channel remains difficult to achieve. Here, we present measurements of the electronic conductance of single-channel Au and Ag atomic size contacts in magnetic fields up to 20 T. We observe a decrease in G which goes up to about 15% in many Au contacts at 20 T. We perform calculations and find that pure Ag and Au do not present a strong field dependence of G, in agreement with previous results at smaller magnetic fields. We also find, however, that residual O_{2} molecules attached close to the contact produce an induced spin-polarized current, which leads to a decrease in G. We discuss the role of the magnetic response of the electrodes in the jump-to-contact. Our results suggest that single channel atomic size conductors with a sizable response to a magnetic field can be built by combining noble metals and magnetically active molecular systems.

The Scanning Tunneling Microscope (STM) is a powerful instrument to measure electronic density of states at surfaces down to atomic scale. Many systems of interest require studying variations as a function of the magnetic field, which is most often applied perpendicular to the surface. Conventional STM setups make it challenging to perform measurements when the magnetic field must be applied in other directions. Here, we describe a new STM, which is small enough to allow for full rotation on a space with a diameter of 37 mm, well below the available space within many magnets. We have installed the STM on a rotatable platform. We show that the new rotatable STM setup preserves the performance of state-of-the-art setups in terms of noise and accuracy. Our new approach significantly enhances control over the direction of the applied magnetic field for STM and opens exciting new possibilities to study quantum materials.

Nitride-based superconductors represent a family of superconducting thin film materials displaying higher quality than their corresponding bare superconductor when used in devices for applications such as cosmic radiation sensing. In recent times, niobium-based and titanium-based nitrides were used to improve the quality of superconducting devices in quantum technology applications. Recently, nitridized aluminum (NitrAl) has been found to display higher critical temperatures and enhanced resilience to magnetic fields compared to those of Al, making it a new interesting candidate for superconducting quantum circuit applications. However, the microscopic properties of NitrAl remain highly unexplored. Here, we use scanning tunneling microscope (STM) to measure the superconducting density of states of a thin film sample of nitridized aluminum (NitrAl), with a room temperature resistivity between pure Al and fully insulating aluminum nitride. We show that the in-gap density of states is zero up to about ħω =250 μ eV and that there is a distribution of values of the superconducting gap around Δ _0=360 μ eV , close to the BCS expectation Δ =1.76 k_BT_c . We also find varying superconducting gap values at the nanometer scale, by approximately 10

The layered compound γ-PtBi_{2} is a topological semimetal with Fermi arcs at the surface joining bulk Weyl points. Recent work has found signatures of surface superconductivity consisting of gap openings compatible with a critical temperature orders of magnitude larger than the bulk value. However, no superconducting vortices have been identified, raising questions about the robustness of the phase coherence. Here, we use very low temperature STM and find robust superconductivity with T_{C}=2.9  K and H_{C2}≈1.8  T linked to the Fermi arcs. We observe quantized superconducting vortices and the Josephson effect, demonstrating two-dimensional macroscopic quantum phase coherence.

WTe2 stands out as a semimetal presenting Fermi level quantum oscillations in most measured quantities under magnetic fields. However, the electronic band structure above and below the Fermi level has not been completely explored. Here we study the electronic band structure of WTe2 by quasiparticle interference with scanning tunneling microscopy and observe, with the support of density functional theory, the electron and hole bands around the Fermi level. We also report on the observation of Landau quantization in atomically resolved measurements and discuss the possible connection with band structure calculations.

Most superconductors exhibit spin-singlet pairing within a single band. In multiband systems with strong spin-orbit coupling, more exotic scenarios can emerge, including Cooper pairs between bands with distinct symmetries. Here, we present evidence of the formation of Cooper pairs between spin-nondegenerate helical surface bands in the superconductor β-Bi_{2}Pd. Scanning tunneling microscopy reveals anisotropic Yu-Shiba-Rusinov (YSR) resonances induced by vanadium impurities, with long-range amplitude modulations attributed to spin-conserving Bogoliubov quasiparticle interference (BQPI). Analysis of BQPI at the subgap YSR energy shows that only a selective subset of normal-state scattering processes contributes to Cooper pair formation, indicating interband mixing. We trace this selectivity to the hybridization of a helical surface band with others via the impurity.

