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We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed.
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Structural and electronic properties of ultrathin nanocrystals of chalcogenide Bi2(Tex Se1-x)3 were studied. The nanocrystals were formed from the parent compound Bi2Te2Se on as-grown and thermally oxidized Si(100) substrates using Ar-assisted physical vapor deposition, resulting in well-faceted single crystals several quintuple layers thick and a few hundreds nanometers large. The chemical composition and structure of the nanocrystals were analyzed by energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, electron backscattering, and X-ray diffraction. The electron transport through nanocrystals connected to superconducting Nb electrodes demonstrated Josephson behavior, with the predominance of the topological channels [Stolyarov et al. Commun. Mater., 2020, 1, 38]. The present paper focuses on the effect of the growth conditions on the morphology, structural, and electronic properties of nanocrystals.
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Made of a thin non-superconducting metal (N) sandwiched by two superconductors (S), SNS Josephson junctions enable novel quantum functionalities by mixing up the intrinsic electronic properties of N with the superconducting correlations induced from S by proximity. Electronic properties of these devices are governed by Andreev quasiparticles (Andreev, A. Sov. Phys. JETP 1965, 20, 1490) which are absent in conventional SIS junctions whose insulating barrier (I) between the two S electrodes owns no electronic states. Here we focus on the Josephson vortex (JV) motion inside Nb-Cu-Nb proximity junctions subject to electric currents and magnetic fields. The results of local (magnetic force microscopy) and global (transport) experiments provided simultaneously are compared with our numerical model, revealing the existence of several distinct dynamic regimes of the JV motion. One of them, identified as a fast hysteretic entry/escape below the critical value of Josephson current, is analyzed and suggested for low-dissipative logic and memory elements.
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The critical step for future quantum industry demands realization of efficient information exchange between different-platform hybrid systems that can harvest advantages of distinct platforms. The major restraining factor for the progress in certain hybrids is weak coupling strength between the elemental particles. In particular, this restriction impedes a promising field of hybrid magnonics. In this work, we propose an approach for realization of on-chip hybrid magnonic systems with unprecedentedly strong coupling parameters. The approach is based on multilayered microstructures containing superconducting, insulating, and ferromagnetic layers with modified photon phase velocities and magnon eigenfrequencies. The enhanced coupling strength is provided by the radically reduced photon mode volume. Study of the microscopic mechanism of the photon-to-magnon coupling evidences formation of the long-range superconducting coherence via thick strong ferromagnetic layers in superconductor/ferromagnet/superconductor trilayer in the presence of magnetization precession. This discovery offers new opportunities in microwave superconducting spintronics for quantum technologies.
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In Josephson junctions, a supercurrent across a nonsuperconducting weak link is carried by electron-hole bound states. Because of the helical spin texture of nondegenerate topological surface states, gapless bound states are established in junctions with topological weak link. These have a characteristic 4π-periodic current phase relation (CΦR) that leads to twice the conventional Shapiro step separation voltage in radio frequency-dependent measurements. In this context, we identify an attenuated first Shapiro step in (Bi0.06Sb0.94)2Te3 (BST) Josephson junctions with AlO x capping layer. We further investigate junctions on narrow, selectively deposited BST nanoribbons, where surface charges are confined to the perimeter of the nanoribbon. Within these junctions, previously identified signatures of gapless bound states are absent. Because of confinement, transverse momentum sub-bands are quantized and a topological gap opening is observed. Surface states within these quantized sub-bands are spin degenerate, which evokes bound states of conventional 2π-periodic CΦR within the BST nanoribbon weak link.
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Topological insulators with broken time-reversal symmetry and the Fermi level within the magnetic gap at the Dirac cone provides exotic topological magneto-electronic phenomena. Here, we introduce an improved magnetically doped topological insulator, Fe-doped BiSbTe2Se (Fe-BSTS) bulk single crystal, with an ideal Fermi level. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements revealed that the surface state possesses a Dirac cone with the Dirac point just below the Fermi level by 12 meV. The normalized dI/dV spectra suggest a gap opening with Δmag â¼55 meV, resulting in the Fermi level within the opened gap. Ionic-liquid gated-transport measurements also support the Dirac point just below the Fermi level and the presence of the magnetic gap. The chemical potential of the surface state can be fully tuned by ionic-liquid gating, and thus the Fe-doped BSTS provides an ideal platform to investigate exotic quantum topological phenomena.
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In pnictide RbEuFe4As4, superconductivity sets in at 36 K and coexists, below 15-19 K, with the long-range magnetic ordering of Eu 4f spins. Here we report scanning tunneling experiments performed on cold-cleaved single crystals of the compound. The data revealed the coexistence of large Rb-terminated and small Eu-terminated terraces, both manifesting 1 × 2 and 2×2 reconstructions. On 2×2 surfaces, a hidden electronic order with a period â¼5 nm was discovered. A superconducting gap of â¼7 meV was seen to be strongly filled with quasiparticle states. The tunneling spectra compared with density functional theory calculations confirmed that flat electronic bands due to Eu 4f orbitals are situated â¼1.8 eV below the Fermi level and thus do not contribute directly to Cooper pair formation.
