A strongly inhomogeneous superfluid in an iron-based superconductor

Phase-Modulated Elastic Properties of 2D Magnetic FeTe: Hexagonal and Tetragonal Polymorphs

2D layered magnets, such as iron chalcogenides, have emerged these years as a new family of unconventional superconductors and provided the key insights to understand the phonon-electron interaction and pairing mechanism. Their mechanical properties are of strategic importance for the potential applications in spintronics and optoelectronics. However, there is still a lack of efficient approach to tune the elastic modulus despite the extensive studies. Herein, the modulated elastic modulus of 2D magnetic FeTe and its thickness-dependence is reported via phase engineering. The grown 2D FeTe by chemical vapor deposition can present various polymorphs, that is tetragonal FeTe (t-FeTe, antiferromagnetic) and hexagonal FeTe (h-FeTe, ferromagnetic). The measured Young's modulus of t-FeTe by nanoindentation method shows an obvious thickness-dependence, from 290.9 ± 9.2 to 113.0 ± 8.7 GPa when the thicknesses increased from 13.2 to 42.5 nm, respectively. In comparison, the elastic modulus of h-FeTe remains unchanged. These results can shed light on the efficient modulation of mechanical properties of 2D magnetic materials and pave the avenues for their practical applications in nanodevices.

Interface-induced superconductivity in magnetic topological insulators

The interface between two different materials can show unexpected quantum phenomena. In this study, we used molecular beam epitaxy to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We observed emergent interface-induced superconductivity in these heterostructures and demonstrated the co-occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer-the three essential ingredients of chiral topological superconductivity (TSC). The unusual coexistence of ferromagnetism and superconductivity is accompanied by a high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. These magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics.

Pair density wave state in a monolayer high-Tc iron-based superconductor

The pair density wave (PDW) is an extraordinary superconducting state in which Cooper pairs carry non-zero momentum^1,2. Evidence for the existence of intrinsic PDW order in high-temperature (high-T_c) cuprate superconductors^3,4 and kagome superconductors⁵ has emerged recently. However, the PDW order in iron-based high-T_c superconductors has not been observed experimentally. Here, using scanning tunnelling microscopy and spectroscopy, we report the discovery of the PDW state in monolayer iron-based high-T_c Fe(Te,Se) films grown on SrTiO₃(001) substrates. The PDW state with a period of λ ≈ 3.6a_Fe (a_Fe is the distance between neighbouring Fe atoms) is observed at the domain walls by the spatial electronic modulations of the local density of states, the superconducting gap and the π-phase shift boundaries of the PDW around the vortices of the intertwined charge density wave order. The discovery of the PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform to study the interplay between the correlated electronic states and unconventional Cooper pairing in high-T_c superconductors.

Inhomogeneous Superconductivity Onset in FeSe Studied by Transport Properties

Heterogeneous superconductivity onset is a common phenomenon in high-Tc superconductors of both the cuprate and iron-based families. It is manifested by a fairly wide transition from the metallic to zero-resistance states. Usually, in these strongly anisotropic materials, superconductivity (SC) first appears as isolated domains. This leads to anisotropic excess conductivity above Tc, and the transport measurements provide valuable information about the SC domain structure deep within the sample. In bulk samples, this anisotropic SC onset gives an approximate average shape of SC grains, while in thin samples, it also indicates the average size of SC grains. In this work, both interlayer and intralayer resistivity were measured as a function of temperature in FeSe samples of various thicknesses. To measure the interlayer resistivity, FeSe mesa structures oriented across the layers were fabricated using FIB. As the sample thickness decreases, a significant increase in superconducting transition temperature Tc is observed: Tc raises from 8 K in bulk material to 12 K in microbridges of thickness ∼40 nm. We applied analytical and numerical calculations to analyze these and earlier data and find the aspect ratio and size of the SC domains in FeSe consistent with our resistivity and diamagnetic response measurements. We propose a simple and fairly accurate method for estimating the aspect ratio of SC domains from Tc anisotropy in samples of various small thicknesses. The relationship between nematic and superconducting domains in FeSe is discussed. We also generalize the analytical formulas for conductivity in heterogeneous anisotropic superconductors to the case of elongated SC domains of two perpendicular orientations with equal volume fractions, corresponding to the nematic domain structure in various Fe-based superconductors.

