The coupling of a spin to an underlying substrate is the basis for a plethora of phenomena. In the case of a metallic substrate, Kondo screening of the adatom magnetic moment can occur. As the substrate turns superconducting, an intriguing situation emerges where the pair breaking due to the adatom spins leads to Yu-Shiba-Rusinov bound states, but also intertwines with Kondo phenomena. Through scanning tunneling spectroscopy, we analyze the interdependence of Kondo screening and superconductivity. Our data obtained on single Fe adatoms on Nb(110) show that the coupling and the resulting YSR states are strongly adsorption site-dependent and reveal a quantum phase transition at a Kondo temperature comparable to the superconducting gap. The experimental signatures are rationalized by combined density functional theory and continuous-time quantum Monte-Carlo calculations to rigorously treat magnetic and hybridization effects on equal footing.
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-orbit…
We study the bound state spectrum and 0-$π$ transitions in ballistic quasi-1D superconductor/ferromagnetic insulator/superconductor (S/FI/S) Josephson junctions. In addition to the Andreev bound states, stemming from the phase coherence, the magnetic barrier gives rise to qualitatively different Yu-Shiba-Rusinov (YSR) bound states with genuine spectral features and spin characteristics. We show that zero-energy YSR states are much more robust against scalar tunneling than their Andreev counterparts and also fingerprint a quantum phase transition from the junctions' 0 into the $π$ phase, connec…
We theoretically study the formation and characteristics of Yu-Shiba-Rusinov bound states within the superconducting gap using a BTK approach in presence of a spin flipper (high spin magnetic impurity). We focus on the zero energy in the conductance spectra and show how a peak is formed at $E=0$ due to the flipping of the magnetic impurity spin but for no flip case a dip forms at $E=0$ in the conductance spectra. This $E=0$ conductance peak is almost quantized at $2e^2/h$ values, however, it arises due to non-topological reasons in contrast to the $E=0$ peak formed due to Majorana states.
Yu-Shiba-Rusinov (YSR) bound states appear when a magnetic atom interacts with a superconductor. Here, we report on spin-resolved spectroscopic studies of YSR states related with Fe atoms deposited on the surface of the topological superconductor FeTe0.55Se0.45 using a spin-polarized scanning tunneling microscope. We clearly identify the spin signature of pairs of YSR bound states at finite energies within the superconducting gap having opposite spin polarization as theoretically predicted. In addition, we also observe zero-energy bound states for some of the adsorbed Fe atoms. In this case, a…
We have implemented the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn- Rostoker (KKR) method for solving, self-consistently, the superconducting state for 3d crystals including substitutional impurities. In this report we extend this theoretical framework to allow for collinear magnetism and apply it to fcc Pb with 3d magnetic impurities. In the presence of magnetic impurities, there is a pair-breaking effect that results in sup-gap Yu-Shiba-Rusinov (YSR) states which we decompose into contributions from the individual orbital character. We determine the spatial extent of the…
When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity1. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap2-4. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes5 suitable for topological quantum computing6. Here we report the first realization of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and wit…
When the exchange interaction between the impurity spin and the spins of itinerant quasiparticles are strong or weak enough, the ground states for a magnetic impurity in a superconductor are the screened or free spins, respectively. In both cases, the lowest excited state is a bound state within the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state. The YSR state is spatially localized, energetically isolated, and fully spin-polarized, leading to applications such as functional scanning probes. While any application demands identifying whether the impurity spin is screened or free…
Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe$_{2}$ with spin orbit coupling
本文研究了超导主体三角晶格中磁性杂质自旋极化束缚态的形貌。在实验上已在2 H-NbSe $_{2}$晶体中观察到这种态[G. C. M 'enard等人，11，1013（2015）]，并揭示了延伸至数十纳米的振荡粒子-空穴不对称性。利用Bogoliubov-de Gennes方法研究了存在自旋轨道相互作用时的Yu-Shiba-Rusinov态。我们还研究了双杂质在三角晶格中几个相对位置的束缚态。
Various promising qubit concepts have been put forward recently based on engineered superconductor (SC) subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a SC strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a SC for the first time. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than …