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An amendment to this paper has been published and can be accessed via a link at the top of the paper.
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Josephson vortices play an essential role in superconducting quantum electronics devices. Often seen as purely conceptual topological objects, 2π-phase singularities, their observation and manipulation are challenging. Here we show that in Superconductor-Normal metal-Superconductor lateral junctions Josephson vortices have a peculiar magnetic fingerprint that we reveal in Magnetic Force Microscopy (MFM) experiments. Based on this discovery, we demonstrate the possibility of the Josephson vortex generation and manipulation by the magnetic tip of a MFM, thus paving a way for the remote inspection and control of individual nano-components of superconducting quantum circuits.
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In this work, a class of metamaterials is proposed on the basis of ferromagnet/superconductor hybridization for applications in magnonics. These metamaterials comprise of a ferromagnetic magnon medium that is coupled inductively to a superconducting periodic microstructure. Spectroscopy of magnetization dynamics in such hybrid evidences formation of areas in the medium with alternating dispersions for spin wave propagation, which is the basic requirement for the development of metamaterials known as magnonic crystals. The spectrum allows for derivation of the impact of the superconducting structure on the dispersion: it takes place due to a diamagnetic response of superconductors on the external and stray magnetic fields. In addition, the spectrum displays a dependence on the superconducting critical state of the structure: the Meissner and the mixed states of a type II superconductor are distinguished. This dependence hints toward nonlinear response of hybrid metamaterials on the magnetic field. Investigation of the spin wave dispersion in hybrid metamaterials shows formation of allowed and forbidden bands for spin wave propagation. The band structures are governed by the geometry of spin wave propagation: in the backward volume geometry the band structure is conventional, while in the surface geometry the band structure is nonreciprocal and is formed by indirect band gaps.
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The interplay of Dirac physics and induced superconductivity at the interface of a 3D topological insulator (TI) with an s-wave superconductor (S) provides a new platform for topologically protected quantum computation based on elusive Majorana modes. To employ such S-TI hybrid devices in future topological quantum computation architectures, a process is required that allows for device fabrication under ultrahigh vacuum conditions. Here, we report on the selective area growth of (Bi,Sb)2Te3 TI thin films and stencil lithography of superconductive Nb for a full in situ fabrication of S-TI hybrid devices via molecular-beam epitaxy. A dielectric capping layer was deposited as a final step to protect the delicate surfaces of the S-TI hybrids at ambient conditions. Transport experiments in as-prepared Josephson junctions show highly transparent S-TI interfaces and a missing first Shapiro step, which indicates the presence of Majorana bound states. To move from single junctions towards complex circuitry for future topological quantum computation architectures, we monolithically integrated two aligned hardmasks to the substrate prior to growth. The presented process provides new possibilities to deliberately combine delicate quantum materials in situ at the nanoscale.
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Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi1-xSbx. Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb-Bi0.97Sb0.03-Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone's very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.
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The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe2(As0.79P0.21)2, a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains-unprecedented opportunity to consider for advanced superconducting hybrids.
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Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm-thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids.
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An array of superconducting islands placed on a normal metal film offers a tunable realization of nanopatterned superconductivity. This system enables investigation of the nature of competing vortex states and phase transitions between them. A square array creates the eggcrate potential in which magnetic field-induced vortices are frozen into a vortex insulator. We observed a vortex insulator-vortex metal transition driven by the applied electric current and determined critical exponents that coincided with those for thermodynamic liquid-gas transition. Our findings offer a comprehensive description of dynamic critical behavior and establish a deep connection between equilibrium and nonequilibrium phase transitions.
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We discuss the dynamic response of odd-frequency Cooper pairs to an electromagnetic field. By using the quasiclassical Green function method, we calculate the impedance (Z=R-iX) of a normal-metal thin film which covers a superconductor. In contrast with the standard relation (i.e., RâªX), the impedance in spin-triplet proximity structures shows anomalous behavior (i.e., R>X) in the low frequency limit. This unusual relation is a result of the penetration of odd-frequency pairs into the normal metal and reflects the negative Cooper pair density.
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We predict anomalous atomic-scale 0-pi transitions in a Josephson junction with a ferromagnetic-insulator (FI) barrier. The ground state of such junction alternates between 0 and pi states when thickness of FI is increasing by a single atomic layer. We find that the mechanism of the 0-pi transition can be attributed to thickness-dependent phase shifts between the wave numbers of electrons and holes in FI. Based on these results, we show that a stable pi state can be realized in junctions based on high-T{c} superconductors with a La2BaCuO5 barrier.
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The local density of states is studied theoretically in terms of the odd-frequency (odd-omega) Cooper pairing induced around a vortex core. We find that a zero energy peak in the density of states at the vortex center is robust against nonmagnetic impurities in a chiral p-wave superconductor owing to an odd-omega s-wave pair amplitude. We suggest how to discriminate a spin-triplet pairing symmetry and spatial chiral-domain structure by scanning tunneling spectroscopy via odd-omega pair amplitudes inside vortex cores.
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We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin singlet or spin triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.
