Resilient Nodeless d-Wave Superconductivity in Monolayer FeSe

Topological superconductivity from unconventional band degeneracy with conventional pairing

We present a new scheme for Majorana modes in systems with nonsymmorphic-symmetry-protected band degeneracy. We reveal that when the gapless fermionic excitations are encoded with conventional superconductivity and magnetism, which can be intrinsic or induced by proximity effect, topological superconductivity and Majorana modes can be obtained. We illustrate this outcome in a system which respects the space group P4/nmm and features a fourfold-degenerate fermionic mode at (π,  π) in the Brillouin zone. We show that in the presence of conventional superconductivity, different types of topological superconductivity, i.e., first-order and second-order topological superconductivity, with coexisting fragile Wannier obstruction in the latter case, can be generated in accordance with the different types of magnetic orders; Majorana modes are shown to exist on the boundary, at the corner and in the vortices. To further demonstrate the effectiveness of our approach, another example related to the space group P4/ncc based on this scheme is also provided. Our study offers insights into constructing topological superconductors based on bulk energy bands and conventional superconductivity and helps to find new material candidates and design new platforms for realizing Majorana modes.

Identifying s-wave pairing symmetry in single-layer FeSe from topologically trivial edge states

Determining the pairing symmetry of single-layer FeSe on SrTiO3 is the key to understanding the enhanced pairing mechanism. It also guides the search for superconductors with high transition temperatures. Despite considerable efforts, it remains controversial whether the symmetry is the sign-preserving s- or the sign-changing s±-wave. Here, we investigate the pairing symmetry of single-layer FeSe from a topological point of view. Using low-temperature scanning tunneling microscopy/spectroscopy, we systematically characterize the superconducting states at edges and corners of single-layer FeSe. The tunneling spectra collected at edges and corners show a full energy gap and a substantial dip, respectively, suggesting the absence of topologically non-trivial edge and corner modes. According to our theoretical calculations, these spectroscopic features can be considered as strong evidence for the sign-preserving s-wave pairing in single-layer FeSe.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Anisotropic Gap Structure and Sign Reversal Symmetry in Monolayer Fe(Se,Te)

The iron-based superconductors are an ideal platform to reveal the enigma of the unconventional superconductivity and potential topological superconductivity. Among them, the monolayer Fe(Se,Te)/SrTiO₃(001), which is proposed to be topological nontrivial, shows interface-enhanced high-temperature superconductivity in the two-dimensional limit. However, the experimental studies on the superconducting pairing mechanism of monolayer Fe(Se,Te) films are still limited. Here, by measuring the quasiparticle interference in monolayer Fe(Se,Te)/SrTiO₃(001), we report the observation of the anisotropic structure of the large superconducting gap and the sign change of the superconducting gap on different electron pockets. The results are well consistent with the "bonding-antibonding" s_±-wave pairing symmetry driven by spin fluctuations in conjunction with spin-orbit coupling. Our work is of basic significance not only for a unified superconducting formalism in the iron-based superconductors, but also for understanding of topological superconductivity in high-temperature superconductors.

Tomonaga-Luttinger Liquid in the Topological Edge Channel of Multilayer FeSe

A two-dimensional topological insulator exhibits helical edge states topologically protected against single-particle backscattering. Such protection breaks down, however, when electron-electron interactions are significant or when edge reconstruction occurs, leading to a suppressed density of states (DOS) at the Fermi level that follows universal scaling with temperature and energy, characteristic of Tomonaga-Luttinger liquid (TLL). Here, we grow multilayer FeSe on SrTiO₃ by molecular beam epitaxy and observe robust edge states at both the {100}Se and the {110}Se steps using scanning tunneling microscopy/spectroscopy. We determine the DOS follows a power law, resulting in the Luttinger parameter K of 0.26 ± 0.02 and 0.43 ± 0.07 for the {100}Se and {110}Se edges, respectively. The smaller K for the {100}Se edge also indicates strong correlations, attributed to ferromagnetic ordering likely present due to checkerboard antiferromagnetic fluctuations in FeSe. These results demonstrate TLL in FeSe helical edge channels, providing an exciting model system for novel topological excitations arising from superconductivity and interacting helical edge states.