Robust quantum systems rely on having a protective environment with minimized relaxation channels. Superconducting gaps play an important role in the design of such environments. The interaction of localized single spins with a conventional superconductor generally leads to intrinsically extremely narrow Yu-Shiba-Rusinov (YSR) resonances protected inside the superconducting gap. However, this may not apply to superconductors with nontrivial, energy dependent order parameters. Exploiting the Fe-doped two-band superconductor NbSe$_2$, we show that due to the nontrivial relation between its compl…
Magnetic adatoms on a superconducting substrate undergo a quantum phase transition as their exchange coupling to the conduction electrons increases. For quantum spins, this transition is accompanied by screening of the adatom spin. Here, we explore the consequences of this screening for the phase diagrams and subgap excitation spectra of dimers of magnetic adatoms coupled by hybridization of their Yu-Shiba-Rusinov states and spin-spin interactions. We specifically account for higher spins, single-ion anisotropy, Ruderman-Kittel-Kasuya-Yosida coupling, and Dzyaloshinsky-Moriya interactions rele…
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…
NbSe$_2$ is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wavefunctions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make Nb…
We calculate the frequency-dependent admittance of a phase-biased Josephson junction spanning a magnetic impurity or a spinful Coulomb-blockaded quantum dot. The local magnetic moment gives rise to Yu-Shiba-Rusinov bound states, which govern the sub-gap absorption as well as the inductive response. We model the system by a superconducting spin-polarized exchange-cotunnel junction and calculate the linear current response to an AC bias voltage, including its dependence on phase bias as well as particle-hole, and source-drain coupling asymmetry. The corresponding inductive admittance is analyzed…
We study the properties of collective Yu-Shiba-Rusinov (YSR) states generated by multiple magnetic adatoms (clusters) placed on the surface of a superconductor. For magnetic clusters with equal distances between their constituents, we demonstrate the formation of effectively spin-unpolarized YSR states with subgap energies independent of the spin configuration of the magnetic impurities. We solve the problem analytically for arbitrary spin structure and analyze both spin-polarized (dispersive energy levels) and spin-unpolarized (pinned energy levels) solutions. While the energies of the spin-p…
Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu-Shiba-Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is greatly enhanced in 2D systems, which should facilitate the formation of coupled states. Here, we observe YSR states on single cobalt phthalocyanine (CoPC) molecules on a 2D superconductor NbSe$_2$ using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). We use STM lateral manipulation to create controlled CoPc dimers and demonstrat…
Motivated by recent scanning tunneling microscopy experiments on single magnetic impurities on superconducting surfaces, we present here a comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound states and (multiple) Andreev reflections. Our theory is based on a combination of an Anderson model with broken spin degeneracy and nonequilibrium Green's function techniques that allows us to describe the electronic transport through a magnetic impurity coupled to superconducting leads for arbitrary junction transparency. Using this combination we are able to elucidate the dif…
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 …
We present a fully relativistic first principles based theoretical approach for the calculation of the spectral properties of magnetic impurities on the surface of a superconducting substrate, providing a material specific framework for the investigation of the Yu--Shiba--Rusinov (YSR) states. By using a suitable orbital decomposition of the local densities of states we discuss in great details the formation of the YSR states for an Mn adatom and for two kinds of Mn dimers placed on the Nb(110) surface and compare our results to recent experimental findings. In case of the adatom we find that …
Magnetic atoms on superconductors induce localized Yu-Shiba-Rusinov (YSR) bound states. The proposal that topological superconductivity and Majorana modes can be engineered in arrays of hybridizing YSR states has led to their intense investigation. Here, we study Majorana modes emerging from bands of hybridized YSR states in artificially constructed Manganese (Mn) chains on superconducting Niobium (Nb). By controlling the chain geometry on the single atom level, we can measure the interaction-induced energy splitting of Majorana modes from both chain's ends with increasing chain length. We fin…
The local magnetic moment of an interacting quantum dot occupied by a single electron can be screened by binding a Bogoliubov quasiparticle from a nearby superconductor. This gives rise to a long-lived discrete spin-singlet state inside the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state. We study the nature of the subgap states induced by a quantum dot embedded between two small superconducting islands. We show that this system has two spin-singlet subgap states with different spatial charge distributions. These states can be put in a linear superposition and coherently manipul…
