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The intermediate behavior near a quantum phase transition is crucial for understanding the quantum criticality of various competing phases and their separate origins, yet remains unexplored for the multiple Yu-Shiba-Rusinov (YSR) states. Here, we investigated the detailed spectroscopic change of the exchange coupling-dependent YSR states near a quantum phase transition. The initially developed one pair of YSR states, induced by the Fe vacancy in monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution showing an evolution into two pairs of YSR peaks yet with dichotomy in their spectral features. Interestingly, while the lower-energy YSR branch enters the quantum phase transition region, the higher-lying one remains rigidly away from the lower-energy counterpart with a constant energy difference. Spectral weight analysis of the higher-energy branch yields an exponential dependence on the exchange coupling, which can be well rationalized by taking the two pairs of YSR states as a result of field splitting by the magnetic anisotropy. Our results unveil the intermediate region of a quantum phase transition with a magnetic anisotropy-induced splitting of the YSR resonance, and highlight a prospect for developing functional electronics based on the flexibly controllable multiple quantum states., Comment: 8 pages, 3 figures

Typical BCS superconductors are microscopically homogeneous in real space governed by the coherent Cooper pairs with high phase stiffness of superfluid density, which is characterized by a coherence length. However, a periodic oscillation of superconducting order parameter may develop driven by breaking the time-reversal or translational invariance. To date, such modulated orders were specific to each material systems, with a periodicity much larger than the lattice constant. Here we report the direct observation of a uniform lattice-scale pair density wave (PDW) in single-layer FeSe/SrTiO3 films, enforced by peculiar interfacial structure of crystal symmetries breaking. Our spectroscopic imaging scanning tunneling microscopy unravels a spatial modulation of Cooper-pairing gap within a single unit-cell, depending on inequivalent atomic sites. Prominent periodic variation of superfluid density is visualized via Josephson current by a superconducting tip, indicating a real-space oscillation of phase stiffness. Such a lattice-scale superconducting modulation, which coexists with a larger length scale of PDW order, indicates the lattice-scale variation of both pairing strength and phase stiffness. Our findings provide new insights into the intertwined density-wave orders of quasiparticle character in correlated electronic systems, and provoke future studies on the unconventional pairing interaction and phase stiffness in the two-dimensional limit., Comment: 15 pages, 4 figures

The photoinduced topological phase transitions and thermal Hall conductivity of a kagome magnet with Heisenberg, Kitaev, and DM interactions under an external magnetic field aligned along the [111] directions is investigated in this study. In the presence of a strong magnetic field perpendicular to the lattice plane in the [111] direction, the system exhibits a fully polarized paramagnetic phase and the magnon band carries an asymmetric Chern number across the phase diagram region. Utilizing magnetic Floquet-Bloch theory, we demonstrate that periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with varying Berry curvature, Chern numbers and thermal Hall conductivities signatures by adjusting light intensity throughout the phase diagram region., Comment: arXiv admin note: text overlap with arXiv:1801.04932 by other authors

Coulomb blockade occurs for electrons tunneling into nanoislands because of the quantization of charge. Here, using spectroscopy measurements of nonmagnetic islands grown on a high-Tc superconductor [one-unit-cell (1-UC) FeSe], we systematically investigate the dynamical Coulomb blockade (DCB), which is found to reflect the Cooper pairing potential in the superconducting substrate. The tunneling spectra are acquired on single-crystalline Pb nanoislands and show a clear suppression of the tunnel current around zero bias-voltage with a gap-like structure. The observed spectral gaps can be attributed to DCB based on our comprehensive investigations, including experiments with finely varying island sizes and calculations of the spectra using the P(E) theory of DCB. Our detailed analysis suggests that the observed DCB can be related to the sign-reversing pairing potential in the 1-UC FeSe substrate below the islands. The sign reversal is furthermore revealed in a transition of the superconducting gap of FeSe from a U- to a V-like lineshape as the distance between neighboring doublet islands is decreased, indicating the presence of a nodal-like gap as expected for a sign-reversing superconductor. Our configuration of nonmagnetic nanoislands on a high-Tc superconductor for spectroscopy measurements may serve as a local, spatially sensitive, and tunable probe for detecting the sign-reversing order parameter in unconventional superconductors.

The orbital multiplicity in multiband superconductors yields orbital differentiation in normal-state properties, and can lead to orbital-selective spin-fluctuation Cooper pairing. This phenomenon has become increasingly pivotal in clarifying the pairing 'enigma' particularly for multiband high-temperature superconductors. In one-unit-cell (1-UC) FeSe/SrTiO3, the thinnest and highest-Tc member of iron-based superconductors, the standard electron-hole Fermi pocket nesting scenario is apparently not applicable since the Gamma-centered hole pockets are absent, so the actual pairing mechanism is the subject of intense debate. Here, by measuring high-resolution Bogoliubov quasiparticle interference, we report observations of highly anisotropic magnetic Cooper pairing in 1-UC FeSe. From a theoretical point of view, it is important to incorporate effects of electronic correlations within a spin-fluctuation pairing calculation, where the dxy orbital becomes coherence-suppressed. The resulting pairing gap is compatible with the experimental findings, which suggests that high-Tc Cooper pairing with orbital selectivity applies to 1-UC FeSe. Our findings imply the general existence of orbital selectivity in iron-based superconductors and the universal importance of electron correlations in high-Tc superconductors.