Observation of Distinct Spatial Distributions of the Zero and Nonzero Energy Vortex Modes in (Li_{0.84}Fe_{0.16})OHFeSe

The energy and spatial distributions of vortex bound state in superconductors carry important information about superconducting pairing and the electronic structure. Although discrete vortex states, and sometimes a zero energy mode, had been observed in several iron-based superconductors, their spatial properties are rarely explored. In this study, we used low-temperature scanning tunneling microscopy to measure the vortex state of (Li,Fe)OHFeSe with high spatial resolution. We found that the nonzero energy states display clear spatial oscillations with a period corresponding to bulk Fermi wavelength; while in contrast, the zero energy mode does not show such oscillation, which suggests its distinct electronic origin. Furthermore, the oscillations of positive and negative energy states near E_{F} are found to be clearly out of phase. Based on a two-band model calculation, we show that our observation is more consistent with an s_{++} wave pairing in the bulk of (Li, Fe)OHFeSe, and superconducting topological states on the surface.

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.

Bosonic Mode and Impurity-Scattering in Monolayer Fe(Te,Se) High-Temperature Superconductors

The electron pairing mechanism has always been one of the most challenging problems in high-temperature superconductors. Fe(Te,Se), as the superconductor with intrinsic topological property, may host Majorana bound states and has attracted tremendous interest. While in bulk Fe(Te,Se) the pairing mechanism has been experimentally investigated, it remains little understood in its two-dimensional limit counterpart. Here, by in situ scanning tunneling spectroscopy, we show clear evidence of the bosonic mode Ω beyond the superconducting gap Δ in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) high-temperature superconductor. Statistically, Ω shows an obvious anticorrelation with Δ and appears below 2Δ, consistent with the spin-excitation nature. Furthermore, the in-gap bound states induced by two types of magnetically different impurities support the sign-reversing pairing scenario. Our results not only suggest that the spin-excitation-like bosonic mode within a sign-reversing pairing plays an essential role in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) but also offer the crucial information for investigating the high-temperature superconductivity in interfacial iron selenides.

Observation of Discrete Conventional Caroli-de Gennes-Matricon States in the Vortex Core of Single-Layer FeSe/SrTiO_{3}

Using low-temperature scanning tunneling microscopy (STM), we studied the vortex states of single-layer FeSe film on a SrTiO_{3} (100) substrate, and the local behaviors of superconductivity at sample boundaries. We clearly observed multiple discrete Caroli-de Gennes-Matricon states in the vortex core, and quantitative analysis shows their energies well follow the formula: E=μΔ^{2}/E_{F}, where μ is a half integer (±1/2,±3/2,±5/2…) and Δ is the mean superconducting gap over the Fermi surface. Meanwhile, a fully gapped spectrum without states near zero bias is observed at the [110]_{Fe} oriented boundary of 1 and 2 ML FeSe films, and atomic step edge of 1 ML FeSe. Accompanied with theoretical calculations, our results indicate an s-wave pairing without sign change in the high-T_{C} FeSe/SrTiO_{3} superconductor.

Spectroscopic Imaging of Quasiparticle Bound States Induced by Strong Nonmagnetic Scatterings in One-Unit-Cell FeSe/SrTiO_{3}

The absence of holelike Fermi pockets in the heavily electron-doped iron selenides (HEDISs) challenges the s_{±}-wave pairing originally proposed for iron pnictides, which consists of opposite signs of the gap function on electron and hole pockets. While the HEDIS compounds have been investigated extensively, a consistent description of the superconducting pairing therein is still lacking. Here, by in situ scanning tunneling spectroscopy and theoretical calculations, we study the effects of strong scatterings from nonmagnetic Pb adatoms on the epitaxially grown HEDIS, one-unit-cell FeSe/SrTiO_{3}(001). Systematic tunneling spectra measured on the Pb adatoms show comprehensive signals of quasiparticle bound states, which can be well explained theoretically within the sign-reversing pairing scenarios. The finding implies that, in addition to previously detected phonons, spin fluctuations play an important role in driving the Cooper pairing in FeSe/SrTiO_{3}(001). The sign reversal in the gap function we revealed here is a significant ingredient in a unified understanding of the high-temperature superconductivity in HEDISs.