On the electron pairing mechanism of copper-oxide high temperature superconductivity

The elementary CuO₂ plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO₅ pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate t/ℏ and across the charge-transfer energy gap [Formula: see text], generate "superexchange" spin-spin interactions of energy [Formula: see text] in an antiferromagnetic correlated-insulator state. However, hole doping this CuO₂ plane converts this into a very-high-temperature superconducting state whose electron pairing is exceptional. A leading proposal for the mechanism of this intense electron pairing is that, while hole doping destroys magnetic order, it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale [Formula: see text]. To explore this hypothesis directly at atomic scale, we combine single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of [Formula: see text] and the electron-pair density n_P in Bi₂Sr₂CaCu₂O_8+x. The responses of both [Formula: see text] and n_P to alterations in the distance δ between planar Cu and apical O atoms are then determined. These data reveal the empirical crux of strongly correlated superconductivity in CuO₂, the response of the electron-pair condensate to varying the charge-transfer energy. Concurrence of predictions from strong-correlation theory for hole-doped charge-transfer insulators with these observations indicates that charge-transfer superexchange is the electron-pairing mechanism of superconductive Bi₂Sr₂CaCu₂O_8+x.

Identification of a nematic pair density wave state in Bi2Sr2CaCu2O8+x

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi₂Sr₂CaCu₂O_8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi₂Sr₂CaCu₂O_8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

Phase-Tunable Synthesis and Etching-Free Transfer of Two-Dimensional Magnetic FeTe

Two-dimensional (2D) Fe-chalcogenides (e.g., FeS, FeSe, and FeTe, etc.) have sparked extensive interest due to their rich phase diagrams including superconductivity, magnetism, and topological state, as well as versatile applications in electronic devices and energy related fields. However, the phase-tunable synthesis and green transfer of such fascinating materials still remain challenging. Herein, we develop a temperature-mediated chemical vapor deposition (CVD) approach to grow ultrathin nonlayered hexagonal and layered tetragonal FeTe nanosheets on mica substrates, with their thicknesses down to ∼2.3 and ∼4.0 nm, respectively. Interestingly, we have observed exciting ferromagnetism with the Curie temperature approaching ∼300 K and high conductivity (∼1.96 × 10⁵ S m^-1) in 2D hexagonal FeTe. More significantly, we have designed a swift, high-efficiency, and etching-free method for the transfer of 2D FeTe nanosheets onto arbitrary substrates, and such a transfer strategy enables the cyclic utilization of growth substrates. These results should propel the further development of phase-tunable synthesis and green transfer of 2D Fe-chalcogenides, as well as their potential applications in spintronic devices.

Roton pair density wave in a strong-coupling kagome superconductor

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter^1-9. Recently, a new family of vanadium-based kagome metals, AV₃Sb₅ (A = K, Rb or Cs), with topological band structures has been discovered^10,11. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures^11-19. Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV₃Sb₅ using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV₃Sb₅ exhibits a V-shaped pairing gap Δ ~ 0.5 meV and is a strong-coupling superconductor (2Δ/k_BT_c ~ 5) that coexists with 4a₀ unidirectional and 2a₀ × 2a₀ charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a₀/3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above T_c, reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-T_c cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Atomic-scale visualization of electronic fluid flow

The most essential characteristic of any fluid is the velocity field, and this is particularly true for macroscopic quantum fluids¹. Although rapid advances^2-7 have occurred in quantum fluid velocity field imaging⁸, the velocity field of a charged superfluid-a superconductor-has never been visualized. Here we use superconducting-tip scanning tunnelling microscopy^9-11 to image the electron-pair density and velocity fields of the flowing electron-pair fluid in superconducting NbSe₂. Imaging of the velocity fields surrounding a quantized vortex^12,13 finds electronic fluid flow with speeds reaching 10,000 km h^-1. Together with independent imaging of the electron-pair density via Josephson tunnelling, we visualize the supercurrent density, which peaks above 3 × 10⁷ A cm^-2. The spatial patterns in electronic fluid flow and magneto-hydrodynamics reveal hexagonal structures coaligned to the crystal lattice and quasiparticle bound states¹⁴, as long anticipated^15-18. These techniques pave the way for electronic fluid flow visualization studies of other charged quantum fluids.

