Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe

Atomic-Site-Dependent Pairing Gap in Monolayer FeSe/SrTiO3(001)-(√13 × √13)

The interfacial FeSe/TiO2-δ coupling induces high-temperature superconductivity in monolayer FeSe films. Using cryogenic atomically resolved scanning tunneling microscopy/spectroscopy, we obtained atomic-site dependent surface density of states, work function, and the pairing gap in the monolayer FeSe on the SrTiO3(001)-(√13 × √13)-R33.7° surface. Our results disclosed the out-of-plane Se-Fe-Se triple layer gradient variation, switched DOS for Fe sites on and off TiO5□, and inequivalent Fe sublattices, which gives global spatial modulation of pairing gap contaminants with the (√13 × √13) pattern. Moreover, the coherent lattice coupling induces strong inversion asymmetry and in-plane anisotropy in the monolayer FeSe, which is demonstrated to correlate with the particle-hole asymmetry in coherence peaks. These results disclose delicate atomic-scale correlations between pairing and lattice-electronic coupling in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover regime, providing insights into understanding the pairing mechanism of multiorbital superconductivity.

Evidence for a finite-momentum Cooper pair in tricolor d-wave superconducting superlattices

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with finite-momentum pairs has long been a challenge, but establishing its existence has long suffered from the lack of an appropriate probe to reveal its momentum. Recently, it has been proposed that the nonreciprocal electron transport is the most powerful probe for the finite-momentum pairs, because it directly couples to the supercurrents. Here we reveal such a pairing state by the non-reciprocal transport on tricolor superlattices with strong spin-orbit coupling combined with broken inversion-symmetry consisting of atomically thin d-wave superconductor CeCoIn5. We find that while the second-harmonic resistance exhibits a distinct dip anomaly at the low-temperature (T)/high-magnetic field (H) corner in the HT-plane for H applied to the antinodal direction of the d-wave gap, such an anomaly is absent for H along the nodal direction. By carefully isolating extrinsic effects due to vortex dynamics, we reveal the presence of a non-reciprocal response originating from intrinsic superconducting properties characterized by finite-momentum pairs. We attribute the high-field state to the helical superconducting state, wherein the phase of the order parameter is spontaneously spatially modulated.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1-xSx and FeSe1-xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe_1-xS_x and FeSe_1-xTe_x which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

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.

Atomic imaging with a 12 T magnetic field perpendicular or parallel to the sample surface by an ultra-stable scanning tunneling microscope

We present the first nonmetallic scanning tunneling microscope (STM) featuring an ultra-stable tip-sample mechanical loop and capable of atomic-resolution imaging within a 12 T magnetic field that could be either perpendicular or parallel to the sample surface. This is also the first STM with an ultra-stable tip-sample mechanical loop but without a standalone scanner. The STM head is constructed only with two parts: an improved spider-drive motor and a zirconia tip holder. The motor performs both the coarse approach and atomic imaging. A supporting spring is set at the fixed end of the motor tube to decrease the tip-sample mechanical loop. The zirconia tip holder performs as the frame of the whole STM head. With the novel design, the STM head in three dimensions can be as small as 7.9 mm × 7.9 mm × 26.5 mm. The device's excellent performance is demonstrated by atomic-resolution images of graphite and NbSe₂ obtained at 300 K and 2 K, as well as the high-resolution dI/dV spectrums of NbSe₂ at variable temperatures. Low drift rates in the X-Y plane and Z direction further prove the imaging stability of our new STM. High-quality imaging of the Charge Density Wave (CDW) structure on a TaS₂ surface shows the STM's good application capability. Continuous atomic images obtained in magnetic fields rangs from 0 T to 12 T with the direction of the magnetic field perpendicular or parallel to the sample surface show the STM's good immunity to high magnetic fields. Our results illustrate the new STM's broad application ability in extreme conditions of low temperature and high magnetic field.

Emergent anisotropy in the Fulde-Ferrell-Larkin-Ovchinnikov state

Exotic superconductivity is formed by unconventional electron pairing and exhibits various unique properties that cannot be explained by the basic theory. The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is known as an exotic superconducting state in that the electron pairs have a finite center-of-mass momentum leading to a spatially modulated pattern of superconductivity. The spatial modulation endows the FFLO state with emergent anisotropy. However, the anisotropy has never been experimentally verified despite numerous efforts over the years. Here, we report detection of anisotropic acoustic responses depending on the sound propagation direction appearing above the Pauli limit. This anisotropy reveals that the two-dimensional FFLO state has a center-of-mass momentum parallel to the nesting vector on the Fermi surface. The present findings will facilitate our understanding of not only superconductivity in solids but also exotic pairings of various particles.

