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Magnetic adatoms on s-wave superconductors induce bound states inside the superconducting gap, called Yu-Shiba-Rusinov states (YSR). The anisotropy of the Fermi surface determines the spatial extension of bound states in a quasi-two-dimensional superconductor. This is especially important in the diluted impurity limit since the orbital overlap determines the coupling of YSR states of neighboring atoms and the formation of the collective YSR system. Here, we build diluted arrays of Mn atoms with different dimensionalities on the surface of $\beta$-Bi$_2$Pd, and we measure the evolution of their YSR spectra with the structure. We detect the coupling as a split of YSR peaks in subgap spectra and find that the split size increases with the number of atoms. The orientation of the structures along different directions of the \bipd substrate modulates the split and particle-hole asymmetry of the YSR states due to the anisotropic character of the Fermi surface, captured by the Green function model. With the aid of the model, we found multiple YSR excitations in an extended 2D array of 25 Mn atoms, and we identified that their spatial distribution reflects a chiral LDOS., Comment: 10 pages, 5 figures

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., Comment: 13 pages, 10 figures

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 unveil non-reciprocal effects. However, coupling is weak and thermal smearing reduces the Cooper pair current magnitude. Here we show that a feedback element induces a time-dependent bistable regime which consists of 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 robust against thermal smearing. By tracing the periodic oscillations in the new bistable regime as a function of the position in a Scanning Tunneling Microscope (STM), we obtain atomic scale map of the critical current in 2H-NbSe$_2$ and find spatial modulations due to a pair density wave. Our results fundamentally improve our understanding of atomic size Josephson junctions and provide a promising new route to study superconducting materials through atomic scale maps of the Josephson coupling., Comment: 51 pages, 14 figures

Electrons can form a two-dimensional electron gas at metal surfaces, where lateral confinement leads to quantum-well states. Such states have been observed for highly itinerant electrons, but it remains an open question whether quantum-well states can be formed from strongly correlated electrons. Here we study atomically flat terraces on surfaces of the heavy-fermion superconductor URu$_2$Si$_2$ using millikelvin scanning tunneling spectroscopy. We observe two-dimensional heavy fermions (2DHF) with an effective mass 17 times the free electron mass that form quantized states separated by a fraction of a meV. Superconductivity at the surface is induced by the bulk into the 2DHF. Our results provide a new route to realize quantum well states in correlated quantum materials.

The orthorhombic compound AuSn4 is compositionally similar to the Dirac node arc semimetal PtSn$_4$. AuSn$_4$ is, contrary to PtSn$_4$, superconducting with a critical temperature of T$_c$ = 2.35 K. Recent measurements present indications for quasi two-dimensional superconducting behavior in AuSn$_4$. Here we present measurements of the superconducting density of states and the band structure of AuSn$_4$ through Scanning Tunneling Microscopy (STM) and Angular Resolved Photoemission Spectroscopy (ARPES). The superconducting gap values in different portions of the Fermi surface are spread around {\Delta}0 = 0.4 meV, which is close to but somewhat larger than $\Delta =$ 1.76kBT$_c$ expected from BCS theory. We observe superconducting features in the tunneling conductance at the surface up to temperatures about 20% larger than bulk Tc. The band structure calculated with Density Functional Theory (DFT) follows well the results of ARPES. The crystal structure presents two possible stackings of Sn layers, giving two nearly degenerate polytypes. This makes AuSn$_4$ a rather unique case with a three dimensional electronic band structure but properties ressembling those of low dimensional layered compounds.

The electronic bandstructure of Au$_2$Pb has a Dirac cone which gaps when undergoing a structural transition into a low temperature superconducting phase. This suggests that the superconducting phase ($T_c=1.1$ K) might hold topological properties at the surface. Here we make Scanning Tunneling Microscopy experiments on the surface of superconducting Au$_2$Pb. We measure the superconducting gap and find a sizeable superconducting density of states at the Fermi level. We discuss possible origins for this finding in terms of superconductivity induced into surface states.