Detection of Bosonic Mode as a Signature of Magnetic Excitation in One-Unit-Cell FeSe on SrTiO3

A "fingerprint" of Cooper pairing mediated by collective bosonic excitation mode is the reconstruction of the quasiparticle-density-of-states (DOS) spectrum with an additional "dip-hump" structure located outside the superconducting coherence peak. Here, we report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on a SrTiO₃(001) substrate. In the quasiparticle-DOS spectrum, the bosonic excitation mode characterized by the dip-hump structure is detected outside the larger superconducting gap. Statistically, the excitation mode shows an anticorrelation with pairing strength in magnitude and yields an energy scale upper-bounded by twice the superconducting gap. The observation coincides with the characteristics of magnetic resonance in cuprates and iron-based superconductors. Furthermore, the local response of superconducting spectra to magnetically distinct Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing over the Fermi surface in 1-UC FeSe. These results clarify the magnetic nature of the bosonic excitation mode and reveal a signature of electron-magnetic-excitation coupling in 1-UC FeSe/SrTiO₃(001) besides the previously established pairing channel of electron-phonon interaction.

Evidence for d-Wave Superconductivity in Single Layer FeSe/SrTiO3 Probed by Quasiparticle Scattering Off Step Edges

The de Gennes extrapolation length is a direction dependent measure of the spatial evolution of the pairing gap near the boundary of a superconductor and thus provides a viable means to probe its symmetry. It is expected to be infinite and isotropic for plain s-wave pairing, and finite and anisotropic for d-wave. Here, we synthesize single-layer FeSe films on SrTiO₃(001) (STO) substrates by molecular beam epitaxy and measure the de Gennes extrapolation length by scanning tunneling microscopy/spectroscopy. We find a 40% reduction of the superconducting gap near specular [110]_Fe edges, yielding an extrapolation length of 8.0 nm. However, near specular [010]_Fe edges, the extrapolation length is nearly infinite. These findings are consistent with a phase changing pairing with 2-fold symmetry, indicating d-wave superconductivity. This is further supported by the presence of in-gap states near the specular [110]_Fe edges, but not the [010]_Fe edges. This work provides direct experimental evidence for d-wave superconductivity in single-layer FeSe/STO and demonstrates quasiparticle scattering at boundaries to be a viable phase sensitive probe of pairing symmetry in Fe-based superconductors.

Superconductivity without Inversion and Time-Reversal Symmetries

Traditionally, in three dimensions, the only symmetries essential for superconductivity are time reversal (T) and inversion (I). Here, we examine superconductivity in two dimensions and find that T and I are not required, and having a combination of either symmetry with a mirror operation (M_{z}) on the basal plane is sufficient. By combining energetic and topological arguments, we classify superconducting states when T and I are not present, a situation encountered in several experimentally relevant systems, such as transition metal dichalcogenides or a two-dimensional Rashba system, when subject to an applied field, and in superconducting monolayer FeSe with Néel antiferromagnetic order. Energetic arguments suggest interesting superconducting states arise. For example, we find a unique pure intraband pairing state with Majorana chiral edge states in Néel-ordered FeSe. Employing topological arguments, we find when the only symmetry is the combination of I with M_{z}, the superconducting states are generically fully gapped and can have topologically protected chiral Majorana edge modes. In all other cases, there are no chiral Majorana edge states, but the superconducting bulk can have point nodes with associated topologically protected flatband Majorana edge modes. Our analysis provides guidance on the design and search for novel two-dimensional superconductors and superconducting heterostructures.

Resonance states near a quantum magnetic impurity in single-layer FeSe superconductors with d-wave symmetry

In this work, we investigate the local density of states (LDOS) near a magnetic impurity in single-layer FeSe superconductors. The two-orbital model with spin-orbit coupling proposed in Agterberg et al (2017 Phys. Rev. Lett. 119 267001) is used to describe the FeSe superconductor. In the strong coupling regime, two impurity resonance peaks appear with opposite resonance energies in the LDOS spectral function. For strong spin-orbit coupling, the superconducting gap in this model is d-wave symmetric with nodes, the spatial distributions of the LDOS at the two resonance energies are fourfold symmetric, which reveals typical characteristic of d-wave pairing. When the spin-orbit coupling is not strong enough to close the superconducting gap, we find that the spatial distribution of the LDOS at one of the resonance energies manifests s-wave symmetry, while the pairing potential preserves d-wave symmetry. This result is consistent with previous experimental investigations.