The famous Fulde–Ferrell–Larkin– Ovchinnikov (FFLO) state is a spatially-modulated superconducting state with a predicted spatial anisotropy, but this anisotropy has never been experimentally verified. Here, the authors present ultrasound evidence for anisotropy of the sound velocity in the FFLO state of a 2D organic superconductor.

Supercurrent diode effect and finite-momentum superconductors

Our work shows a fascinating application of finite-momentum superconductivity, the supercurrent diode effect, which is being reported in a growing number of experiments. We show that, under external magnetic field, Cooper pairs can acquire finite momentum so that critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal.

When both inversion and time-reversal symmetries are broken, the critical current of a superconductor can be nonreciprocal. In this work, we show that, in certain classes of two-dimensional superconductors with antisymmetric spin–orbit coupling, Cooper pairs acquire a finite momentum upon the application of an in-plane magnetic field, and, as a result, critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal. This supercurrent diode effect is also manifested in the polarity dependence of in-plane critical fields induced by a supercurrent. These nonreciprocal effects may be found in polar SrTiO₃ film, few-layer MoTe₂ in the T_d phase, and twisted bilayer graphene in which the valley degree of freedom plays a role analogous to spin.

Intrinsic Superconducting Diode Effect

Stimulated by the recent experiment [F. Ando et al., Nature (London) 584, 373 (2020).NATUAS0028-083610.1038/s41586-020-2590-4], we propose an intrinsic mechanism to cause the superconducting diode effect (SDE). SDE refers to the nonreciprocity of the critical current for the metal-superconductor transition. Among various mechanisms for the critical current, the depairing current is known to be intrinsic to each material and has recently been observed in several superconducting systems. We clarify the temperature scaling of the nonreciprocal depairing current near the critical temperature and point out its significant enhancement at low temperatures. It is also found that the nonreciprocal critical current shows sign reversals upon increasing the magnetic field. These behaviors are understood by the nonreciprocity of the Landau critical momentum and the change in the nature of the helical superconductivity. The intrinsic SDE unveils the rich phase diagram and functionalities of noncentrosymmetric superconductors.

Quasiparticle Nodal Plane in the Fulde-Ferrell-Larkin-Ovchinnikov State of FeSe

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields H applied perpendicular to the ab plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy performed on the same crystal demonstrates that the order parameter vanishes at the surface upon entering the high-field phase. These results provide the first demonstration of a pinned planar node perpendicular to H, which is consistent with a putative FFLO state.

Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in bulk NbS2

We present measurements of the magnetic torque, specific heat and thermal expansion of the bulk transition metal dichalcogenide (TMD) superconductor NbS₂ in high magnetic fields, with its layer structure aligned strictly parallel to the field using a piezo rotary positioner. The upper critical field of superconducting TMDs in the 2D form is known to be dramatically enhanced by a special form of Ising spin orbit coupling. This Ising superconductivity is very robust to the Pauli paramagnetic effect and can therefore exist beyond the Pauli limit for superconductivity. We find that superconductivity beyond the Pauli limit still exists in bulk single crystals of NbS₂ for a precisely parallel field alignment. However, the comparison of our upper critical field transition line with numerical simulations rather points to the development of a Fulde-Ferrell-Larkin-Ovchinnikov state above the Pauli limit as a cause. This is also consistent with the observation of a magnetic field driven phase transition in the thermodynamic quantities within the superconducting state near the Pauli limit.

Superconductivity is often destroyed under magnetic field larger than a critical value called Pauli limit. Here, the authors report superconductivity beyond the Pauli limit in bulk single crystals of NbS₂, suggesting the development of a Fulde-Ferrell-Larkin-Ovchinnikov state.

Control of Macromolecule Chains Structure in a Nanofiber

Mechanical property is one of the most important properties of nanofiber membranes. Electrospinning is widely used in the preparation of nanofibers due to its advantages such as good stability and easy operation. Compared with some nature silk, the mechanical properties of nanofibers prepared by electrospinning are poor. Based on the principle of vortex spinning and DNA structure, this paper designed an air vortex electrospinning device that can control the structure of macromolecular chains in nanofibers. When a weak air vortex is generated in the electrospinning process, the macromolecule chains will entangle with each other and form a DNA-like structure so as to improve the mechanical property. In addition, when a strong air vortex is generated during the electrospinning process, the nanofibers will adhere to each other, thereby enhancing the mechanical property and enlarging the pore size.

Anisotropic effect of a magnetic field on the neutron spin resonance in FeSe

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (E r = 3.6 meV) of superconducting FeSe (T c = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasiparticle excitations between the hole and electron Fermi surfaces.