Bilayer graphene has two non-equivalent sublattices and, therefore, the same adatom impurity can manifest in spectrally distinct ways-sharp versus broad resonances near the charge neutrality-depending on the sublattice it adsorbs at. Employing Green's function analytical methods and the numerical Kwant package we investigate the spectral and transport interplay between the resonances and superconducting coherence induced in bilayer graphene by proximity to an s-wave superconductor. Analyzing doping and temperature dependencies of quasi-particle spin-relaxation rates, energies of Yu-Shiba-Rusin…
Magnetic atoms can break the Cooper pairs of superconductors, leading to the formation of Yu-Shiba-Rusinov (YSR) bound states inside superconducting gaps. Theory predicts that the YSR bound states can be controlled by tuning the electron density at the Fermi energy, but it has not been studied deeply. In this work, we studied the nature of YSR bound states in response to the potential scattering U by tuning the electron density at the Fermi energy. By comparing two systems, Mn-phthalocyanine molecules on Pb(111) and Co atoms on PbSe/Pb(111), we demonstrate that the sign of U can be unambiguous…
Diode effect in microwave irradiated Josephson junctions with Yu-Shiba-Rusinov states
Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）
We study the sensitivity of Yu-Shiba-Rusinov states, bound states that form around magnetic scatterers in superconductors, to the presence of nonmagnetic disorder in both two and three dimensional systems. We formulate a scattering approach to this problem and reduce the effects of disorder to two contributions: disorder-induced normal reflection and a random phase of the amplitude for Andreev reflection. We find that both of these are small even for moderate amounts of disorder. In the dirty limit in which the disorder-induced mean free path is smaller than the superconducting coherence lengt…
Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an $s$-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities---the Hebel-Slichter effect---and decreases when impurities have spin-orbit coupling. This distinct temperature~dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that th…
A magnetic impurity on a superconductor induces Yu-Shiba-Rusinov (YSR) bound states, detected by tunneling spectroscopy as long-lived quasiparticle excitations inside the superconducting gap. Coupled YSR states constitute basic elements to engineer artificial superconducting states, but their substrate-mediated interactions are generally weak. In this paper, we report that intramolecular (Hund's like) exchange interactions produce coupled YSR states across a molecular platform. We measured YSR spectra along a magnetic iron-porphyrin on Pb(111) and found evidences of two orbital interaction cha…
Tunneling across superconducting junctions proceeds by a rich variety of processes, which transfer single electrons, Cooper pairs, or even larger numbers of electrons by multiple Andreev reflections. Photon-assisted tunneling combined with the venerable Tien-Gordon model has long been a powerful tool to identify tunneling processes between superconductors. Here, we probe superconducting tunnel junctions including an impurity-induced Yu-Shiba-Rusinov (YSR) state by exposing a scanning tunneling microscope with a superconducting tip to microwave radiation. We find that a simple Tien-Gordon descr…
By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the en…
The experimental advances in the study of time-dependent phenomena has opened a new path to investigating the complex electronic structure of strongly correlated and topological materials. Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities in $s$-wave superconductors provide an ideal candidate system to study the response of a system to time-dependent manipulations of the magnetic environment. Here, we show that by imposing a time-dependent change in the magnetic exchange coupling, by changing the relative alignment of magnetic moments in an impurity dimer, or through a periodic driv…
The combination of different exotic properties in materials paves the way for the emergence of their new potential applications. An example is the recently found coexistence of the mutually antagonistic ferromagnetism and superconductivity in hydrogenated boron-doped diamond, which promises to be an attractive system with which to explore unconventional physics. Here, we show the emergence of Yu-Shiba-Rusinov (YSR) bands with a spatial extent of tens of nanometers in ferromagnetic superconducting diamond using scanning tunneling spectroscopy. We demonstrate theoretically how a two-dimensional …