The magnetoresistance of iron pnictide superconductors is often dominated by electron-electron correlations and deviates from the H$^2$ or saturating behaviors expected for uncorrelated metals. Contrary to similar Fe-based pnictide systems, the superconductor LaRu$_2$P$_2$ (T$_c$ = 4 K) shows no enhancement of electron-electron correlations. Here we report a non-saturating magnetoresistance deviating from the H$^2$ or saturating behaviors in LaRu$_2$P$_2$. We have grown and characterized high quality single crystals of LaRu$_2$P$_2$ and measured a magnetoresistance following H$^{1.3}$ up to 22 T. We discuss our result by comparing the bandstructure of LaRu$_2$P$_2$ with Fe based pnictide superconductors. The different orbital structures of Fe and Ru leads to a 3D Fermi surface with negligible bandwidth renormalization in LaRu$_2$P$_2$, that contains a large open sheet over the whole Brillouin zone. We show that the large magnetoresistance in LaRu$_2$P$_2$ is unrelated to the one obtained in materials with strong electron-electron correlations and that it is compatible instead with conduction due to open orbits on the rather complex Fermi surface structure of LaRu$_2$P$_2$., Comment: 12 pages, 4 figures

High critical temperature superconductivity often occurs in systems where an antiferromagnetic order is brought near $T=0K$ by slightly modifying pressure or doping. CaKFe$_4$As$_4$ is a superconducting, stoichiometric iron pnictide compound showing optimal superconducting critical temperature with $T_c$ as large as $38$ K. Doping with Ni induces a decrease in $T_c$ and the onset of spin-vortex antiferromagnetic order, which consists of spins pointing inwards to or outwards from alternating As sites on the diagonals of the in-plane square Fe lattice. Here we study the band structure of CaK(Fe$_{0.95}$Ni$_{0.05}$)$_4$As$_4$ (T$_c$ = 10 K, T$_N$ = 50 K) using quasiparticle interference with a Scanning Tunneling Microscope (STM) and show that the spin-vortex order induces a Fermi surface reconstruction and a fourfold superconducting gap anisotropy., Comment: 5 pages, 4 figures, Supplemental Material on request

Particles occupying sites of a random lattice present density fluctuations at all length scales. It has been proposed that increasing interparticle interactions reduces long range density fluctuations, deviating from random behaviour. This leads to power laws in the structure factor and the number variance that can be used to characterize deviations from randomness which eventually lead to disordered hyperuniformity. It is not yet fully clear how to link density fluctuations with interactions in a disordered hyperuniform system. Interactions between superconducting vortices are very sensitive to vortex pinning, to the crystal structure of the superconductor and to the value of the magnetic field. This creates lattices with different degrees of disorder. Here we study disordered vortex lattices in several superconducting compounds (Co-doped NbSe$_2$, LiFeAs and CaKFe$_4$As$_4$) and in two amorphous W-based thin films, one with strong nanostructured pinning (W-film-1) and another one with weak or nearly absent pinning (W-film-2). We calculate for each case the structure factor and number variance and compare to calculations on an interacting set of partially pinned particles. We find that random density fluctuations appear when pinning overcomes interactions and show that the suppression of density fluctuations is indeed correlated to the presence of interactions. Furthermore, we find that we can describe all studied vortex lattices within a single framework consisting of a continous deviation from hyperuniformity towards random distributions when increasing the strength of pinning with respect to the intervortex interaction.

The superconducting transition leads to a sharp resistance drop in a temperature interval that can be a small fraction of the critical temperature T$_c$. A superconductor exactly at T$_c$ is thus very sensitive to all kinds of thermal perturbations, including the heat dissipated by the measurement current. We show that the interaction between electrical and thermal currents leads to a sizeable imaginary impedance at frequencies of order of tens of Hz at the resistive transition of single crystals of the layered material 2H-NbSe$_2$. We explain the result using models developed for transition edge sensors. By measuring under magnetic fields and at high currents, we find that the imaginary impedance is strongly influenced by the heat associated with vortex motion and out-of-equilibrium quasiparticles.