Electronic properties of the bulk and surface states of Fe1+yTe1-xSex

The idea of employing non-Abelian statistics for error-free quantum computing ignited interest in reports of topological surface superconductivity and Majorana zero modes (MZMs) in FeTe_0.55Se_0.45. However, the topological features and superconducting properties are not observed uniformly across the sample surface. The understanding and practical control of these electronic inhomogeneities present a prominent challenge for potential applications. Here, we combine neutron scattering, scanning angle-resolved photoemission spectroscopy, and microprobe composition and resistivity measurements to characterize the electronic state of Fe_1+yTe_1-xSe_x. We establish a phase diagram in which the superconductivity is observed only at sufficiently low Fe concentration, in association with distinct antiferromagnetic correlations, whereas the coexisting topological surface state occurs only at sufficiently high Te concentration. We find that FeTe_0.55Se_0.45 is located very close to both phase boundaries, which explains the inhomogeneity of superconducting and topological states. Our results demonstrate the compositional control required for use of topological MZMs in practical applications.

Millikelvin scanning tunneling microscope at 20/22 T with a graphite enabled stick-slip approach and an energy resolution below 8 μeV: Application to conductance quantization at 20 T in single atom point contacts of Al and Au and to the charge density wave of 2H-NbSe2

We describe a scanning tunneling microscope (STM) that operates at magnetic fields up to 22 T and temperatures down to 80 mK. We discuss the design of the STM head, with an improved coarse approach, the vibration isolation system, and efforts to improve the energy resolution using compact filters for multiple lines. We measure the superconducting gap and Josephson effect in aluminum and show that we can resolve features in the density of states as small as 8 μeV. We measure the quantization of conductance in atomic size contacts and make atomic resolution and density of states images in the layered material 2H-NbSe₂. The latter experiments are performed by continuously operating the STM at magnetic fields of 20 T in periods of several days without interruption.

Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide

Among the most intriguing of the many phases of cuprate superconductors is the so-called pair density wave (PDW) state. PDW is characterized by a spatially modulated density of Cooper pairs and can be detected with a scanning tunneling microscope equipped with a superconducting tip. Liu et al. used Josephson tunneling microscopy, modified for the task, to detect PDW in niobium diselenide, a superconductor with a layered hexagonal structure. The PDW state is expected to appear in other transition metal dichalcogenides as well.

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Correlating Josephson supercurrents and Shiba states in quantum spins unconventionally coupled to superconductors

Local spins coupled to superconductors give rise to several emerging phenomena directly linked to the competition between Cooper pair formation and magnetic exchange. These effects are generally scrutinized using a spectroscopic approach which relies on detecting the in-gap bound modes arising from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states. However, the impact of local magnetic impurities on the superconducting order parameter remains largely unexplored. Here, we use scanning Josephson spectroscopy to directly visualize the effect of magnetic perturbations on Cooper pair tunneling between superconducting electrodes at the atomic scale. By increasing the magnetic impurity orbital occupation by adding one electron at a time, we reveal the existence of a direct correlation between Josephson supercurrent suppression and YSR states. Moreover, in the metallic regime, we detect zero bias anomalies which break the existing framework based on competing Kondo and Cooper pair singlet formation mechanisms. Based on first-principle calculations, these results are rationalized in terms of unconventional spin-excitations induced by the finite magnetic anisotropy energy. Our findings have far reaching implications for phenomena that rely on the interplay between quantum spins and superconductivity.

The impact of local magnetic impurities on superconducting order parameter remains largely unexplored. Here, the authors visualize the effect of different magnetic perturbations on a superconductor, unveiling a rich correlation of the interplay between quantum spins and superconductivity in different spectroscopic regimes.

Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe0.55Se0.45

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe_0.55Se_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 energy shift is caused by the low superfluid density in FeTe_0.55Se_0.45, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Imaging the energy gap modulations of the cuprate pair-density-wave state

The defining characteristic^1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)^3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling⁵, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi₂Sr₂CaCu₂O_8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a₀)(1/8, 0) and Q ≈ (2π/a₀)(0, 1/8) (where a₀ is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state^6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi₂Sr₂CaCu₂O_8+δ.