The ultimate spatial limit to establish a Josephson coupling between two superconducting electrodes is an atomic-scale junction. The Josephson effect in such ultrasmall junctions has been used to unveil new switching dynamics, study coupling close to superconducting bound states or reveal non-reciprocal effects. However, the Josephson coupling is weak and the sensitivity to temperature reduces the Cooper pair current magnitude. Here we show that a feedback element induces a time-dependent bistable regime which consists of spontaneous periodic oscillations between two different Cooper pair tunneling states (corresponding to the DC and AC Josephson regimes respectively). The amplitude of the time-averaged current within the bistable regime is almost independent of temperature. By tracing the periodic oscillations in the new bistable regime as a function of the position in a Scanning Tunneling Microscope, we obtain atomic scale maps of the critical current in 2H-NbSe2 and find spatial modulations due to a pair density wave. Our results fundamentally improve our understanding of atomic size Josephson junctions including a feedback element in the circuit and provide a promising new route to study superconducting materials through atomic scale maps of the Josephson coupling.

Most superconducting mechanisms pair electrons within the same band, forming spin singlets. However, the discovery of multi-band superconductivity has opened new scenarios for pairing, particularly in systems with strong spin-orbit coupling. Here, we reveal inter-band pairing in the superconductor by mapping the amplitude of sub-gap Yu-Shiba-Rusinov (YSR) states around Vanadium adatoms deposited on its surface. The surface of is characterized by spin-helical-like bands near the Fermi level. Scanning tunneling spectroscopy reveals anisotropic YSR amplitude oscillations around the impurity, driven by spin-conserving Bogoliubov quasiparticle interference (BQPI). Analysis of the BQPI patterns at the YSR energy exposes inter-band pairing in this material. Interestingly, only a small subset of all possible inter-band scattering processes observed in the normal state contribute to the BQPI patterns. Combining experimental data and theory, we demonstrate that the observed band selectivity results from the hybridization of the band coupled with the impurity with other bands. Our findings reveal unconventional pairing mechanisms in and highlight the crucial role of spin-orbit interactions in their formation.

PtPb _4 is a type II superconductor with a bulk critical temperature T_c≈ 3 K and an upper critical field of H_c2=0.36 T. PtPb _4 is related to non-superconducting PtSn _4 , which presents nodal arc states at the surface. Here, we measure the superconducting density of states of PtPb _4 using millikelvin Scanning Tunneling Microscopy (STM). We observe a fully opened superconducting gap of Δ =0.48 meV similar to expectations from Bardeen, Cooper and Schrieffer (BCS) theory ( Δ _0=1.76k_BT_c=0.49 meV). Measurements under magnetic fields applied perpendicular to the surface show a spatially inhomogeneous gap structure, presenting superconducting signatures at fields as high as 1.5 T, significantly above H_c2=0.36 T. On some locations, we find that the superconducting density of states does not vanish above T_c . We can find signatures of a superconducting gap up to 5 K. We discuss possible reasons for the observation of superconducting properties above T_c and H_c2 , emphasizing the role played by structural defects.

The spatially uniform electronic density characteristic of a metal can become unstable at low temperatures, leading to the formation of charge density waves (CDWs). These CDWs, observed in dichalcogenides, cuprates, and pnictides arise from features in the atomic lattice and its interaction with the electronic band structure that facilitate charge ordering. However, CDWs are rarely observed in presence of Kondo screening and heavy fermion quasiparticles. The heavy fermion topological superconductor candidate UTe_2 presents a notable exception, exhibiting a CDW whose origin remains elusive. Here we report high resolution Scanning Tunneling Microscopy (STM) experiments that reveal the primitive wavevectors of the CDW in UTe_2. This allows for a refined identification of the nesting wavevectors in the electronic bandstructure. Although these wavevectors have no specific influence on the bulk properties, for example on antiferromagnetic fluctuations, they cause the interactions leading to the CDW at the surface. The heavy fermion hybridization pattern is spatially modulated specifically at the nesting wavevectors, suggesting that surface induced modifications in the U 5f electron valence enable a novel form of purely electron-driven charge ordering.