A Yu-Shiba-Rusinov (YSR) state is a localized in-gap state induced by a magnetic impurity in a superconductor. Recent experiments used an STM tip to manipulate the exchange coupling between an Fe adatom and the ${\rm FeTe}_{0.55}{\rm Se}_{0.45}$ superconductor possessing a $Z_2$ nontrivial band structure with topological surface states. As the tip moves close to the single Fe adatom, the energy of the in-gap state is modulated and exhibits two unusual zero-energy crossings, which cannot be understood by coupling the magnetic impurity to the superconducting topological surface Dirac cone. Here,…
A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $\hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zero-bias conductanc…
Odd-parity ground state in dilute Yu-Shiba-Rusinov dimers and chains
Freie Universität Berlin（柏林自由大学）；Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin（达勒姆复杂量子系统中心及物理系，柏林自由大学）；Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel（基尔大学实验与应用物理学研究所）；Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY（鲁普雷希特·亨塞尔实验室，德国电子同步加速器研究所）
We study the subgap Yu-Shiba-Rusinov (YSR) states in the Richardson's model of a superconductor with a magnetic impurity for different electron pairing strengths from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the strong-coupling Bose-Einstein-condensate (BEC) regime. We observe that the effect of the increasing pairing strength on the YSR excitation spectrum as a function of hybridisation strength and impurity on-site potential is only quantitative and, in fact, rather weak when the results are appropriately rescaled. We furthermore show that the problem is analytically solva…
Spin-polarized currents and noise in NS junctions with Yu-Shiba-Rusinov impurities
被磁性杂质无序化的传统超导体表现出与原始超导体截然不同的物理性质。在我们之前的工作[Phys. Rev. B 92，245430（2015）]中，我们探索了两种极端情况下这种系统的光谱和热力学性质：完全随机和铁磁排列的杂质磁矩。在这里，我们考虑这些系统的输运性质，并表明它们有可能被用于超导自旋电子器件。每个磁性杂质贡献一个Yu-Shiba-Rusinov（YSR）束缚态的频谱，驻留在子带隙能量。假设YSR态形成金属带，我们证明了当杂质是铁磁有序的时，这些态所携带的隧穿电流可以是高度自旋极化的。自旋极化可以通过简单地调节偏置电压来切换。此外，即使当杂质自旋完全不相关时，如果隧道界面是自旋激活的，仍然可以实现电流的几乎100%的自旋极化。我们计算电流和噪声，隧道和完全透明的制度之间的接口的变化参数，并分析单粒子和Andreev反射过程的相对作用。
Theoretical descriptions of Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities inside the gap of a superconductor typically rely on a classical spin model or are restricted to spin-1/2 quantum spins. These models fail to account for important aspects of YSR states induced by transition-metal impurities, including the effects of higher quantum spins coupled to several conduction-electron channels, crystal or ligand-field effects, and magnetic anisotropy. We introduce and explore a zero-bandwidth model, which incorporates these aspects, is readily solved numerically, and analytically t…
We investigate the spatial evolution of Yu-Shiba-Rusinov (YSR) states resulting from the interaction between Copper phthalocyanine molecules and a superconducting Vanadium (100) surface with submolecular resolution. Each molecule creates several YSR states at different energies showing distinctly different spatial intensity patterns. Surprisingly, on the molecules the largest YSR intensities are found not at the metal center, but close to one of the pyrrolic N-atoms, demonstrating strong molecular substrate interactions via the organic ligands. Energy resolved YSR maps reveal that the differen…
In this work we fabricate and characterize a functionalized superconducting (SC) Nb tip of a scanning tunnelling microscope (STM). The tip is functionalized with a Tetracyanoquinodimethane molecule (TCNQ) that accepts charge from the tip and develops a magnetic moment. As a consequence, in scanning tunnelling spectroscopy (STS), sharp, bias symmetric sub-gap states identified as Yu-Shiba-Rusinov (YSR) bound states appear against the featureless density of states of a metallic gr/Ir(111) sample. Although the coupling regime of the magnetic impurity with the SC tip depends on the initial absorpt…
The interplay of a potential and magnetic disorder in superconductors remains an active field of research for decades. Within the framework of the Usadel equation, we study the local density of states near a solitary classical magnetic impurity in a dirty superconducting film. We find that a potential disorder results in broadening of the delta-function in the local density of states at the Yu-Shiba-Rusinov (YSR) energy. This broadening is proportional to the square root of a normal-state spreading resistance of the film. We demonstrate that mesoscopic fluctuations caused by a potential disord…
Magnetic impurities on a superconductor induce sub-gap Yu-Shiba-Rusinov (YSR) bound states, localized at the impurity site and fading away from it for distances up to several nanometers. In this article, we present a theoretical method to calculate the spatial distribution of the YSR spectrum of a two-dimensional superconductor with arbitrary Fermi contours (FCs) in the presence of magnetic impurities. Based on the Green's Function (GF) formalism, we obtain a general analytical expression by approximating an arbitrary contour shape to a regular polygon. This method allows us to show the connec…