Superlattice potentials are theoretically predicted to modify the single-particle electronic structures. The resulting Coulomb-interaction-dominated low-energy physics would generate highly novel many-body phenomena. Here, by in situ tunneling spectroscopy, we show the signatures of superstructure-modulated correlated electron states in epitaxial bilayer graphene (BLG) on 6H-SiC(0001). As the carrier density is locally quasi-'tuned' by the superlattice potentials of a 6x6 interface reconstruction phase, the spectral-weight transfer occurs between the two broad peaks flanking the charge-neutral point. Such detected non-rigid band shift beyond the single-particle band description implies the existence of correlation effects, probably attributed to the modified interlayer coupling in epitaxial BLG by the 6x6 reconstruction as in magic-angle BLG by the Moire potentials. Quantitative analysis suggests the intrinsic interface reconstruction shows a high carrier tunability of around 1/2 filling range, equivalent to the back gating by a voltage of around 70 V in a typical gated BLG/SiO2/Si device. The finding in interface-modulated epitaxial BLG with reconstruction phase extends the BLG platform with electron correlations beyond the magic-angle situation, and may stimulate further investigations on correlated states in graphene systems and other van der Waals materials.

Pursuing the confinement of linearly dispersive relativistic fermions is of interest in both fundamental physics and potential applications. Here, we report strong STM evidence for the equally spaced, strikingly sharp, and densely distributed quantum well states (QWSs) near Fermi energy in Pb(111) nanoislands, van-der-Waals epitaxially grown on graphitized 6H-SiC(0001). The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially 'simulate' the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry-Perot fittings based on the relativistic fermions. First-principles calculations further reveal that the spin-orbit coupling strengthens the relativistic nature of electrons near Fermi energy. Our finding uncovers the unique equally spaced quantum states in electronic systems beyond Landau levels, and may inspire future studies on confined relativistic quasiparticles in flourishing topological materials and applications in structurally simpler quantum cascade laser.

Intriguing novel phenomena in lead films inspire new understanding of quantum physics, such as quantum size effect and quantum phase transitions etc. The improvement of the sample quality makes it even more promising to explore the intrinsic properties in two-dimensional system. In this paper, we show that the crystalline interfacial striped incommensurate layer can increase the quality of the lead films and significantly enhance the magnitude of magnetoresistance. By performing systematic transport measurement, a predominant anomalous linear magnetoresistance is revealed, and the widely used Parish-Littlewood model and Abrikosov's explanation fail to describe the observation. Instead, we propose a new model of linear magnetoresistance based on linear band structure, which shows a good agreement with the experimental results. Our studies reveal a novel origin of linear magnetoresistance which may also be helpful to understand the linear magnetoresistance in other materials with linear dispersion of electronic structure.

Majorana zero-energy bound states (ZEBSs) have been proposed to exist at the ends of one-dimensional Rashba nanowires proximity-coupled to an s-wave superconductor in an external magnetic field induced Zeeman field. Such hybrid structures have been a central platform in the search for non-Abelian Majorana zero modes (MZMs) toward fault-tolerant topological quantum computing. Here we report the discovery of ZEBSs simultaneously appearing at each end of a one-dimensional atomic line defect in monolayer iron-based high-temperature superconductor FeTe0.5Se0.5 films grown on SrTiO3(001) substrates. The spectroscopic properties of the ZEBSs, including the temperature and tunneling barrier dependences, as well as their fusion induced by coupling on line defects of different lengths are found to be robust and consistent with those of the MZMs. These observations suggest a realization of topological Shockley defects at the ends of an atomic line defect in a two-dimensional s-wave superconductor that can host a Kramers pair of MZMs protected by time-reversal symmetry along the chain. Our findings reveal an unprecedented class of topological line defect excitations in two-dimensional superconductor FeTe0.5Se0.5 monolayer films and offer an advantageous platform for generating topological zero-energy excitations at higher operating temperatures, in a single material, and under zero external magnetic field., Comment: The final version of the manuscript can be found in Nature Physics

High temperature superconductivity in one unit cell (1 UC) FeSe on SrTiO3 heterostructure has become a research frontier in condensed matter physics and material science. The superconducting transition temperature (Tc) of ultrathin FeSe film is significantly enhanced compared to its bulk counterpart and possibly approaches the liquid nitrogen region according to in situ spectroscopic measurements. Particularly, the Fermi surface topology of 1 UC FeSe consists of no hole pockets at Brillouin zone center, which poses a great challenge to the well accepted s+- wave pairing nesting the sign different electron hole Fermi pockets in iron based superconductors. In this review, we present the explorations of Tc enhancement, electron pairing and topological phases in 1 UC FeSe on SrTiO3. The potential coexistence of high temperature superconductivity and topological electronic states promotes such two dimensional heterostructure as the candidate of next generation connate high temperature topological superconductor and (or) topological quantum computation platform.