Disordered hyperuniform materials are very promising for applications but the successful route for synthesizing them requires to understand the interactions induced by the host media that can switch off this hidden order. With this aim we study the model system of vortices in the $\beta$-Bi$_2$Pd superconductor where correlated defects seem to play a determinant role for the nucleation of a gel vortex phase at low densities. We directly image vortices in extended fields-of-view and show that the disordered vortex structure in this material is anti-hyperuniform, contrasting with the case of vortex structures nucleated in samples with point-like disorder. Based on numerical simulations, we show that this anti-hyperuniform structure arises both, from the interaction of a diluted vortex structure with a fourfold-symmetric correlated disorder quite likely generated when cleaving the samples and from the out of equilibrium nature of the quenched configuration.

Nano-patterned magnetic materials have opened new venues on the investigation of strongly correlated phenomena including artificial spin-ice systems, geometric frustration, magnetic monopoles, for technologically important applications such as reconfigurable ferromagnetism. With the advent of atomically thin two-dimensional (2D) van der Waals (vdW) magnets a pertinent question is whether such compounds could make their way into this realm where interactions can be tailored so that unconventional states of matter could be assessed. Here we show that square islands of CrGeTe3 vdW ferromagnets distributed in a grid manifest antiferromagnetic correlations, essential to enable frustration resulting in an artificial spin-ice. By using a combination of SQUID-on-tip microscopy, focused ion beam lithography, and atomistic spin dynamic simulations, we show that pristine, isolated CGT flakes as small as 150*150*60 nm3 have tunable dipole-dipole interactions, which can be precisely controlled by their lateral spacing. There is a crossover between non-interacting islands and significant inter-island anticorrelation depending how they are spatially distributed allowing the creation of complex magnetic patterns not observable at the isolated flakes. Our findings suggest that the cross-talk between the nano-patterned magnets can be explored in the generation of even more complex spin configurations where exotic interactions may be manipulated in an unprecedent way.

We provide the superconducting density of states of the pnictide superconductor LaRu2P2(Tc= 4.1 K), measured using millikelvin scanning tunneling microscopy. From the tunneling conductance, we extract a density of states which shows the opening of a s-wave single superconducting gap. The temperature dependence of the gap also follows BCS theory. Under magnetic fields, vortices present Caroli de Gennes Matricon states, although these are strongly broadened by defect scattering. From the vortex core size we obtain a superconducting coherence length ofξ = 50 nm, compatible with the value extracted from macroscopicHc2measurements. We discuss the comparison between s-wave LaRu2P2and pnictide unconventional multiple gap and strongly correlated Fe based superconductors.

The coercivity of single-domain magnetic nanoparticles typically decreases with the nanoparticle size and reaches zero when thermal fluctuations overcome the magnetic anisotropy. Here, we used SQUID-on-tip microscopy to investigate the coercivity of square-shaped CrGeTe3 nanoislands with a wide range of sizes and width-to-thickness aspect ratios. The results reveal an anomalous size-dependent coercivity, with smaller islands exhibiting higher coercivity. The nonconventional scaling of the coercivity in CrGeTe3 nanoislands was found to be inversely proportional to the island width and thickness (1/wd). This scaling implies that the nanoisland magnetic anisotropy is proportional to the perimeter rather than the volume, suggesting a magnetic edge state. In addition, we observe that 1600 nm wide islands display multi-domain structures with zero net remnant field, corresponding to the magnetic properties of pristine CrGeTe3 flakes. Our findings highlight the significant influence of edge states on the magnetic properties of CrGeTe3 and deepen our understanding of low-dimensional magnetic systems.