A perturbed system relaxes towards an equilibrium given by a minimum in the potential energy landscape. This often occurs by thermally activated jumps over metastable states. The corresponding dynamics is named creep and follows Arrhenius' law. Here we consider the situation where the equilibrium position depends on temperature. We show that this effect occurs in the vortex lattice of the anisotropic superconductor $2\mathrm{H}$-$\mathrm{Nb}\mathrm{Se}_{2}$ when the magnetic field is tilted away from the principal axes, and that it leads to the peculiar appearance of creep when cooling the sample. Temperature determines the system's ground state and at the same time brings the system back to equilibrium, playing a dual and antagonistic role. We expect that cooling induced creep occurs in correlated systems with many degrees of freedom allowing to tune the equilibrium state via heat treatment., Comment: 7 pages, 4 figures

A gel consists of a network of particles or molecules formed for example using the sol-gel process, by which a solution transforms into a porous solid. Particles or molecules in a gel are mainly organized on a scaffold that makes up a porous system. Quantized vortices in type II superconductors mostly form spatially homogeneous ordered or amorphous solids. Here we present high-resolution imaging of the vortex lattice displaying dense vortex clusters separated by sparse or entirely vortex-free regions in $\beta$-Bi$_2$Pd superconductor. We find that the intervortex distance diverges upon decreasing the magnetic field and that vortex lattice images follow a multifractal behavior. These properties, characteristic of gels, establish the presence of a novel vortex distribution, distinctly different from the well-studied disordered and glassy phases observed in high-temperature and conventional superconductors. The observed behavior is caused by a scaffold of one-dimensional structural defects with enhanced stress close to the defects. The vortex gel might often occur in type-II superconductors at low magnetic fields. Such vortex distributions should allow to considerably simplify control over vortex positions and manipulation of quantum vortex states.

Many practical applications of high T$_c$ superconductors involve layered materials and magnetic fields applied on an arbitrary direction with respect to the layers. When the anisotropy is very large, Cooper pair currents can circulate either within or perpendicular to the layers. Thus, tilted magnetic fields lead to intertwined lattices of Josephson and Abrikosov vortices, with quantized circulation across and within layers, respectively. Transport in such intertwined lattices has been studied in detail, but direct observation and manipulation of vortices remains challenging. Here we present magnetic force microscopy experiments in tilted magnetic fields in the extremely quasi-two dimensional superconductor $Bi_{2}Sr_{2}CaCu_{2}O_{8}$. We trigger Abrikosov vortex motion in between Josephson vortices, and find that Josephson vortices in different layers can be brought on top of each other. Our measurements suggest that intertwined lattices in tilted magnetic fields can be intrinsically easy to manipulate thanks to the mutual interaction between Abrikosov and Josephson vortices.

We show that biaxial strain induces alternating tetragonal superconducting and orthorhombic nematic domains in Co substituted CaFe2As2. We use Atomic Force, Magnetic Force and Scanning Tunneling Microscopy (AFM, MFM and STM) to identify the domains and characterize their properties, finding in particular that tetragonal superconducting domains are very elongated, more than several tens of micron long and about 30 nm wide, have the same Tc than unstrained samples and hold vortices in a magnetic field. Thus, biaxial strain produces a phase separated state, where each phase is equivalent to what is found at either side of the first order phase transition between antiferromagnetic orthorhombic and superconducting tetragonal phases found in unstrained samples when changing Co concentration. Having such alternating superconducting domains separated by normal conducting domains with sizes of order of the coherence length opens opportunities to build Josephson junction networks or vortex pinning arrays and suggests that first order quantum phase transitions lead to nanometric size phase separation under the influence of strain.

We image vortex creep at very low temperatures using Scanning Tunneling Microscopy (STM) in the superconductor Rh$_9$In$_4$S$_4$ ($T_c$=2.25 K). We measure the superconducting gap of Rh$_9$In$_4$S$_4$, finding $\Delta\approx 0.33$meV and image a hexagonal vortex lattice up to close to H$_{c2}$, observing slow vortex creep at temperatures as low as 150 mK. We estimate thermal and quantum barriers for vortex motion and show that thermal fluctuations likely cause vortex creep, in spite of being at temperatures $T/T_c<0.1$. We study creeping vortex lattices by making images during long times and show that the vortex lattice remains hexagonal during creep with vortices moving along one of the high symmetry axis of the vortex lattice. Furthermore, the creep velocity changes with the scanning window suggesting that creep depends on the local arrangements of pinning centers. Vortices fluctuate on small scale erratic paths, indicating that the vortex lattice makes jumps trying different arrangements during its travel along the main direction for creep. The images provide a visual account of how vortex lattice motion maintains hexagonal order, while showing dynamic properties characteristic of a glass., Comment: 11 pages, 9 figures, 3 videos