We study the magnetic field induced superconductor-metal transition (SMT) in ultrathin crystalline Pb films. By performing ultralow temperature transport measurement, the divergent critical exponent as an indication of quantum Griffiths singularity (QGS) is observed when approaching zero temperature quantum critical point. Distinctively, the phase boundary of SMT exhibits an anomalous behavior in low temperature regime that the onset critical field decreases with decreasing temperatures, which distinguishes our observation from earlier reports of QGS in various two-dimensional superconductors. We demonstrate that this observed anomalous phase boundary has its origin from the superconducting fluctuations in ultrathin Pb films. Our findings reveal a novel aspect of the QGS of SMT in two-dimentional superconducting systems with anomalous phase boundary.

Majorana zero modes (MZMs) that obey the non-Abelian statistics have been intensively investigated for potential applications in topological quantum computing. The prevailing signals in tunneling experiments "fingerprinting" the existence of MZMs are the zero-energy bound states (ZEBSs). However, nearly all of the previously reported ZEBSs showing signatures of the MZMs are observed in difficult-to-fabricate heterostructures at very low temperatures and additionally require applied magnetic field. Here, by using in-situ scanning tunneling spectroscopy, we detect the ZEBSs upon the interstitial Fe adatoms deposited on two different high-temperature superconducting one-unit-cell-thick iron chalcogenides on SrTiO3(001). The spectroscopic results resemble the phenomenological characteristics of the MZMs inside the vortex cores of topological superconductors. Our experimental findings may extend the MZM explorations in connate topological superconductors towards an applicable temperature regime and down to the two-dimensional limit. While a concrete understanding of the observations is lacking, possible explanations involving novel 2D superconducting states with spin-orbit coupling, spontaneous nucleation of anomalous vortices at the magnetic sites, and noncoplanar magnetic ordering may further stimulate theoretical understandings of the scarcely captured ZEBSs in strongly correlated systems with multiband Cooper pairing.

Two dimensional (2D) superconducting systems are of great importance to exploring exotic quantum physics. Recent development of fabrication techniques stimulates the studies of high quality single crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity) in 4 monolayer (ML) to 6 ML crystalline Pb films grown on striped incommensurate (SIC) Pb layers on Si(111) substrates by molecular beam epitaxy (MBE). Anomalous large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that in superconducting heterostructures the interface can induce Zeeman-type spin-orbit interaction (SOI) and modulate the superconductivity.

We report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on SrTiO3(001) (STO) substrate. In quasiparticle density of states, bosonic excitation mode characterized by the "dip-hump" structure is detected outside the larger superconducting gap with energy comparable with phonon and spin resonance modes in heavily electron-doped iron selenides. Statistically, the excitation mode, which is intimately correlated with superconductivity, shows an anticorrelation with pairing strength and yields an energy scale upper-bounded by twice the superconducting gap coinciding with the characteristics of magnetic resonance in cuprates and iron-based superconductors. The local response of tunneling spectra to magnetically different Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing. These results support the magnetic nature of the excitation mode and possibly reveal a signature of electron-magnetic-excitation coupling in high-temperature superconductivity of 1-UC FeSe/STO.

Since the dramatic interface enhancement of superconducting transition temperature (Tc) was reported in one unit-cell FeSe film grown on SrTiO3 substrate (1-UC FeSe/STO) by molecular beam epitaxy (MBE), related research on this system has become a new frontier in condensed matter physics. In this paper, we present a brief review on this rapidly developing field, mainly focusing on the superconducting properties of 1-UC FeSe/STO. Experimental evidences for the high-temperature superconductivity in 1-UC FeSe/STO, including the direct evidences revealed by transport and diamagnetic measurements, and other evidences from scanning tunneling microscope (STM) and angle-resolved photoemission spectroscopy (ARPES), are overviewed. Potential mechanisms of the enhanced superconductivity are discussed. There are accumulating arguments suggesting that the strengthened Cooper pairing in 1-UC FeSe/STO originates from the interface effects, specifically charge transfer and coupling to phonon modes in TiO2 plane. The study of superconductivity in 1-UC FeSe/STO not only sheds a new light on the mechanism of high-temperature superconductors with layered structures, but also provides the insight to explore new superconductors by interface engineering.